idx int64 1 56k | question stringlengths 15 155 | answer stringlengths 2 29.2k ⌀ | question_cut stringlengths 15 100 | answer_cut stringlengths 2 200 ⌀ | conversation stringlengths 47 29.3k | conversation_cut stringlengths 47 301 |
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39,501 | How to detect outliers in skewed data set? | From a scientific point of view you only remove an outlier if: it's a data entry error, measurement error, or scientifically impossible. Otherwise don't remove an outlier. Try using boxplot, cleveland plot, conditional cleveland plot, and track the outliers. If you still can't justify them then try transforming your va... | How to detect outliers in skewed data set? | From a scientific point of view you only remove an outlier if: it's a data entry error, measurement error, or scientifically impossible. Otherwise don't remove an outlier. Try using boxplot, cleveland | How to detect outliers in skewed data set?
From a scientific point of view you only remove an outlier if: it's a data entry error, measurement error, or scientifically impossible. Otherwise don't remove an outlier. Try using boxplot, cleveland plot, conditional cleveland plot, and track the outliers. If you still can't... | How to detect outliers in skewed data set?
From a scientific point of view you only remove an outlier if: it's a data entry error, measurement error, or scientifically impossible. Otherwise don't remove an outlier. Try using boxplot, cleveland |
39,502 | How to detect outliers in skewed data set? | In addition to the other responses, don't forget to state how you identified the outliers and to provide individual details of them in your report. | How to detect outliers in skewed data set? | In addition to the other responses, don't forget to state how you identified the outliers and to provide individual details of them in your report. | How to detect outliers in skewed data set?
In addition to the other responses, don't forget to state how you identified the outliers and to provide individual details of them in your report. | How to detect outliers in skewed data set?
In addition to the other responses, don't forget to state how you identified the outliers and to provide individual details of them in your report. |
39,503 | How to detect outliers in skewed data set? | If one cannot prespecify conditions upon which data should be excluded from an analysis independent of observed results, then the process of removing outliers via visual inspection or some data-driven automated process introduces great bias into any analysis.
This is because you greatly inflate the type I error by adm... | How to detect outliers in skewed data set? | If one cannot prespecify conditions upon which data should be excluded from an analysis independent of observed results, then the process of removing outliers via visual inspection or some data-driven | How to detect outliers in skewed data set?
If one cannot prespecify conditions upon which data should be excluded from an analysis independent of observed results, then the process of removing outliers via visual inspection or some data-driven automated process introduces great bias into any analysis.
This is because ... | How to detect outliers in skewed data set?
If one cannot prespecify conditions upon which data should be excluded from an analysis independent of observed results, then the process of removing outliers via visual inspection or some data-driven |
39,504 | What are good techniques for modeling small datasets? | Neural networks can be notoriously difficult to work with (too many potential difficulties, such as local minima, over-fitting etc.). A kernel method is likely to be easier to work with, such as kernel ridge regression, the support vector machine, kernel logistic regression or Gaussian process classifiers, using a rad... | What are good techniques for modeling small datasets? | Neural networks can be notoriously difficult to work with (too many potential difficulties, such as local minima, over-fitting etc.). A kernel method is likely to be easier to work with, such as kern | What are good techniques for modeling small datasets?
Neural networks can be notoriously difficult to work with (too many potential difficulties, such as local minima, over-fitting etc.). A kernel method is likely to be easier to work with, such as kernel ridge regression, the support vector machine, kernel logistic r... | What are good techniques for modeling small datasets?
Neural networks can be notoriously difficult to work with (too many potential difficulties, such as local minima, over-fitting etc.). A kernel method is likely to be easier to work with, such as kern |
39,505 | What are good techniques for modeling small datasets? | It might be a data issue and not a classifier issue (Neural Networks, Logistic Regression ..etc) problem, because when data has a shape ( say it could be divided into two classes ) 800 points should be fine as training set.
It might be that the decision boundary is a funny one (Not linear for example), have you tried... | What are good techniques for modeling small datasets? | It might be a data issue and not a classifier issue (Neural Networks, Logistic Regression ..etc) problem, because when data has a shape ( say it could be divided into two classes ) 800 points should b | What are good techniques for modeling small datasets?
It might be a data issue and not a classifier issue (Neural Networks, Logistic Regression ..etc) problem, because when data has a shape ( say it could be divided into two classes ) 800 points should be fine as training set.
It might be that the decision boundary i... | What are good techniques for modeling small datasets?
It might be a data issue and not a classifier issue (Neural Networks, Logistic Regression ..etc) problem, because when data has a shape ( say it could be divided into two classes ) 800 points should b |
39,506 | What are good techniques for modeling small datasets? | Given how small the data set is, have you tried investigating it using any non-parametric methods? For example, I bet you could easily do a full leave-one-out cross validation test using a nearest neighbour classifier on your 800 sample training set, and see what the estimated classification error rate is then. If it's... | What are good techniques for modeling small datasets? | Given how small the data set is, have you tried investigating it using any non-parametric methods? For example, I bet you could easily do a full leave-one-out cross validation test using a nearest nei | What are good techniques for modeling small datasets?
Given how small the data set is, have you tried investigating it using any non-parametric methods? For example, I bet you could easily do a full leave-one-out cross validation test using a nearest neighbour classifier on your 800 sample training set, and see what th... | What are good techniques for modeling small datasets?
Given how small the data set is, have you tried investigating it using any non-parametric methods? For example, I bet you could easily do a full leave-one-out cross validation test using a nearest nei |
39,507 | Adding a quadratic term: should I use the squared original (and not the squared standardized?) | Let the variable be $x$, its mean be $\mu$, and its standard deviation $\sigma$, so that the standardized variable is $z = (x-\mu)/\sigma$. By expanding $z^2$ and collecting like powers of $x$ you can rewrite your model as
$$\eqalign{
y &= \beta_0 + \beta_1 x + \beta_2 z^2 + \varepsilon \\
&= \beta_0 + \beta_1 x + \be... | Adding a quadratic term: should I use the squared original (and not the squared standardized?) | Let the variable be $x$, its mean be $\mu$, and its standard deviation $\sigma$, so that the standardized variable is $z = (x-\mu)/\sigma$. By expanding $z^2$ and collecting like powers of $x$ you ca | Adding a quadratic term: should I use the squared original (and not the squared standardized?)
Let the variable be $x$, its mean be $\mu$, and its standard deviation $\sigma$, so that the standardized variable is $z = (x-\mu)/\sigma$. By expanding $z^2$ and collecting like powers of $x$ you can rewrite your model as
$... | Adding a quadratic term: should I use the squared original (and not the squared standardized?)
Let the variable be $x$, its mean be $\mu$, and its standard deviation $\sigma$, so that the standardized variable is $z = (x-\mu)/\sigma$. By expanding $z^2$ and collecting like powers of $x$ you ca |
39,508 | R2jags does not remove the burn in part sometimes? | I had exactly the same problem! After reading the R2jags::jags source I came to the same conclusion as @Hao Ye, I will expand on more detail:
First, I noticed that this happens only for some models:
if you remove the dgamma from your example and use dunif instead, i.e. if you modify your example this way:
...
inits <-... | R2jags does not remove the burn in part sometimes? | I had exactly the same problem! After reading the R2jags::jags source I came to the same conclusion as @Hao Ye, I will expand on more detail:
First, I noticed that this happens only for some models:
| R2jags does not remove the burn in part sometimes?
I had exactly the same problem! After reading the R2jags::jags source I came to the same conclusion as @Hao Ye, I will expand on more detail:
First, I noticed that this happens only for some models:
if you remove the dgamma from your example and use dunif instead, i.e... | R2jags does not remove the burn in part sometimes?
I had exactly the same problem! After reading the R2jags::jags source I came to the same conclusion as @Hao Ye, I will expand on more detail:
First, I noticed that this happens only for some models:
|
39,509 | R2jags does not remove the burn in part sometimes? | I think I'm a year too late to this party... (and I feel like this question might belong in stackoverflow, instead)
The issue seems to be that the jags() function treats n.burnin as the number of adaptation steps. Not all models require adaptation, which is why Baoyue has seen two progress bars for some models, but not... | R2jags does not remove the burn in part sometimes? | I think I'm a year too late to this party... (and I feel like this question might belong in stackoverflow, instead)
The issue seems to be that the jags() function treats n.burnin as the number of adap | R2jags does not remove the burn in part sometimes?
I think I'm a year too late to this party... (and I feel like this question might belong in stackoverflow, instead)
The issue seems to be that the jags() function treats n.burnin as the number of adaptation steps. Not all models require adaptation, which is why Baoyue ... | R2jags does not remove the burn in part sometimes?
I think I'm a year too late to this party... (and I feel like this question might belong in stackoverflow, instead)
The issue seems to be that the jags() function treats n.burnin as the number of adap |
39,510 | R2jags does not remove the burn in part sometimes? | Since I run a lot of analyses in JAGS and prefer the output format from R2jags I decided to hack together a temporary solution to this problem.
Essentially I added an argument to the jags() function in R2jags, n.adapt, to specify the number of 'adaptation' iterations and got rid of the code chunk that sets n.adapt = n.... | R2jags does not remove the burn in part sometimes? | Since I run a lot of analyses in JAGS and prefer the output format from R2jags I decided to hack together a temporary solution to this problem.
Essentially I added an argument to the jags() function i | R2jags does not remove the burn in part sometimes?
Since I run a lot of analyses in JAGS and prefer the output format from R2jags I decided to hack together a temporary solution to this problem.
Essentially I added an argument to the jags() function in R2jags, n.adapt, to specify the number of 'adaptation' iterations a... | R2jags does not remove the burn in part sometimes?
Since I run a lot of analyses in JAGS and prefer the output format from R2jags I decided to hack together a temporary solution to this problem.
Essentially I added an argument to the jags() function i |
39,511 | R2jags does not remove the burn in part sometimes? | I've experienced this problem in my own models as well. A solution (i.e., work around until this bug is fixed): switch the prior from tau to sigma.
Instead of
tau~dgamma(0.001,0.001)
sigma2<-1/tau
try
sigma2 ~ dgamma(0.001, 0.001)
tau<-1/sigma2
or
sigma2 ~ dgamma(0.001, 0.001)
tau <- 1/pow(sigma2,2)
This seems to ... | R2jags does not remove the burn in part sometimes? | I've experienced this problem in my own models as well. A solution (i.e., work around until this bug is fixed): switch the prior from tau to sigma.
Instead of
tau~dgamma(0.001,0.001)
sigma2<-1/tau
t | R2jags does not remove the burn in part sometimes?
I've experienced this problem in my own models as well. A solution (i.e., work around until this bug is fixed): switch the prior from tau to sigma.
Instead of
tau~dgamma(0.001,0.001)
sigma2<-1/tau
try
sigma2 ~ dgamma(0.001, 0.001)
tau<-1/sigma2
or
sigma2 ~ dgamma(0... | R2jags does not remove the burn in part sometimes?
I've experienced this problem in my own models as well. A solution (i.e., work around until this bug is fixed): switch the prior from tau to sigma.
Instead of
tau~dgamma(0.001,0.001)
sigma2<-1/tau
t |
39,512 | R2jags does not remove the burn in part sometimes? | Following up to Jason Hill's answer, while this fixes the problem, you shouldn't do it. If $\tau$, the precision, is the inverse of $\sigma^2$ (the variance), and $\tau$ is distributed gamma, then it follows that $\sigma^2$ will not be distributed gamma, but inverse gamma. I don't think JAGS supports that parameterizat... | R2jags does not remove the burn in part sometimes? | Following up to Jason Hill's answer, while this fixes the problem, you shouldn't do it. If $\tau$, the precision, is the inverse of $\sigma^2$ (the variance), and $\tau$ is distributed gamma, then it | R2jags does not remove the burn in part sometimes?
Following up to Jason Hill's answer, while this fixes the problem, you shouldn't do it. If $\tau$, the precision, is the inverse of $\sigma^2$ (the variance), and $\tau$ is distributed gamma, then it follows that $\sigma^2$ will not be distributed gamma, but inverse ga... | R2jags does not remove the burn in part sometimes?
Following up to Jason Hill's answer, while this fixes the problem, you shouldn't do it. If $\tau$, the precision, is the inverse of $\sigma^2$ (the variance), and $\tau$ is distributed gamma, then it |
39,513 | R2jags does not remove the burn in part sometimes? | I encountered this same problem and tried to download Ken Kellner's fix. However, it appears his code is no longer online.
Based on his suggestions I was able to modify the R2jags::jags.R file to check if adaption is needed before running the adapt function. If it is not needed, then it simply calls update to burn in t... | R2jags does not remove the burn in part sometimes? | I encountered this same problem and tried to download Ken Kellner's fix. However, it appears his code is no longer online.
Based on his suggestions I was able to modify the R2jags::jags.R file to chec | R2jags does not remove the burn in part sometimes?
I encountered this same problem and tried to download Ken Kellner's fix. However, it appears his code is no longer online.
Based on his suggestions I was able to modify the R2jags::jags.R file to check if adaption is needed before running the adapt function. If it is n... | R2jags does not remove the burn in part sometimes?
I encountered this same problem and tried to download Ken Kellner's fix. However, it appears his code is no longer online.
Based on his suggestions I was able to modify the R2jags::jags.R file to chec |
39,514 | Tolerance bound for a normalized variable | Damn! After starting the bounty I realized the answer is easy: The quantile has form $\frac{\mu}{\sigma}+z_p$, and there are some known methods to get a confidence interval about the "effect size" $\frac{\mu}{\sigma}$ (or by inverting the bounds of a confidence interval about the coefficient of variation; such a confid... | Tolerance bound for a normalized variable | Damn! After starting the bounty I realized the answer is easy: The quantile has form $\frac{\mu}{\sigma}+z_p$, and there are some known methods to get a confidence interval about the "effect size" $\f | Tolerance bound for a normalized variable
Damn! After starting the bounty I realized the answer is easy: The quantile has form $\frac{\mu}{\sigma}+z_p$, and there are some known methods to get a confidence interval about the "effect size" $\frac{\mu}{\sigma}$ (or by inverting the bounds of a confidence interval about t... | Tolerance bound for a normalized variable
Damn! After starting the bounty I realized the answer is easy: The quantile has form $\frac{\mu}{\sigma}+z_p$, and there are some known methods to get a confidence interval about the "effect size" $\f |
39,515 | Tolerance bound for a normalized variable | In Environmental Statistics with S-Plus (CRC Press, 2001), Steven Millard and Nagaraj Neerchal state that a
$\beta$-content tolerance interval with confidence level $(1-\alpha)100$% is constructed so that it contains at least $\beta 100$% of the population (i.e., the coverage is at least $\beta 100$%) with probability... | Tolerance bound for a normalized variable | In Environmental Statistics with S-Plus (CRC Press, 2001), Steven Millard and Nagaraj Neerchal state that a
$\beta$-content tolerance interval with confidence level $(1-\alpha)100$% is constructed so | Tolerance bound for a normalized variable
In Environmental Statistics with S-Plus (CRC Press, 2001), Steven Millard and Nagaraj Neerchal state that a
$\beta$-content tolerance interval with confidence level $(1-\alpha)100$% is constructed so that it contains at least $\beta 100$% of the population (i.e., the coverage ... | Tolerance bound for a normalized variable
In Environmental Statistics with S-Plus (CRC Press, 2001), Steven Millard and Nagaraj Neerchal state that a
$\beta$-content tolerance interval with confidence level $(1-\alpha)100$% is constructed so |
39,516 | What to do when assumptions are not met in a chi squared test? | One solution would be to use a bootstrap test as an approximation to a permutation test. Permutation tests are exact and most powerful; in this case there are too many permutations to calculate every one of them, so you'd approximate the test with the bootstrap.
Basically, you:
1) Calculate your test statistic, labe... | What to do when assumptions are not met in a chi squared test? | One solution would be to use a bootstrap test as an approximation to a permutation test. Permutation tests are exact and most powerful; in this case there are too many permutations to calculate every | What to do when assumptions are not met in a chi squared test?
One solution would be to use a bootstrap test as an approximation to a permutation test. Permutation tests are exact and most powerful; in this case there are too many permutations to calculate every one of them, so you'd approximate the test with the boot... | What to do when assumptions are not met in a chi squared test?
One solution would be to use a bootstrap test as an approximation to a permutation test. Permutation tests are exact and most powerful; in this case there are too many permutations to calculate every |
39,517 | What to do when assumptions are not met in a chi squared test? | In the SPSS crosstabs procedure you can use an exact test and/or you can use the bootstrap. Exact offers a Monte Carlo and exact choice. Bootstrap offers the same bootstrapping technique available for a bunch of procedures. Both are available from the Crosstabs dialog if you have the relevant add-on options. | What to do when assumptions are not met in a chi squared test? | In the SPSS crosstabs procedure you can use an exact test and/or you can use the bootstrap. Exact offers a Monte Carlo and exact choice. Bootstrap offers the same bootstrapping technique available f | What to do when assumptions are not met in a chi squared test?
In the SPSS crosstabs procedure you can use an exact test and/or you can use the bootstrap. Exact offers a Monte Carlo and exact choice. Bootstrap offers the same bootstrapping technique available for a bunch of procedures. Both are available from the Cr... | What to do when assumptions are not met in a chi squared test?
In the SPSS crosstabs procedure you can use an exact test and/or you can use the bootstrap. Exact offers a Monte Carlo and exact choice. Bootstrap offers the same bootstrapping technique available f |
39,518 | Nonparametric alternative to ANOVA for testing the difference between several brand preferences | The answer is Friedman test. It is nonparametric and as you can see on Wikipedia, there is also very similar example as yours ("n wine judges each rate k different wines. Are any wines ranked consistently higher or lower than the others?").
See R package pgirmess and friedman.test() function that takes datamatrix as in... | Nonparametric alternative to ANOVA for testing the difference between several brand preferences | The answer is Friedman test. It is nonparametric and as you can see on Wikipedia, there is also very similar example as yours ("n wine judges each rate k different wines. Are any wines ranked consiste | Nonparametric alternative to ANOVA for testing the difference between several brand preferences
The answer is Friedman test. It is nonparametric and as you can see on Wikipedia, there is also very similar example as yours ("n wine judges each rate k different wines. Are any wines ranked consistently higher or lower tha... | Nonparametric alternative to ANOVA for testing the difference between several brand preferences
The answer is Friedman test. It is nonparametric and as you can see on Wikipedia, there is also very similar example as yours ("n wine judges each rate k different wines. Are any wines ranked consiste |
39,519 | Nonparametric alternative to ANOVA for testing the difference between several brand preferences | There are two solutions much better than Friedman.
ART (Aligned-Rank Transform) ANOVA with Error term specified
Wald-Type Statistics
Both allow for more than one categorical covariate and interactions between them. | Nonparametric alternative to ANOVA for testing the difference between several brand preferences | There are two solutions much better than Friedman.
ART (Aligned-Rank Transform) ANOVA with Error term specified
Wald-Type Statistics
Both allow for more than one categorical covariate and interactio | Nonparametric alternative to ANOVA for testing the difference between several brand preferences
There are two solutions much better than Friedman.
ART (Aligned-Rank Transform) ANOVA with Error term specified
Wald-Type Statistics
Both allow for more than one categorical covariate and interactions between them. | Nonparametric alternative to ANOVA for testing the difference between several brand preferences
There are two solutions much better than Friedman.
ART (Aligned-Rank Transform) ANOVA with Error term specified
Wald-Type Statistics
Both allow for more than one categorical covariate and interactio |
39,520 | Interpreting a confidence interval. | The key concepts with confidence intervals are coverage, correctness and accuracy.
Coverage
The coverage or confidence level should be explained first. It is the percentage of times the random interval is expected to include the true value of the parameter.
The way this is best shown is to take a probability statement... | Interpreting a confidence interval. | The key concepts with confidence intervals are coverage, correctness and accuracy.
Coverage
The coverage or confidence level should be explained first. It is the percentage of times the random interv | Interpreting a confidence interval.
The key concepts with confidence intervals are coverage, correctness and accuracy.
Coverage
The coverage or confidence level should be explained first. It is the percentage of times the random interval is expected to include the true value of the parameter.
The way this is best show... | Interpreting a confidence interval.
The key concepts with confidence intervals are coverage, correctness and accuracy.
Coverage
The coverage or confidence level should be explained first. It is the percentage of times the random interv |
39,521 | Interpreting a confidence interval. | A 95% confidence interval for parameter $\mu$ means:
An interval constructed in this way will contain the true value of $\mu$ with a probability of 95%.
Do not say: there is a 95% probability that $\mu$ is in this interval. Everyone says it ... but please don't. $\mu$ is either in that particular interval or not.
You m... | Interpreting a confidence interval. | A 95% confidence interval for parameter $\mu$ means:
An interval constructed in this way will contain the true value of $\mu$ with a probability of 95%.
Do not say: there is a 95% probability that $\m | Interpreting a confidence interval.
A 95% confidence interval for parameter $\mu$ means:
An interval constructed in this way will contain the true value of $\mu$ with a probability of 95%.
Do not say: there is a 95% probability that $\mu$ is in this interval. Everyone says it ... but please don't. $\mu$ is either in th... | Interpreting a confidence interval.
A 95% confidence interval for parameter $\mu$ means:
An interval constructed in this way will contain the true value of $\mu$ with a probability of 95%.
Do not say: there is a 95% probability that $\m |
39,522 | How do I reject or fail to reject the null hypothesis that p1 = p2 = p3 = p4? | You have a contingency table with $C=2$ columns and $R=4$ rows.
Right Wrong
1st 20 5 25
2nd 22 8 30
3rd 15 7 22
4th 14 9 23
71 29 100
Let $N_{ij}$ be the number of observations in the $(i,j)$-cell. Define
$$
N_{i+}=\su... | How do I reject or fail to reject the null hypothesis that p1 = p2 = p3 = p4? | You have a contingency table with $C=2$ columns and $R=4$ rows.
Right Wrong
1st 20 5 25
2nd 22 8 30
3rd 15 7 22
4th 14 9 2 | How do I reject or fail to reject the null hypothesis that p1 = p2 = p3 = p4?
You have a contingency table with $C=2$ columns and $R=4$ rows.
Right Wrong
1st 20 5 25
2nd 22 8 30
3rd 15 7 22
4th 14 9 23
71 29 100
Let $N_{ij... | How do I reject or fail to reject the null hypothesis that p1 = p2 = p3 = p4?
You have a contingency table with $C=2$ columns and $R=4$ rows.
Right Wrong
1st 20 5 25
2nd 22 8 30
3rd 15 7 22
4th 14 9 2 |
39,523 | How do I reject or fail to reject the null hypothesis that p1 = p2 = p3 = p4? | ANOVA is not appropriate in this case. Think of this as a 2x4 contingency table. I think the generalization of Fisher's exact test to RxC tables will do exactly what you want. Zen has provided detailed calculations for the Fisher test using program in R (I think it is in R). His proposed chi square approximate test ... | How do I reject or fail to reject the null hypothesis that p1 = p2 = p3 = p4? | ANOVA is not appropriate in this case. Think of this as a 2x4 contingency table. I think the generalization of Fisher's exact test to RxC tables will do exactly what you want. Zen has provided detai | How do I reject or fail to reject the null hypothesis that p1 = p2 = p3 = p4?
ANOVA is not appropriate in this case. Think of this as a 2x4 contingency table. I think the generalization of Fisher's exact test to RxC tables will do exactly what you want. Zen has provided detailed calculations for the Fisher test using... | How do I reject or fail to reject the null hypothesis that p1 = p2 = p3 = p4?
ANOVA is not appropriate in this case. Think of this as a 2x4 contingency table. I think the generalization of Fisher's exact test to RxC tables will do exactly what you want. Zen has provided detai |
39,524 | GLM model is singular | Singularity refers to the covariance matrix for the covariates. A matrix is singular when at least one variable can be expressed as an exact linear combination of some of the others. The best thing to do is to find which variables are creating the singularity and remove at least one of the variables from the model. | GLM model is singular | Singularity refers to the covariance matrix for the covariates. A matrix is singular when at least one variable can be expressed as an exact linear combination of some of the others. The best thing | GLM model is singular
Singularity refers to the covariance matrix for the covariates. A matrix is singular when at least one variable can be expressed as an exact linear combination of some of the others. The best thing to do is to find which variables are creating the singularity and remove at least one of the varia... | GLM model is singular
Singularity refers to the covariance matrix for the covariates. A matrix is singular when at least one variable can be expressed as an exact linear combination of some of the others. The best thing |
39,525 | Dividing a uniform by a normal random variable: What's the distribution? | Let $X$ and $Y$ be two independent random variables and define $Z=\frac{X}{Y}$. Consider the change of variable $(X,Y)\leftrightarrow (Z,Y)$, then the corresponding inverse transformation is $(ZY,Y)$. Therefore, the Jacobian matrix is given by (see this and this links for a reference of this procedure)
\begin{eqnarray}... | Dividing a uniform by a normal random variable: What's the distribution? | Let $X$ and $Y$ be two independent random variables and define $Z=\frac{X}{Y}$. Consider the change of variable $(X,Y)\leftrightarrow (Z,Y)$, then the corresponding inverse transformation is $(ZY,Y)$. | Dividing a uniform by a normal random variable: What's the distribution?
Let $X$ and $Y$ be two independent random variables and define $Z=\frac{X}{Y}$. Consider the change of variable $(X,Y)\leftrightarrow (Z,Y)$, then the corresponding inverse transformation is $(ZY,Y)$. Therefore, the Jacobian matrix is given by (se... | Dividing a uniform by a normal random variable: What's the distribution?
Let $X$ and $Y$ be two independent random variables and define $Z=\frac{X}{Y}$. Consider the change of variable $(X,Y)\leftrightarrow (Z,Y)$, then the corresponding inverse transformation is $(ZY,Y)$. |
39,526 | Regression $R^2$ and correlations | For two predictors, it is easy to write out the equation in algebraic form:
$R^2 = \frac{r^2_{x1,y} + r^2_{x2,y} - 2r_{x1,y}r_{x2,y}r_{x1,x2}}{1-r^2_{x1,x2}}$.
As pointed out by @gung, you also need to know the correlation between $x1$ and $x2$.
EDIT: Just a quick example (in R) to illustrate this equation:
set.seed(12... | Regression $R^2$ and correlations | For two predictors, it is easy to write out the equation in algebraic form:
$R^2 = \frac{r^2_{x1,y} + r^2_{x2,y} - 2r_{x1,y}r_{x2,y}r_{x1,x2}}{1-r^2_{x1,x2}}$.
As pointed out by @gung, you also need t | Regression $R^2$ and correlations
For two predictors, it is easy to write out the equation in algebraic form:
$R^2 = \frac{r^2_{x1,y} + r^2_{x2,y} - 2r_{x1,y}r_{x2,y}r_{x1,x2}}{1-r^2_{x1,x2}}$.
As pointed out by @gung, you also need to know the correlation between $x1$ and $x2$.
EDIT: Just a quick example (in R) to ill... | Regression $R^2$ and correlations
For two predictors, it is easy to write out the equation in algebraic form:
$R^2 = \frac{r^2_{x1,y} + r^2_{x2,y} - 2r_{x1,y}r_{x2,y}r_{x1,x2}}{1-r^2_{x1,x2}}$.
As pointed out by @gung, you also need t |
39,527 | Regression $R^2$ and correlations | I'm sure there is, but I don't know it. Moreover it would be fairly complex, because you would also have to account for the correlations amongst the covariates. That is, you would need $corr(X_1,X_2)$ as well. The resulting formula would need to be expressed in matrix notation to make it possible to fit on one line ... | Regression $R^2$ and correlations | I'm sure there is, but I don't know it. Moreover it would be fairly complex, because you would also have to account for the correlations amongst the covariates. That is, you would need $corr(X_1,X_2 | Regression $R^2$ and correlations
I'm sure there is, but I don't know it. Moreover it would be fairly complex, because you would also have to account for the correlations amongst the covariates. That is, you would need $corr(X_1,X_2)$ as well. The resulting formula would need to be expressed in matrix notation to ma... | Regression $R^2$ and correlations
I'm sure there is, but I don't know it. Moreover it would be fairly complex, because you would also have to account for the correlations amongst the covariates. That is, you would need $corr(X_1,X_2 |
39,528 | Regression $R^2$ and correlations | If you compute the inverse of the correlation matrix of a set of variables, then take one minus the reciprocal of the diagonal elements ($1-\frac{1}{r_{ii}}$) then the results are the same as the $R^2$ value for the given term as response variable and all others as predictors.
> summary(lm( Sepal.Length ~ .-Species, da... | Regression $R^2$ and correlations | If you compute the inverse of the correlation matrix of a set of variables, then take one minus the reciprocal of the diagonal elements ($1-\frac{1}{r_{ii}}$) then the results are the same as the $R^2 | Regression $R^2$ and correlations
If you compute the inverse of the correlation matrix of a set of variables, then take one minus the reciprocal of the diagonal elements ($1-\frac{1}{r_{ii}}$) then the results are the same as the $R^2$ value for the given term as response variable and all others as predictors.
> summar... | Regression $R^2$ and correlations
If you compute the inverse of the correlation matrix of a set of variables, then take one minus the reciprocal of the diagonal elements ($1-\frac{1}{r_{ii}}$) then the results are the same as the $R^2 |
39,529 | Checking Poisson distribution plot using mean and variance relationship? | There are three issues here:
The simulation probably doesn't do exactly what it seems.
The analysis does not evaluate whether the relationship between mean and variance is linear.
What can one do to check whether data appear Poisson?
Many answers to #3 have appeared elsewhere on our site, so I will focus on the first... | Checking Poisson distribution plot using mean and variance relationship? | There are three issues here:
The simulation probably doesn't do exactly what it seems.
The analysis does not evaluate whether the relationship between mean and variance is linear.
What can one do to | Checking Poisson distribution plot using mean and variance relationship?
There are three issues here:
The simulation probably doesn't do exactly what it seems.
The analysis does not evaluate whether the relationship between mean and variance is linear.
What can one do to check whether data appear Poisson?
Many answer... | Checking Poisson distribution plot using mean and variance relationship?
There are three issues here:
The simulation probably doesn't do exactly what it seems.
The analysis does not evaluate whether the relationship between mean and variance is linear.
What can one do to |
39,530 | What test is appropriate for binary outcome with repeated measures and binary, ordinal and continuous independent variables? | Let $Y_i$ be $1$ if patient $i$ is positive and $0$ otherwise and let $X_{i1}, ..., X_{ip}$ be the $p$ predictor variables for patient $i$. A standard tool for determining whether variables are related to an individual's probability that $Y_i = 1$ is the logistic regression model:
$$ \log \left( \frac{ P(Y_i = 1 | X_i... | What test is appropriate for binary outcome with repeated measures and binary, ordinal and continuou | Let $Y_i$ be $1$ if patient $i$ is positive and $0$ otherwise and let $X_{i1}, ..., X_{ip}$ be the $p$ predictor variables for patient $i$. A standard tool for determining whether variables are relate | What test is appropriate for binary outcome with repeated measures and binary, ordinal and continuous independent variables?
Let $Y_i$ be $1$ if patient $i$ is positive and $0$ otherwise and let $X_{i1}, ..., X_{ip}$ be the $p$ predictor variables for patient $i$. A standard tool for determining whether variables are r... | What test is appropriate for binary outcome with repeated measures and binary, ordinal and continuou
Let $Y_i$ be $1$ if patient $i$ is positive and $0$ otherwise and let $X_{i1}, ..., X_{ip}$ be the $p$ predictor variables for patient $i$. A standard tool for determining whether variables are relate |
39,531 | How to calculate mean and standard deviation in R given confidence interval and a normal or gamma distribution? | Please read the erratum at the end of the answer.
First note that there is not enough information to solve this problem. In both cases, $n$ the sample size is missing. In the case of the Gaussian distribution, assuming you know $n$, you can easily do it by following @Michael Chernick's instructions. In R that would giv... | How to calculate mean and standard deviation in R given confidence interval and a normal or gamma di | Please read the erratum at the end of the answer.
First note that there is not enough information to solve this problem. In both cases, $n$ the sample size is missing. In the case of the Gaussian dist | How to calculate mean and standard deviation in R given confidence interval and a normal or gamma distribution?
Please read the erratum at the end of the answer.
First note that there is not enough information to solve this problem. In both cases, $n$ the sample size is missing. In the case of the Gaussian distribution... | How to calculate mean and standard deviation in R given confidence interval and a normal or gamma di
Please read the erratum at the end of the answer.
First note that there is not enough information to solve this problem. In both cases, $n$ the sample size is missing. In the case of the Gaussian dist |
39,532 | How to calculate mean and standard deviation in R given confidence interval and a normal or gamma distribution? | If you mean the true parameters, of course, the answer is no. But if you mean that you want to recover the sample estimates from the confidence interval, the answer is yes, for the normal distribution if the sample size $n$ is also given.
If the confidence interval was $(1,6)$, then $1= \overline{X}-1.96 \cdot S/\sqrt... | How to calculate mean and standard deviation in R given confidence interval and a normal or gamma di | If you mean the true parameters, of course, the answer is no. But if you mean that you want to recover the sample estimates from the confidence interval, the answer is yes, for the normal distributio | How to calculate mean and standard deviation in R given confidence interval and a normal or gamma distribution?
If you mean the true parameters, of course, the answer is no. But if you mean that you want to recover the sample estimates from the confidence interval, the answer is yes, for the normal distribution if the... | How to calculate mean and standard deviation in R given confidence interval and a normal or gamma di
If you mean the true parameters, of course, the answer is no. But if you mean that you want to recover the sample estimates from the confidence interval, the answer is yes, for the normal distributio |
39,533 | How to calculate mean and standard deviation in R given confidence interval and a normal or gamma distribution? | You can construct a confidence interval around anything that can be estimated, whether it be a mean, standard deviation, even a maximum for any given probability distribution.
Assuming you have a CI around the mean estimated from an experiment in which a finite sample of size $n$ were taken from independent, identicall... | How to calculate mean and standard deviation in R given confidence interval and a normal or gamma di | You can construct a confidence interval around anything that can be estimated, whether it be a mean, standard deviation, even a maximum for any given probability distribution.
Assuming you have a CI a | How to calculate mean and standard deviation in R given confidence interval and a normal or gamma distribution?
You can construct a confidence interval around anything that can be estimated, whether it be a mean, standard deviation, even a maximum for any given probability distribution.
Assuming you have a CI around th... | How to calculate mean and standard deviation in R given confidence interval and a normal or gamma di
You can construct a confidence interval around anything that can be estimated, whether it be a mean, standard deviation, even a maximum for any given probability distribution.
Assuming you have a CI a |
39,534 | How to calculate mean and standard deviation in R given confidence interval and a normal or gamma distribution? | If what is given are the quantiles from a normal distribution (although not the same as confidence intervals) then a solution to the problem reduces to find the distribution parameters from quantiles.
For the normal distribution we want to find $\mu$ and $\sigma$ such that the random variable $X$ satisfies:
$$
P(X<x_1)... | How to calculate mean and standard deviation in R given confidence interval and a normal or gamma di | If what is given are the quantiles from a normal distribution (although not the same as confidence intervals) then a solution to the problem reduces to find the distribution parameters from quantiles. | How to calculate mean and standard deviation in R given confidence interval and a normal or gamma distribution?
If what is given are the quantiles from a normal distribution (although not the same as confidence intervals) then a solution to the problem reduces to find the distribution parameters from quantiles.
For the... | How to calculate mean and standard deviation in R given confidence interval and a normal or gamma di
If what is given are the quantiles from a normal distribution (although not the same as confidence intervals) then a solution to the problem reduces to find the distribution parameters from quantiles. |
39,535 | Properties of spectral decomposition | In the particular example in the question, the properties of a symmetric matrix have been confused with those of a positive definite one, which explains the discrepancies noted.
A brief tour of symmetry and positive semidefiniteness
Symmetric positive (semi)definite matrices play an important role in
statistical theory... | Properties of spectral decomposition | In the particular example in the question, the properties of a symmetric matrix have been confused with those of a positive definite one, which explains the discrepancies noted.
A brief tour of symmet | Properties of spectral decomposition
In the particular example in the question, the properties of a symmetric matrix have been confused with those of a positive definite one, which explains the discrepancies noted.
A brief tour of symmetry and positive semidefiniteness
Symmetric positive (semi)definite matrices play an... | Properties of spectral decomposition
In the particular example in the question, the properties of a symmetric matrix have been confused with those of a positive definite one, which explains the discrepancies noted.
A brief tour of symmet |
39,536 | Calculating P-value for Spearman's rank correlation coefficient example on Wikipedia | In the next section in the article, "determining significance", there is the equation
$t=r\sqrt{\frac{n-2}{1-r^2}}$
If you plug in their estimate of r into that equation you get a t statistic of -0.505, which you can compare to a standard t distribution via a table or a computer. For example (EDITED- thanks to @whuber... | Calculating P-value for Spearman's rank correlation coefficient example on Wikipedia | In the next section in the article, "determining significance", there is the equation
$t=r\sqrt{\frac{n-2}{1-r^2}}$
If you plug in their estimate of r into that equation you get a t statistic of -0.50 | Calculating P-value for Spearman's rank correlation coefficient example on Wikipedia
In the next section in the article, "determining significance", there is the equation
$t=r\sqrt{\frac{n-2}{1-r^2}}$
If you plug in their estimate of r into that equation you get a t statistic of -0.505, which you can compare to a stand... | Calculating P-value for Spearman's rank correlation coefficient example on Wikipedia
In the next section in the article, "determining significance", there is the equation
$t=r\sqrt{\frac{n-2}{1-r^2}}$
If you plug in their estimate of r into that equation you get a t statistic of -0.50 |
39,537 | Calculating P-value for Spearman's rank correlation coefficient example on Wikipedia | In R I would suggest using the functions rcorr from the Hmisc package and the custom function flattenCorrMatrix (http://www.sthda.com/english/wiki/print.php?id=78) which you can find online. rcorr calculates the correlation matrix and the flatten function will give you easy access to correlation and p values.
Something... | Calculating P-value for Spearman's rank correlation coefficient example on Wikipedia | In R I would suggest using the functions rcorr from the Hmisc package and the custom function flattenCorrMatrix (http://www.sthda.com/english/wiki/print.php?id=78) which you can find online. rcorr cal | Calculating P-value for Spearman's rank correlation coefficient example on Wikipedia
In R I would suggest using the functions rcorr from the Hmisc package and the custom function flattenCorrMatrix (http://www.sthda.com/english/wiki/print.php?id=78) which you can find online. rcorr calculates the correlation matrix and ... | Calculating P-value for Spearman's rank correlation coefficient example on Wikipedia
In R I would suggest using the functions rcorr from the Hmisc package and the custom function flattenCorrMatrix (http://www.sthda.com/english/wiki/print.php?id=78) which you can find online. rcorr cal |
39,538 | Calculating P-value for Spearman's rank correlation coefficient example on Wikipedia | Spearman correlation coefficient is a Pearson correlation coefficient calculated on the ranks of observations. Hence, you can apply p-value formulae of Pearson correlation $r$ to Spearman $\rho$.
For instance, the estimator of the variance is $\sigma^2_\rho=\frac{(n-2)}{1-\rho^2}$, you can use it in usual way to calcul... | Calculating P-value for Spearman's rank correlation coefficient example on Wikipedia | Spearman correlation coefficient is a Pearson correlation coefficient calculated on the ranks of observations. Hence, you can apply p-value formulae of Pearson correlation $r$ to Spearman $\rho$.
For | Calculating P-value for Spearman's rank correlation coefficient example on Wikipedia
Spearman correlation coefficient is a Pearson correlation coefficient calculated on the ranks of observations. Hence, you can apply p-value formulae of Pearson correlation $r$ to Spearman $\rho$.
For instance, the estimator of the vari... | Calculating P-value for Spearman's rank correlation coefficient example on Wikipedia
Spearman correlation coefficient is a Pearson correlation coefficient calculated on the ranks of observations. Hence, you can apply p-value formulae of Pearson correlation $r$ to Spearman $\rho$.
For |
39,539 | How to improve standard visualizations of a univariate distribution? | A simple idea that satisfies both seeing the entire distribution and one that potentially allows space to place the labels is to use a jittered, one-dimensional dot plot.
In this example I have just arbitrarily chosen points with a value over 25 to label, as well as made the points semi-transparent (even with jitterin... | How to improve standard visualizations of a univariate distribution? | A simple idea that satisfies both seeing the entire distribution and one that potentially allows space to place the labels is to use a jittered, one-dimensional dot plot.
In this example I have just | How to improve standard visualizations of a univariate distribution?
A simple idea that satisfies both seeing the entire distribution and one that potentially allows space to place the labels is to use a jittered, one-dimensional dot plot.
In this example I have just arbitrarily chosen points with a value over 25 to l... | How to improve standard visualizations of a univariate distribution?
A simple idea that satisfies both seeing the entire distribution and one that potentially allows space to place the labels is to use a jittered, one-dimensional dot plot.
In this example I have just |
39,540 | How to improve standard visualizations of a univariate distribution? | Expanding on the idea from @Andy, I would suggest this alternative which incorporates the two original plots included in the questions:
I created this plot in R with the following code:
data <- data.frame( Id = paste('case',1:5000), x = exp(rnorm(5000)))
outlier.cut = 10
outliers <- data[ data$x > outlier.cut, ]
outl... | How to improve standard visualizations of a univariate distribution? | Expanding on the idea from @Andy, I would suggest this alternative which incorporates the two original plots included in the questions:
I created this plot in R with the following code:
data <- data.f | How to improve standard visualizations of a univariate distribution?
Expanding on the idea from @Andy, I would suggest this alternative which incorporates the two original plots included in the questions:
I created this plot in R with the following code:
data <- data.frame( Id = paste('case',1:5000), x = exp(rnorm(5000... | How to improve standard visualizations of a univariate distribution?
Expanding on the idea from @Andy, I would suggest this alternative which incorporates the two original plots included in the questions:
I created this plot in R with the following code:
data <- data.f |
39,541 | Is my data distribution normal? (Tried Shapiro and Kolmogornov-Smirnov tests) | It's definitely not normal, and it's not just the large sample size. That qq-plot is really clear. The wikipedia page about kurtosis may be useful to you; it mentions the Pearson type VII family of distributions, with an image of densities quite similar to yours. | Is my data distribution normal? (Tried Shapiro and Kolmogornov-Smirnov tests) | It's definitely not normal, and it's not just the large sample size. That qq-plot is really clear. The wikipedia page about kurtosis may be useful to you; it mentions the Pearson type VII family of | Is my data distribution normal? (Tried Shapiro and Kolmogornov-Smirnov tests)
It's definitely not normal, and it's not just the large sample size. That qq-plot is really clear. The wikipedia page about kurtosis may be useful to you; it mentions the Pearson type VII family of distributions, with an image of densities ... | Is my data distribution normal? (Tried Shapiro and Kolmogornov-Smirnov tests)
It's definitely not normal, and it's not just the large sample size. That qq-plot is really clear. The wikipedia page about kurtosis may be useful to you; it mentions the Pearson type VII family of |
39,542 | Difference between bias-variance dilemma and overfitting | I think they're related, but not identical problems.
For example, its entirely possible to run into the bias-variance dilemma arguably well before a model is "overfit". For example, in survival analysis one might reasonably argue that a constant hazard (exponential distribution) is so unlikely that you should always "p... | Difference between bias-variance dilemma and overfitting | I think they're related, but not identical problems.
For example, its entirely possible to run into the bias-variance dilemma arguably well before a model is "overfit". For example, in survival analys | Difference between bias-variance dilemma and overfitting
I think they're related, but not identical problems.
For example, its entirely possible to run into the bias-variance dilemma arguably well before a model is "overfit". For example, in survival analysis one might reasonably argue that a constant hazard (exponenti... | Difference between bias-variance dilemma and overfitting
I think they're related, but not identical problems.
For example, its entirely possible to run into the bias-variance dilemma arguably well before a model is "overfit". For example, in survival analys |
39,543 | Difference between bias-variance dilemma and overfitting | I view "overfitting" as an example of a bias-variance trade-off (I wouldn't call it a "dilemma") that has gone too far toward the variance end.
The usual example I have in mind for the bias-variance trade-off is the case of a linear model in which all covariates have some effect, but where it would best to drop those... | Difference between bias-variance dilemma and overfitting | I view "overfitting" as an example of a bias-variance trade-off (I wouldn't call it a "dilemma") that has gone too far toward the variance end.
The usual example I have in mind for the bias-variance | Difference between bias-variance dilemma and overfitting
I view "overfitting" as an example of a bias-variance trade-off (I wouldn't call it a "dilemma") that has gone too far toward the variance end.
The usual example I have in mind for the bias-variance trade-off is the case of a linear model in which all covariate... | Difference between bias-variance dilemma and overfitting
I view "overfitting" as an example of a bias-variance trade-off (I wouldn't call it a "dilemma") that has gone too far toward the variance end.
The usual example I have in mind for the bias-variance |
39,544 | How to reduce question set of a poorly designed questionnaire? | @Peter and @ Jonathan have some good ideas. Without repeating, I'll add two more.
If you need to shorten your survey and you won't suffer by reducing the sample size you could give different people somewhat different surveys.
Reanalyze old data two ways: with and without questions you suspect are less important. The... | How to reduce question set of a poorly designed questionnaire? | @Peter and @ Jonathan have some good ideas. Without repeating, I'll add two more.
If you need to shorten your survey and you won't suffer by reducing the sample size you could give different people | How to reduce question set of a poorly designed questionnaire?
@Peter and @ Jonathan have some good ideas. Without repeating, I'll add two more.
If you need to shorten your survey and you won't suffer by reducing the sample size you could give different people somewhat different surveys.
Reanalyze old data two ways: ... | How to reduce question set of a poorly designed questionnaire?
@Peter and @ Jonathan have some good ideas. Without repeating, I'll add two more.
If you need to shorten your survey and you won't suffer by reducing the sample size you could give different people |
39,545 | How to reduce question set of a poorly designed questionnaire? | I've been there before! Legacy surveys: can't live with them, can't live without them...
While I agree with @Peter Flom's approach to look at correlations and reduce the number of highly correlated statements (this is a standard approach to reducing what I call "brick walls" of rating scales in surveys, and has the adv... | How to reduce question set of a poorly designed questionnaire? | I've been there before! Legacy surveys: can't live with them, can't live without them...
While I agree with @Peter Flom's approach to look at correlations and reduce the number of highly correlated st | How to reduce question set of a poorly designed questionnaire?
I've been there before! Legacy surveys: can't live with them, can't live without them...
While I agree with @Peter Flom's approach to look at correlations and reduce the number of highly correlated statements (this is a standard approach to reducing what I ... | How to reduce question set of a poorly designed questionnaire?
I've been there before! Legacy surveys: can't live with them, can't live without them...
While I agree with @Peter Flom's approach to look at correlations and reduce the number of highly correlated st |
39,546 | How to reduce question set of a poorly designed questionnaire? | One thing you could do is look at correlations among all the questions and see if any are very high (say, over .9 or some such). For those pairs, you could eliminate one question at random. That would shorten things, at least.
You could also look at Cronbach's alpha for the items you think are under each factor, and e... | How to reduce question set of a poorly designed questionnaire? | One thing you could do is look at correlations among all the questions and see if any are very high (say, over .9 or some such). For those pairs, you could eliminate one question at random. That would | How to reduce question set of a poorly designed questionnaire?
One thing you could do is look at correlations among all the questions and see if any are very high (say, over .9 or some such). For those pairs, you could eliminate one question at random. That would shorten things, at least.
You could also look at Cronba... | How to reduce question set of a poorly designed questionnaire?
One thing you could do is look at correlations among all the questions and see if any are very high (say, over .9 or some such). For those pairs, you could eliminate one question at random. That would |
39,547 | How to reduce question set of a poorly designed questionnaire? | I would go for Item Response Theory (IRT). IRT not only lets you check for unidimensionality but also things like Item Information Curves (or Item Response Functions), which might come in handy if you want to reduce the number of items but still want to precisely measure participants broadly on the whole latent scale.
... | How to reduce question set of a poorly designed questionnaire? | I would go for Item Response Theory (IRT). IRT not only lets you check for unidimensionality but also things like Item Information Curves (or Item Response Functions), which might come in handy if you | How to reduce question set of a poorly designed questionnaire?
I would go for Item Response Theory (IRT). IRT not only lets you check for unidimensionality but also things like Item Information Curves (or Item Response Functions), which might come in handy if you want to reduce the number of items but still want to pre... | How to reduce question set of a poorly designed questionnaire?
I would go for Item Response Theory (IRT). IRT not only lets you check for unidimensionality but also things like Item Information Curves (or Item Response Functions), which might come in handy if you |
39,548 | Extracting fixed effects table output from lme object | The answer is quite easy:
summary(fm2Orth.lm)$tTable
will give you the full table (not just the coefficients).
In general, use:
names(fm2Orth.lm)
and
names(summary(fm2Orth.lm))
to see what objects are contained in those lists. Then you can explore those objects and you will often find what you need.
EDIT: Since this... | Extracting fixed effects table output from lme object | The answer is quite easy:
summary(fm2Orth.lm)$tTable
will give you the full table (not just the coefficients).
In general, use:
names(fm2Orth.lm)
and
names(summary(fm2Orth.lm))
to see what objects | Extracting fixed effects table output from lme object
The answer is quite easy:
summary(fm2Orth.lm)$tTable
will give you the full table (not just the coefficients).
In general, use:
names(fm2Orth.lm)
and
names(summary(fm2Orth.lm))
to see what objects are contained in those lists. Then you can explore those objects a... | Extracting fixed effects table output from lme object
The answer is quite easy:
summary(fm2Orth.lm)$tTable
will give you the full table (not just the coefficients).
In general, use:
names(fm2Orth.lm)
and
names(summary(fm2Orth.lm))
to see what objects |
39,549 | Extracting fixed effects table output from lme object | The class of the output of lme is, not surprisingly, lme. You can find this by running class(fm2orth.lm).
As a consequence, when you call summary on it, what is really called is summary.lme. This function is not exported from the nlme package (you can discover this when you type summary.lme at the prompt: you get a mes... | Extracting fixed effects table output from lme object | The class of the output of lme is, not surprisingly, lme. You can find this by running class(fm2orth.lm).
As a consequence, when you call summary on it, what is really called is summary.lme. This func | Extracting fixed effects table output from lme object
The class of the output of lme is, not surprisingly, lme. You can find this by running class(fm2orth.lm).
As a consequence, when you call summary on it, what is really called is summary.lme. This function is not exported from the nlme package (you can discover this ... | Extracting fixed effects table output from lme object
The class of the output of lme is, not surprisingly, lme. You can find this by running class(fm2orth.lm).
As a consequence, when you call summary on it, what is really called is summary.lme. This func |
39,550 | Workflow for using R with LyX for a statistical analysis? [closed] | Tal, I also jumped on the Lyx-Swave bandwagon and acutally started off writing my Psychology Masters thesis using Lyx.
However, I abandoned Lyx due to various problems (e.g. adhering to the new APA 6th standard and other journal-specifics, correct formatting of references etc.) and converted to straight tex. I found i... | Workflow for using R with LyX for a statistical analysis? [closed] | Tal, I also jumped on the Lyx-Swave bandwagon and acutally started off writing my Psychology Masters thesis using Lyx.
However, I abandoned Lyx due to various problems (e.g. adhering to the new APA 6 | Workflow for using R with LyX for a statistical analysis? [closed]
Tal, I also jumped on the Lyx-Swave bandwagon and acutally started off writing my Psychology Masters thesis using Lyx.
However, I abandoned Lyx due to various problems (e.g. adhering to the new APA 6th standard and other journal-specifics, correct form... | Workflow for using R with LyX for a statistical analysis? [closed]
Tal, I also jumped on the Lyx-Swave bandwagon and acutally started off writing my Psychology Masters thesis using Lyx.
However, I abandoned Lyx due to various problems (e.g. adhering to the new APA 6 |
39,551 | Workflow for using R with LyX for a statistical analysis? [closed] | Here's my take your questions. Your mileage may vary.
1) For tools, everything except R + LyX is icing on the cake. In my case, I use Emacs + ESS + AUCTeX, Org-Mode, the terminal, and RStudio. Again, R + LyX will get you by in a pinch.
2) LyX gets rid of (read: hides) a lot of the extra folders/crap of which you nee... | Workflow for using R with LyX for a statistical analysis? [closed] | Here's my take your questions. Your mileage may vary.
1) For tools, everything except R + LyX is icing on the cake. In my case, I use Emacs + ESS + AUCTeX, Org-Mode, the terminal, and RStudio. Agai | Workflow for using R with LyX for a statistical analysis? [closed]
Here's my take your questions. Your mileage may vary.
1) For tools, everything except R + LyX is icing on the cake. In my case, I use Emacs + ESS + AUCTeX, Org-Mode, the terminal, and RStudio. Again, R + LyX will get you by in a pinch.
2) LyX gets ri... | Workflow for using R with LyX for a statistical analysis? [closed]
Here's my take your questions. Your mileage may vary.
1) For tools, everything except R + LyX is icing on the cake. In my case, I use Emacs + ESS + AUCTeX, Org-Mode, the terminal, and RStudio. Agai |
39,552 | Workflow for using R with LyX for a statistical analysis? [closed] | I suppose I should probably give a full answer, so here it is.
I don't use Lyx, I use vanilla LaTeX. I tried using Lyx, but it confused me, and I actually found plain latex to be much more understandable. For my money, the interface to Lyx was too much like a word processor and hid the code from me (although I didn't u... | Workflow for using R with LyX for a statistical analysis? [closed] | I suppose I should probably give a full answer, so here it is.
I don't use Lyx, I use vanilla LaTeX. I tried using Lyx, but it confused me, and I actually found plain latex to be much more understanda | Workflow for using R with LyX for a statistical analysis? [closed]
I suppose I should probably give a full answer, so here it is.
I don't use Lyx, I use vanilla LaTeX. I tried using Lyx, but it confused me, and I actually found plain latex to be much more understandable. For my money, the interface to Lyx was too much ... | Workflow for using R with LyX for a statistical analysis? [closed]
I suppose I should probably give a full answer, so here it is.
I don't use Lyx, I use vanilla LaTeX. I tried using Lyx, but it confused me, and I actually found plain latex to be much more understanda |
39,553 | What is the maximum for Pearson's chi square statistic? | For some intuition about this, consider the square case ($k$ rows and columns), with $N=nk$. Then the maximal Chi Square occurs when all the marginal total are equal (in this case $n$), and the values in the table are $n$ along the diagonal and $0$ for the off diagonal, so that you have perfect association between the... | What is the maximum for Pearson's chi square statistic? | For some intuition about this, consider the square case ($k$ rows and columns), with $N=nk$. Then the maximal Chi Square occurs when all the marginal total are equal (in this case $n$), and the value | What is the maximum for Pearson's chi square statistic?
For some intuition about this, consider the square case ($k$ rows and columns), with $N=nk$. Then the maximal Chi Square occurs when all the marginal total are equal (in this case $n$), and the values in the table are $n$ along the diagonal and $0$ for the off di... | What is the maximum for Pearson's chi square statistic?
For some intuition about this, consider the square case ($k$ rows and columns), with $N=nk$. Then the maximal Chi Square occurs when all the marginal total are equal (in this case $n$), and the value |
39,554 | Determining trends in text | There are a number of statistical NLP projects out there, with NLTK one of the more active Open Source ones. However tracking word frequency over time and over a few hundred documents is probably a simple enough problem to code yourself.
You will want to start with converting your documents to a format easy to process... | Determining trends in text | There are a number of statistical NLP projects out there, with NLTK one of the more active Open Source ones. However tracking word frequency over time and over a few hundred documents is probably a si | Determining trends in text
There are a number of statistical NLP projects out there, with NLTK one of the more active Open Source ones. However tracking word frequency over time and over a few hundred documents is probably a simple enough problem to code yourself.
You will want to start with converting your documents ... | Determining trends in text
There are a number of statistical NLP projects out there, with NLTK one of the more active Open Source ones. However tracking word frequency over time and over a few hundred documents is probably a si |
39,555 | Determining trends in text | Text Mining Process Overview
Here is a quick summary of generic approach/process for identifying trends in text. There are great open source tools available (R, python, etc) to carry out the process mentioned here.
Brief Description Of Data Processing Steps
Explore Corpus - Understand the types of variables, their fun... | Determining trends in text | Text Mining Process Overview
Here is a quick summary of generic approach/process for identifying trends in text. There are great open source tools available (R, python, etc) to carry out the process m | Determining trends in text
Text Mining Process Overview
Here is a quick summary of generic approach/process for identifying trends in text. There are great open source tools available (R, python, etc) to carry out the process mentioned here.
Brief Description Of Data Processing Steps
Explore Corpus - Understand the ty... | Determining trends in text
Text Mining Process Overview
Here is a quick summary of generic approach/process for identifying trends in text. There are great open source tools available (R, python, etc) to carry out the process m |
39,556 | Determining trends in text | It sounds to me that you might be talking about performing sentiment analysis (if not, the previous two answers are very good, but skip to the last paragraph below). If that is the case, you I have some suggestions for you. I would recommend you to start from reading the draft of the introductory book "Sentiment analys... | Determining trends in text | It sounds to me that you might be talking about performing sentiment analysis (if not, the previous two answers are very good, but skip to the last paragraph below). If that is the case, you I have so | Determining trends in text
It sounds to me that you might be talking about performing sentiment analysis (if not, the previous two answers are very good, but skip to the last paragraph below). If that is the case, you I have some suggestions for you. I would recommend you to start from reading the draft of the introduc... | Determining trends in text
It sounds to me that you might be talking about performing sentiment analysis (if not, the previous two answers are very good, but skip to the last paragraph below). If that is the case, you I have so |
39,557 | High frequency data series cleaning in R | There's a package for that. Check out RTAQ.
Small plug: there's a quantitative finance stack exchange you may be interested in. | High frequency data series cleaning in R | There's a package for that. Check out RTAQ.
Small plug: there's a quantitative finance stack exchange you may be interested in. | High frequency data series cleaning in R
There's a package for that. Check out RTAQ.
Small plug: there's a quantitative finance stack exchange you may be interested in. | High frequency data series cleaning in R
There's a package for that. Check out RTAQ.
Small plug: there's a quantitative finance stack exchange you may be interested in. |
39,558 | High frequency data series cleaning in R | To detect an anomaly, you need a model which provides an expectation. Intervention Detection yields the answer to the question " What is the probability of observing what I observed before I observed it ? I suggest that you focus on shorter time series and use an automatic modeling algorithm that forms an ARIMA model b... | High frequency data series cleaning in R | To detect an anomaly, you need a model which provides an expectation. Intervention Detection yields the answer to the question " What is the probability of observing what I observed before I observed | High frequency data series cleaning in R
To detect an anomaly, you need a model which provides an expectation. Intervention Detection yields the answer to the question " What is the probability of observing what I observed before I observed it ? I suggest that you focus on shorter time series and use an automatic model... | High frequency data series cleaning in R
To detect an anomaly, you need a model which provides an expectation. Intervention Detection yields the answer to the question " What is the probability of observing what I observed before I observed |
39,559 | High frequency data series cleaning in R | I'm not convinced "cleaning" is required. Modeling high frequency data is addressed in the academic quantfi literature using functional forms such as GARCH and especially HARCH for the prediction of short-term volatility. This literature dates back to the 90s, e.g., this paper by Dacorogna, et al., http://long-memory.c... | High frequency data series cleaning in R | I'm not convinced "cleaning" is required. Modeling high frequency data is addressed in the academic quantfi literature using functional forms such as GARCH and especially HARCH for the prediction of s | High frequency data series cleaning in R
I'm not convinced "cleaning" is required. Modeling high frequency data is addressed in the academic quantfi literature using functional forms such as GARCH and especially HARCH for the prediction of short-term volatility. This literature dates back to the 90s, e.g., this paper b... | High frequency data series cleaning in R
I'm not convinced "cleaning" is required. Modeling high frequency data is addressed in the academic quantfi literature using functional forms such as GARCH and especially HARCH for the prediction of s |
39,560 | High frequency data series cleaning in R | Mayby try some "moving deletator" - in window of p observations compute standard deviation and then delete obs for which absolute difference to previous observation is x times bigger then standard deviation in that window. But this method could don't work with densely packed outliers (one after another) which is showed... | High frequency data series cleaning in R | Mayby try some "moving deletator" - in window of p observations compute standard deviation and then delete obs for which absolute difference to previous observation is x times bigger then standard dev | High frequency data series cleaning in R
Mayby try some "moving deletator" - in window of p observations compute standard deviation and then delete obs for which absolute difference to previous observation is x times bigger then standard deviation in that window. But this method could don't work with densely packed out... | High frequency data series cleaning in R
Mayby try some "moving deletator" - in window of p observations compute standard deviation and then delete obs for which absolute difference to previous observation is x times bigger then standard dev |
39,561 | High frequency data series cleaning in R | One note. A lot of the spikes are trades that are printed as part of a derivatives transaction. Most data sources that you will use have a field for condition code. Eliminate all non-continuous market trades. You will still have some spikes but at least they are real. | High frequency data series cleaning in R | One note. A lot of the spikes are trades that are printed as part of a derivatives transaction. Most data sources that you will use have a field for condition code. Eliminate all non-continuous mar | High frequency data series cleaning in R
One note. A lot of the spikes are trades that are printed as part of a derivatives transaction. Most data sources that you will use have a field for condition code. Eliminate all non-continuous market trades. You will still have some spikes but at least they are real. | High frequency data series cleaning in R
One note. A lot of the spikes are trades that are printed as part of a derivatives transaction. Most data sources that you will use have a field for condition code. Eliminate all non-continuous mar |
39,562 | Does high log-likelihood imply high R^2 | No, since for linear regression log likelihood is a sum of squared residuals plus some other terms, log likelihood is scale dependent. So for the same model multiplying the regressors by some constant will change log likelihood but R squared will remain the same. | Does high log-likelihood imply high R^2 | No, since for linear regression log likelihood is a sum of squared residuals plus some other terms, log likelihood is scale dependent. So for the same model multiplying the regressors by some constant | Does high log-likelihood imply high R^2
No, since for linear regression log likelihood is a sum of squared residuals plus some other terms, log likelihood is scale dependent. So for the same model multiplying the regressors by some constant will change log likelihood but R squared will remain the same. | Does high log-likelihood imply high R^2
No, since for linear regression log likelihood is a sum of squared residuals plus some other terms, log likelihood is scale dependent. So for the same model multiplying the regressors by some constant |
39,563 | Does high log-likelihood imply high R^2 | If all your models have normally distributed errors and are fit to exactly the same data, then there is a straightforward, increasing relationship between likelihood and R^2, since they're both ultimately about the sum of squared errors. But in general, no, you can't look at a pair of log likelihood values and assume m... | Does high log-likelihood imply high R^2 | If all your models have normally distributed errors and are fit to exactly the same data, then there is a straightforward, increasing relationship between likelihood and R^2, since they're both ultima | Does high log-likelihood imply high R^2
If all your models have normally distributed errors and are fit to exactly the same data, then there is a straightforward, increasing relationship between likelihood and R^2, since they're both ultimately about the sum of squared errors. But in general, no, you can't look at a pa... | Does high log-likelihood imply high R^2
If all your models have normally distributed errors and are fit to exactly the same data, then there is a straightforward, increasing relationship between likelihood and R^2, since they're both ultima |
39,564 | Is this a reasonable approach to fitting distributions? | One problematic feature is that there may be a continuum of optimal solutions. In most settings the quantiles are continuous functions of the parameters. When the distributions are continuous, almost surely there will be positive intervals between the data values. Suppose your objective function is optimized by a pa... | Is this a reasonable approach to fitting distributions? | One problematic feature is that there may be a continuum of optimal solutions. In most settings the quantiles are continuous functions of the parameters. When the distributions are continuous, almos | Is this a reasonable approach to fitting distributions?
One problematic feature is that there may be a continuum of optimal solutions. In most settings the quantiles are continuous functions of the parameters. When the distributions are continuous, almost surely there will be positive intervals between the data value... | Is this a reasonable approach to fitting distributions?
One problematic feature is that there may be a continuum of optimal solutions. In most settings the quantiles are continuous functions of the parameters. When the distributions are continuous, almos |
39,565 | Is this a reasonable approach to fitting distributions? | What you are proposing is called quantile matching, though the way you propose to do it will be exhausting. The ex-Gaussian distribution can be found in the package gamlss.dist with quantiles as qexGAUS etc.; it uses nu where you use tau.
A similar quantile matching method can be used in the function fitdist in the p... | Is this a reasonable approach to fitting distributions? | What you are proposing is called quantile matching, though the way you propose to do it will be exhausting. The ex-Gaussian distribution can be found in the package gamlss.dist with quantiles as qexGA | Is this a reasonable approach to fitting distributions?
What you are proposing is called quantile matching, though the way you propose to do it will be exhausting. The ex-Gaussian distribution can be found in the package gamlss.dist with quantiles as qexGAUS etc.; it uses nu where you use tau.
A similar quantile matc... | Is this a reasonable approach to fitting distributions?
What you are proposing is called quantile matching, though the way you propose to do it will be exhausting. The ex-Gaussian distribution can be found in the package gamlss.dist with quantiles as qexGA |
39,566 | Is this a reasonable approach to fitting distributions? | Take a look at the QQ-Plot (under my answer) in the following link:
Need help identifying a distribution by its histogram | Is this a reasonable approach to fitting distributions? | Take a look at the QQ-Plot (under my answer) in the following link:
Need help identifying a distribution by its histogram | Is this a reasonable approach to fitting distributions?
Take a look at the QQ-Plot (under my answer) in the following link:
Need help identifying a distribution by its histogram | Is this a reasonable approach to fitting distributions?
Take a look at the QQ-Plot (under my answer) in the following link:
Need help identifying a distribution by its histogram |
39,567 | Is it impossible for clinical and laboratory data to be normally distributed? | You are correct, a positive-only value cannot be really normally distributed. However depending on the particular circumstances, its distribution could be sufficiently close to normal for statistical methodology assuming normality to apply. I want to note that very few methods actually require normality of the data, of... | Is it impossible for clinical and laboratory data to be normally distributed? | You are correct, a positive-only value cannot be really normally distributed. However depending on the particular circumstances, its distribution could be sufficiently close to normal for statistical | Is it impossible for clinical and laboratory data to be normally distributed?
You are correct, a positive-only value cannot be really normally distributed. However depending on the particular circumstances, its distribution could be sufficiently close to normal for statistical methodology assuming normality to apply. I... | Is it impossible for clinical and laboratory data to be normally distributed?
You are correct, a positive-only value cannot be really normally distributed. However depending on the particular circumstances, its distribution could be sufficiently close to normal for statistical |
39,568 | Is it impossible for clinical and laboratory data to be normally distributed? | Many biological measurements take positive values only and to such variables applies the rule of thumb: If $\text{mean} < 2\cdot\text{SD}$ then the distribution is not normal.
Explanation: for normally distributed values the majority of values are in the interval $[\text{mean}\pm2\cdot\text{SD}]$, and a normal distrib... | Is it impossible for clinical and laboratory data to be normally distributed? | Many biological measurements take positive values only and to such variables applies the rule of thumb: If $\text{mean} < 2\cdot\text{SD}$ then the distribution is not normal.
Explanation: for normal | Is it impossible for clinical and laboratory data to be normally distributed?
Many biological measurements take positive values only and to such variables applies the rule of thumb: If $\text{mean} < 2\cdot\text{SD}$ then the distribution is not normal.
Explanation: for normally distributed values the majority of valu... | Is it impossible for clinical and laboratory data to be normally distributed?
Many biological measurements take positive values only and to such variables applies the rule of thumb: If $\text{mean} < 2\cdot\text{SD}$ then the distribution is not normal.
Explanation: for normal |
39,569 | Detecting abnormal points in point cloud | An outlier detector for your irregular ("vector") point data is available in GRASS as v.outlier.
An overview of spatial outlier detection methods appears in a 2004 paper by Cheng and Li.
An older method, specialized for topographic data, relies on "drainage enforcement" (making the water flow downhill continuously with... | Detecting abnormal points in point cloud | An outlier detector for your irregular ("vector") point data is available in GRASS as v.outlier.
An overview of spatial outlier detection methods appears in a 2004 paper by Cheng and Li.
An older meth | Detecting abnormal points in point cloud
An outlier detector for your irregular ("vector") point data is available in GRASS as v.outlier.
An overview of spatial outlier detection methods appears in a 2004 paper by Cheng and Li.
An older method, specialized for topographic data, relies on "drainage enforcement" (making ... | Detecting abnormal points in point cloud
An outlier detector for your irregular ("vector") point data is available in GRASS as v.outlier.
An overview of spatial outlier detection methods appears in a 2004 paper by Cheng and Li.
An older meth |
39,570 | Detecting abnormal points in point cloud | You could fit some sort of smooth function for $z(x,y)$, perhaps using locally weighted scatterplot smoothing (LOWESS or LOESS), then look for points where the residual for $z$ (i.e. the difference between the observed and fitted values) is greater than some fixed multiple of the standard error of prediction. That shou... | Detecting abnormal points in point cloud | You could fit some sort of smooth function for $z(x,y)$, perhaps using locally weighted scatterplot smoothing (LOWESS or LOESS), then look for points where the residual for $z$ (i.e. the difference be | Detecting abnormal points in point cloud
You could fit some sort of smooth function for $z(x,y)$, perhaps using locally weighted scatterplot smoothing (LOWESS or LOESS), then look for points where the residual for $z$ (i.e. the difference between the observed and fitted values) is greater than some fixed multiple of th... | Detecting abnormal points in point cloud
You could fit some sort of smooth function for $z(x,y)$, perhaps using locally weighted scatterplot smoothing (LOWESS or LOESS), then look for points where the residual for $z$ (i.e. the difference be |
39,571 | Detecting abnormal points in point cloud | Are the points relatively dense on your surface? Then I would suggest counting the number of points in a sphere around every point. Choose the radius of your sphere to be a bit less than the distance the "abnormal" points have to the regular surface - maybe half of what they typically have. Then throw out the points wh... | Detecting abnormal points in point cloud | Are the points relatively dense on your surface? Then I would suggest counting the number of points in a sphere around every point. Choose the radius of your sphere to be a bit less than the distance | Detecting abnormal points in point cloud
Are the points relatively dense on your surface? Then I would suggest counting the number of points in a sphere around every point. Choose the radius of your sphere to be a bit less than the distance the "abnormal" points have to the regular surface - maybe half of what they typ... | Detecting abnormal points in point cloud
Are the points relatively dense on your surface? Then I would suggest counting the number of points in a sphere around every point. Choose the radius of your sphere to be a bit less than the distance |
39,572 | Detecting abnormal points in point cloud | I think this problem relies only in the outliers of variable $z$.
The surveyor scans a grid of $x$,$y$ points that are "well-behaved". On the other hand $z$ points may contain abnormal values (in statistics we call them outliers).
I would suggest to explore the values of $z$, and the plot of $(x,y,z)$.
From those plots... | Detecting abnormal points in point cloud | I think this problem relies only in the outliers of variable $z$.
The surveyor scans a grid of $x$,$y$ points that are "well-behaved". On the other hand $z$ points may contain abnormal values (in stat | Detecting abnormal points in point cloud
I think this problem relies only in the outliers of variable $z$.
The surveyor scans a grid of $x$,$y$ points that are "well-behaved". On the other hand $z$ points may contain abnormal values (in statistics we call them outliers).
I would suggest to explore the values of $z$, an... | Detecting abnormal points in point cloud
I think this problem relies only in the outliers of variable $z$.
The surveyor scans a grid of $x$,$y$ points that are "well-behaved". On the other hand $z$ points may contain abnormal values (in stat |
39,573 | Expected number of uniques in a non-uniformly distributed population | Let $X_i$ be the random variable equal to $1$ when there is exactly one ball of color $i$ ($i = 1, 2, \ldots, m$; to avoid confusion I write $m$ instead of $N$). The count of color $i$ follows a Binomial($p_i$, $n$) distribution, implying the expectation of $X_i$ is
$$\eqalign{
\mathbb{E}[X_i] = &\sum_{j=0}^{n} \bino... | Expected number of uniques in a non-uniformly distributed population | Let $X_i$ be the random variable equal to $1$ when there is exactly one ball of color $i$ ($i = 1, 2, \ldots, m$; to avoid confusion I write $m$ instead of $N$). The count of color $i$ follows a Bino | Expected number of uniques in a non-uniformly distributed population
Let $X_i$ be the random variable equal to $1$ when there is exactly one ball of color $i$ ($i = 1, 2, \ldots, m$; to avoid confusion I write $m$ instead of $N$). The count of color $i$ follows a Binomial($p_i$, $n$) distribution, implying the expecta... | Expected number of uniques in a non-uniformly distributed population
Let $X_i$ be the random variable equal to $1$ when there is exactly one ball of color $i$ ($i = 1, 2, \ldots, m$; to avoid confusion I write $m$ instead of $N$). The count of color $i$ follows a Bino |
39,574 | Expected number of uniques in a non-uniformly distributed population | I will give the outline of the solution. Numbers of each coloured ball in a draw follows multinomial distribution as tshauck pointed out. Let $R$ denote the number of red balls, $G$ - number of green balls, $B$ - number of blue balls and $Y$ - number of yellow balls in the draw of the size $n$. Then the probability th... | Expected number of uniques in a non-uniformly distributed population | I will give the outline of the solution. Numbers of each coloured ball in a draw follows multinomial distribution as tshauck pointed out. Let $R$ denote the number of red balls, $G$ - number of green | Expected number of uniques in a non-uniformly distributed population
I will give the outline of the solution. Numbers of each coloured ball in a draw follows multinomial distribution as tshauck pointed out. Let $R$ denote the number of red balls, $G$ - number of green balls, $B$ - number of blue balls and $Y$ - number... | Expected number of uniques in a non-uniformly distributed population
I will give the outline of the solution. Numbers of each coloured ball in a draw follows multinomial distribution as tshauck pointed out. Let $R$ denote the number of red balls, $G$ - number of green |
39,575 | Expected number of uniques in a non-uniformly distributed population | Maybe I'm being naive here, but would the Multinomial Distribution not work for this?
P(1 unique) = P(1 Blue) + P(1 Red) + P(1 Blue), there are probably a lot of details that would need to be fill in, like P(1 Blue) = The multinomial distribution for all possible combinations of the other ball combinations where there'... | Expected number of uniques in a non-uniformly distributed population | Maybe I'm being naive here, but would the Multinomial Distribution not work for this?
P(1 unique) = P(1 Blue) + P(1 Red) + P(1 Blue), there are probably a lot of details that would need to be fill in, | Expected number of uniques in a non-uniformly distributed population
Maybe I'm being naive here, but would the Multinomial Distribution not work for this?
P(1 unique) = P(1 Blue) + P(1 Red) + P(1 Blue), there are probably a lot of details that would need to be fill in, like P(1 Blue) = The multinomial distribution for ... | Expected number of uniques in a non-uniformly distributed population
Maybe I'm being naive here, but would the Multinomial Distribution not work for this?
P(1 unique) = P(1 Blue) + P(1 Red) + P(1 Blue), there are probably a lot of details that would need to be fill in, |
39,576 | How can a statistician be relevant today? [closed] | Statisticians often work in some form of consultation. As you said, many people need to validate a certain hypothesis, in science, medicine, etc. A statistician can analyze the data, but more importantly set up the proper experimental design. Much of science is based on the ability to do certain inferences. As long as ... | How can a statistician be relevant today? [closed] | Statisticians often work in some form of consultation. As you said, many people need to validate a certain hypothesis, in science, medicine, etc. A statistician can analyze the data, but more importan | How can a statistician be relevant today? [closed]
Statisticians often work in some form of consultation. As you said, many people need to validate a certain hypothesis, in science, medicine, etc. A statistician can analyze the data, but more importantly set up the proper experimental design. Much of science is based o... | How can a statistician be relevant today? [closed]
Statisticians often work in some form of consultation. As you said, many people need to validate a certain hypothesis, in science, medicine, etc. A statistician can analyze the data, but more importan |
39,577 | How can a statistician be relevant today? [closed] | The role of the statistician continues to be essential. I would say that there is a shortage of people with good statistical thinking. Testing hypotheses is required in any scientific rigorous decision process.
Novel health interventions (such as drugs against cancer) could not be developed without the support of a st... | How can a statistician be relevant today? [closed] | The role of the statistician continues to be essential. I would say that there is a shortage of people with good statistical thinking. Testing hypotheses is required in any scientific rigorous decisi | How can a statistician be relevant today? [closed]
The role of the statistician continues to be essential. I would say that there is a shortage of people with good statistical thinking. Testing hypotheses is required in any scientific rigorous decision process.
Novel health interventions (such as drugs against cancer)... | How can a statistician be relevant today? [closed]
The role of the statistician continues to be essential. I would say that there is a shortage of people with good statistical thinking. Testing hypotheses is required in any scientific rigorous decisi |
39,578 | In an underdetermined linear regression setup, why does the residual sum of squares equal 0? | That need not be the case.
It is routine to say that a polynomial of degree greater than the sample size will give a perfect fit to the data. However, this will not be the case if two points have equal feature ($X$) values but unequal outcome ($y$) values. No function can accommodate that. At least one of those points ... | In an underdetermined linear regression setup, why does the residual sum of squares equal 0? | That need not be the case.
It is routine to say that a polynomial of degree greater than the sample size will give a perfect fit to the data. However, this will not be the case if two points have equa | In an underdetermined linear regression setup, why does the residual sum of squares equal 0?
That need not be the case.
It is routine to say that a polynomial of degree greater than the sample size will give a perfect fit to the data. However, this will not be the case if two points have equal feature ($X$) values but ... | In an underdetermined linear regression setup, why does the residual sum of squares equal 0?
That need not be the case.
It is routine to say that a polynomial of degree greater than the sample size will give a perfect fit to the data. However, this will not be the case if two points have equa |
39,579 | In an underdetermined linear regression setup, why does the residual sum of squares equal 0? | With one predictor (and an intercept): two points determines a lines exactly, with less than two points there are infinitely many lines that pass through that point ...
With two predictors (and an intercept): three points determines a plane exactly, with less than three points infinitely many planes will fit perfectly ... | In an underdetermined linear regression setup, why does the residual sum of squares equal 0? | With one predictor (and an intercept): two points determines a lines exactly, with less than two points there are infinitely many lines that pass through that point ...
With two predictors (and an int | In an underdetermined linear regression setup, why does the residual sum of squares equal 0?
With one predictor (and an intercept): two points determines a lines exactly, with less than two points there are infinitely many lines that pass through that point ...
With two predictors (and an intercept): three points deter... | In an underdetermined linear regression setup, why does the residual sum of squares equal 0?
With one predictor (and an intercept): two points determines a lines exactly, with less than two points there are infinitely many lines that pass through that point ...
With two predictors (and an int |
39,580 | In an underdetermined linear regression setup, why does the residual sum of squares equal 0? | $\DeclareMathOperator{\rank}{rank}$
Suppose all observations of explanatory variables are identical, then it can be shown that
\begin{align}
RSS = \sum_{i = 1}^n(y_i - \bar{y})^2. \tag{1}
\end{align}
Hence $RSS > 0$ unless $y_1, \ldots, y_n$ are all identical.
The reason of this example cannot provide a perfect fit is ... | In an underdetermined linear regression setup, why does the residual sum of squares equal 0? | $\DeclareMathOperator{\rank}{rank}$
Suppose all observations of explanatory variables are identical, then it can be shown that
\begin{align}
RSS = \sum_{i = 1}^n(y_i - \bar{y})^2. \tag{1}
\end{align}
| In an underdetermined linear regression setup, why does the residual sum of squares equal 0?
$\DeclareMathOperator{\rank}{rank}$
Suppose all observations of explanatory variables are identical, then it can be shown that
\begin{align}
RSS = \sum_{i = 1}^n(y_i - \bar{y})^2. \tag{1}
\end{align}
Hence $RSS > 0$ unless $y_1... | In an underdetermined linear regression setup, why does the residual sum of squares equal 0?
$\DeclareMathOperator{\rank}{rank}$
Suppose all observations of explanatory variables are identical, then it can be shown that
\begin{align}
RSS = \sum_{i = 1}^n(y_i - \bar{y})^2. \tag{1}
\end{align}
|
39,581 | Why does mean-centering in a univariate logistic regression change p-values? | The statsmodels package does not include an intercept. When you include an intercept, only the intercept p-value changes (which makes sense for centering the feature).
import numpy as np
import statsmodels.api as sm
x = [5, 5, 6, 6, 5, 6]
y = [1, 1, 1, 1, 2, 2]
xc = x - np.mean(x)
lr3 = sm.MNLogit(y, sm.tools.add_const... | Why does mean-centering in a univariate logistic regression change p-values? | The statsmodels package does not include an intercept. When you include an intercept, only the intercept p-value changes (which makes sense for centering the feature).
import numpy as np
import statsm | Why does mean-centering in a univariate logistic regression change p-values?
The statsmodels package does not include an intercept. When you include an intercept, only the intercept p-value changes (which makes sense for centering the feature).
import numpy as np
import statsmodels.api as sm
x = [5, 5, 6, 6, 5, 6]
y = ... | Why does mean-centering in a univariate logistic regression change p-values?
The statsmodels package does not include an intercept. When you include an intercept, only the intercept p-value changes (which makes sense for centering the feature).
import numpy as np
import statsm |
39,582 | Is a 0.05 absolute difference in AUC values enough to declare statistically significant difference? | Whether a given difference in AUC is statistically significant does not only depend on the absolute difference, but also on the variability of the AUC scores, just the same as for a difference in means between groups (plus distributional assumptions, which people typically handwave away with reference to the CLT).
As G... | Is a 0.05 absolute difference in AUC values enough to declare statistically significant difference? | Whether a given difference in AUC is statistically significant does not only depend on the absolute difference, but also on the variability of the AUC scores, just the same as for a difference in mean | Is a 0.05 absolute difference in AUC values enough to declare statistically significant difference?
Whether a given difference in AUC is statistically significant does not only depend on the absolute difference, but also on the variability of the AUC scores, just the same as for a difference in means between groups (pl... | Is a 0.05 absolute difference in AUC values enough to declare statistically significant difference?
Whether a given difference in AUC is statistically significant does not only depend on the absolute difference, but also on the variability of the AUC scores, just the same as for a difference in mean |
39,583 | Element-wise comparisons of sorted subsets of random numbers yield nonrandom results | This is exactly as it should be. A nice illustration of how our intuition can go wrong.
Let's start by considering the case of having only two entries per array:
$$ (a_1, a_2)\quad\text{and}\quad(b_1, b_2). $$
We will disregard ties, which make stuff only more complicated, not more interesting.
Suppose $a_1<b_1$ (so yo... | Element-wise comparisons of sorted subsets of random numbers yield nonrandom results | This is exactly as it should be. A nice illustration of how our intuition can go wrong.
Let's start by considering the case of having only two entries per array:
$$ (a_1, a_2)\quad\text{and}\quad(b_1, | Element-wise comparisons of sorted subsets of random numbers yield nonrandom results
This is exactly as it should be. A nice illustration of how our intuition can go wrong.
Let's start by considering the case of having only two entries per array:
$$ (a_1, a_2)\quad\text{and}\quad(b_1, b_2). $$
We will disregard ties, w... | Element-wise comparisons of sorted subsets of random numbers yield nonrandom results
This is exactly as it should be. A nice illustration of how our intuition can go wrong.
Let's start by considering the case of having only two entries per array:
$$ (a_1, a_2)\quad\text{and}\quad(b_1, |
39,584 | Element-wise comparisons of sorted subsets of random numbers yield nonrandom results | We can relate this to Donsker's theorem. The ordered sequence that you generate is similar to an empirical distribution function and will approach a Brownian bridge.
So basically your question is about the distribution of positive and negative values of a Brownian bridge that starts at 0 and ends at 0.
A Brownian bridg... | Element-wise comparisons of sorted subsets of random numbers yield nonrandom results | We can relate this to Donsker's theorem. The ordered sequence that you generate is similar to an empirical distribution function and will approach a Brownian bridge.
So basically your question is abou | Element-wise comparisons of sorted subsets of random numbers yield nonrandom results
We can relate this to Donsker's theorem. The ordered sequence that you generate is similar to an empirical distribution function and will approach a Brownian bridge.
So basically your question is about the distribution of positive and ... | Element-wise comparisons of sorted subsets of random numbers yield nonrandom results
We can relate this to Donsker's theorem. The ordered sequence that you generate is similar to an empirical distribution function and will approach a Brownian bridge.
So basically your question is abou |
39,585 | How Do Researchers Measure "Non-Linear Effects" in Statistics? | Are there any types of Regression Models that can address this issue?
Absolutely! This is possible without even venturing outside of linear regression (remember that linear regression refers to linearity in the parameters).
A relationship like you describe kind of looks like a cubic function. Consequently, you might w... | How Do Researchers Measure "Non-Linear Effects" in Statistics? | Are there any types of Regression Models that can address this issue?
Absolutely! This is possible without even venturing outside of linear regression (remember that linear regression refers to linea | How Do Researchers Measure "Non-Linear Effects" in Statistics?
Are there any types of Regression Models that can address this issue?
Absolutely! This is possible without even venturing outside of linear regression (remember that linear regression refers to linearity in the parameters).
A relationship like you describe... | How Do Researchers Measure "Non-Linear Effects" in Statistics?
Are there any types of Regression Models that can address this issue?
Absolutely! This is possible without even venturing outside of linear regression (remember that linear regression refers to linea |
39,586 | How Do Researchers Measure "Non-Linear Effects" in Statistics? | Dave's answer explains well your final question. I wanted to write a few words on your first bold sentence
But it seems to me that the Regression Model would still "insist" that there is a linear relationship.
This is the not a good way to think about what a Regression Model actually does. It is rather the other way ar... | How Do Researchers Measure "Non-Linear Effects" in Statistics? | Dave's answer explains well your final question. I wanted to write a few words on your first bold sentence
But it seems to me that the Regression Model would still "insist" that there is a linear rela | How Do Researchers Measure "Non-Linear Effects" in Statistics?
Dave's answer explains well your final question. I wanted to write a few words on your first bold sentence
But it seems to me that the Regression Model would still "insist" that there is a linear relationship.
This is the not a good way to think about what ... | How Do Researchers Measure "Non-Linear Effects" in Statistics?
Dave's answer explains well your final question. I wanted to write a few words on your first bold sentence
But it seems to me that the Regression Model would still "insist" that there is a linear rela |
39,587 | Is it possible to use propensity score matching (or something similar) to create a control group if you do not yet have outcome data? | Not only can you do that, this this one of the main motivations for using matching methods (such as PSM) over other methods. You can perform the matching to select a subset of individuals that you need to follow up on instead of collecting outcome data on the full sample. This is especially useful when getting outcome ... | Is it possible to use propensity score matching (or something similar) to create a control group if | Not only can you do that, this this one of the main motivations for using matching methods (such as PSM) over other methods. You can perform the matching to select a subset of individuals that you nee | Is it possible to use propensity score matching (or something similar) to create a control group if you do not yet have outcome data?
Not only can you do that, this this one of the main motivations for using matching methods (such as PSM) over other methods. You can perform the matching to select a subset of individual... | Is it possible to use propensity score matching (or something similar) to create a control group if
Not only can you do that, this this one of the main motivations for using matching methods (such as PSM) over other methods. You can perform the matching to select a subset of individuals that you nee |
39,588 | Is it possible to use propensity score matching (or something similar) to create a control group if you do not yet have outcome data? | It's not strictly pertinent to your question, but without outcome data you can also use unsupervised machine learning techniques (eg clustering) to get better insights on your study population, and potentially inform patient characterization. | Is it possible to use propensity score matching (or something similar) to create a control group if | It's not strictly pertinent to your question, but without outcome data you can also use unsupervised machine learning techniques (eg clustering) to get better insights on your study population, and po | Is it possible to use propensity score matching (or something similar) to create a control group if you do not yet have outcome data?
It's not strictly pertinent to your question, but without outcome data you can also use unsupervised machine learning techniques (eg clustering) to get better insights on your study popu... | Is it possible to use propensity score matching (or something similar) to create a control group if
It's not strictly pertinent to your question, but without outcome data you can also use unsupervised machine learning techniques (eg clustering) to get better insights on your study population, and po |
39,589 | Question on Linear Regression: What is a good transformation for this data? | Modeling is often facilitated, in the sense of being simpler or more easily interpreted, when variables have approximately symmetric distributions. (Be careful, though: when the variables are response variables in regressions, usually you want to make their residuals approximately symmetric.) I will say a little more... | Question on Linear Regression: What is a good transformation for this data? | Modeling is often facilitated, in the sense of being simpler or more easily interpreted, when variables have approximately symmetric distributions. (Be careful, though: when the variables are respons | Question on Linear Regression: What is a good transformation for this data?
Modeling is often facilitated, in the sense of being simpler or more easily interpreted, when variables have approximately symmetric distributions. (Be careful, though: when the variables are response variables in regressions, usually you want... | Question on Linear Regression: What is a good transformation for this data?
Modeling is often facilitated, in the sense of being simpler or more easily interpreted, when variables have approximately symmetric distributions. (Be careful, though: when the variables are respons |
39,590 | Question on Linear Regression: What is a good transformation for this data? | Determine a transformation on the response to facilitate linear modeling
facilitate is vague, possibly intentionally so. In my opinion, log transformation is appropriate for two reasons.
First, it is likely that if you want to use ordinary linear regression it will give residuals with approximately normal distribution... | Question on Linear Regression: What is a good transformation for this data? | Determine a transformation on the response to facilitate linear modeling
facilitate is vague, possibly intentionally so. In my opinion, log transformation is appropriate for two reasons.
First, it is | Question on Linear Regression: What is a good transformation for this data?
Determine a transformation on the response to facilitate linear modeling
facilitate is vague, possibly intentionally so. In my opinion, log transformation is appropriate for two reasons.
First, it is likely that if you want to use ordinary lin... | Question on Linear Regression: What is a good transformation for this data?
Determine a transformation on the response to facilitate linear modeling
facilitate is vague, possibly intentionally so. In my opinion, log transformation is appropriate for two reasons.
First, it is |
39,591 | Central Limit Theorem and the Sample Sum | You are correct that you can express $Z$ either of the ways that you wrote; that’s what it means to be “equal”. However, you have a misunderstanding about the central limit theorem, which explicitly concerns $Z$, not $\bar X$.
People often like thinking of the sample mean converging so that the following holds asymptot... | Central Limit Theorem and the Sample Sum | You are correct that you can express $Z$ either of the ways that you wrote; that’s what it means to be “equal”. However, you have a misunderstanding about the central limit theorem, which explicitly c | Central Limit Theorem and the Sample Sum
You are correct that you can express $Z$ either of the ways that you wrote; that’s what it means to be “equal”. However, you have a misunderstanding about the central limit theorem, which explicitly concerns $Z$, not $\bar X$.
People often like thinking of the sample mean conver... | Central Limit Theorem and the Sample Sum
You are correct that you can express $Z$ either of the ways that you wrote; that’s what it means to be “equal”. However, you have a misunderstanding about the central limit theorem, which explicitly c |
39,592 | Central Limit Theorem and the Sample Sum | Yes, you are correct. Consider:
$$
\begin{aligned}
Z &= \frac{\sum_{i=1}^{n} X_i-n\mu}{\sqrt{n}\sigma}\\
&=\frac{n\bar{X}-n\mu}{n\frac{1}{\sqrt n}\sigma}\\
&=\frac{n}{n}\frac{\bar{X}-\mu}{\frac{\sigma}{\sqrt n}}\\
&=\frac{\bar{X}-\mu}{\frac{\sigma}{\sqrt n}}
\end{aligned}
$$
Although, as Dave points out, the CLT techni... | Central Limit Theorem and the Sample Sum | Yes, you are correct. Consider:
$$
\begin{aligned}
Z &= \frac{\sum_{i=1}^{n} X_i-n\mu}{\sqrt{n}\sigma}\\
&=\frac{n\bar{X}-n\mu}{n\frac{1}{\sqrt n}\sigma}\\
&=\frac{n}{n}\frac{\bar{X}-\mu}{\frac{\sigma | Central Limit Theorem and the Sample Sum
Yes, you are correct. Consider:
$$
\begin{aligned}
Z &= \frac{\sum_{i=1}^{n} X_i-n\mu}{\sqrt{n}\sigma}\\
&=\frac{n\bar{X}-n\mu}{n\frac{1}{\sqrt n}\sigma}\\
&=\frac{n}{n}\frac{\bar{X}-\mu}{\frac{\sigma}{\sqrt n}}\\
&=\frac{\bar{X}-\mu}{\frac{\sigma}{\sqrt n}}
\end{aligned}
$$
Alt... | Central Limit Theorem and the Sample Sum
Yes, you are correct. Consider:
$$
\begin{aligned}
Z &= \frac{\sum_{i=1}^{n} X_i-n\mu}{\sqrt{n}\sigma}\\
&=\frac{n\bar{X}-n\mu}{n\frac{1}{\sqrt n}\sigma}\\
&=\frac{n}{n}\frac{\bar{X}-\mu}{\frac{\sigma |
39,593 | definition of scoring function | Both "positively oriented" and "negatively oriented" scoring rules are common in the literature. Better papers explicitly note which convention they use.
Unfortunately, not everyone knows about the two common conventions. So people who think "their" convention is the "normal" one will not note which convention they are... | definition of scoring function | Both "positively oriented" and "negatively oriented" scoring rules are common in the literature. Better papers explicitly note which convention they use.
Unfortunately, not everyone knows about the tw | definition of scoring function
Both "positively oriented" and "negatively oriented" scoring rules are common in the literature. Better papers explicitly note which convention they use.
Unfortunately, not everyone knows about the two common conventions. So people who think "their" convention is the "normal" one will not... | definition of scoring function
Both "positively oriented" and "negatively oriented" scoring rules are common in the literature. Better papers explicitly note which convention they use.
Unfortunately, not everyone knows about the tw |
39,594 | definition of scoring function | I think it’s useful here to refer back to wikipedia.
The first equation you quote above is for a proper scoring rule. This is one where the highest possible score is reported by using the true probability distribution.
I can’t access the second document referenced in the question so I can only guess that it is a) a typ... | definition of scoring function | I think it’s useful here to refer back to wikipedia.
The first equation you quote above is for a proper scoring rule. This is one where the highest possible score is reported by using the true probabi | definition of scoring function
I think it’s useful here to refer back to wikipedia.
The first equation you quote above is for a proper scoring rule. This is one where the highest possible score is reported by using the true probability distribution.
I can’t access the second document referenced in the question so I can... | definition of scoring function
I think it’s useful here to refer back to wikipedia.
The first equation you quote above is for a proper scoring rule. This is one where the highest possible score is reported by using the true probabi |
39,595 | What is reasonable to do with small -tiny- datasets?. Dealing with rare diseases | Such datasets are too small for reliable biomarker development. The only hope is a proof-of-concept study, which is really a proof-of-signal-existence study where you have to put all your eggs in one basket and examine the degree to which that basket relates to an outcome. The basket needs to be arrived at using unsup... | What is reasonable to do with small -tiny- datasets?. Dealing with rare diseases | Such datasets are too small for reliable biomarker development. The only hope is a proof-of-concept study, which is really a proof-of-signal-existence study where you have to put all your eggs in one | What is reasonable to do with small -tiny- datasets?. Dealing with rare diseases
Such datasets are too small for reliable biomarker development. The only hope is a proof-of-concept study, which is really a proof-of-signal-existence study where you have to put all your eggs in one basket and examine the degree to which ... | What is reasonable to do with small -tiny- datasets?. Dealing with rare diseases
Such datasets are too small for reliable biomarker development. The only hope is a proof-of-concept study, which is really a proof-of-signal-existence study where you have to put all your eggs in one |
39,596 | A formal definition of a "measure of association" | Books on this topic include Correlation and Dependence by Samuel Kotz and Dominique Drouet and Multivariate Models and Multivariate Dependence Concepts by Harry Joe. The second is more practical, the first more theoretical.
And there is a paper by A Rényi: On measures of dependence in Acta Mathematica Academiae Scient... | A formal definition of a "measure of association" | Books on this topic include Correlation and Dependence by Samuel Kotz and Dominique Drouet and Multivariate Models and Multivariate Dependence Concepts by Harry Joe. The second is more practical, the | A formal definition of a "measure of association"
Books on this topic include Correlation and Dependence by Samuel Kotz and Dominique Drouet and Multivariate Models and Multivariate Dependence Concepts by Harry Joe. The second is more practical, the first more theoretical.
And there is a paper by A Rényi: On measures o... | A formal definition of a "measure of association"
Books on this topic include Correlation and Dependence by Samuel Kotz and Dominique Drouet and Multivariate Models and Multivariate Dependence Concepts by Harry Joe. The second is more practical, the |
39,597 | A formal definition of a "measure of association" | Below are some desiderata that might be useful. I'm not certain these desiderata will work, but this would be a reasonable starting point for inquiry. Essentially, you need some kind of property to ensure that the "measure" is well-ordered, specified as an inequality that the measure must satisfy. Here I have used t... | A formal definition of a "measure of association" | Below are some desiderata that might be useful. I'm not certain these desiderata will work, but this would be a reasonable starting point for inquiry. Essentially, you need some kind of property to | A formal definition of a "measure of association"
Below are some desiderata that might be useful. I'm not certain these desiderata will work, but this would be a reasonable starting point for inquiry. Essentially, you need some kind of property to ensure that the "measure" is well-ordered, specified as an inequality ... | A formal definition of a "measure of association"
Below are some desiderata that might be useful. I'm not certain these desiderata will work, but this would be a reasonable starting point for inquiry. Essentially, you need some kind of property to |
39,598 | A formal definition of a "measure of association" | I think about this a little differently than I used to, and will respond to myself here. kjetil's answer is still the best researched answer here and Ben's answer is thought provoking. The following are just my idiosyncratic brain droppings.
Beginning with a definition of statistical independence
$$F_{X_1, \cdots, X_n}... | A formal definition of a "measure of association" | I think about this a little differently than I used to, and will respond to myself here. kjetil's answer is still the best researched answer here and Ben's answer is thought provoking. The following a | A formal definition of a "measure of association"
I think about this a little differently than I used to, and will respond to myself here. kjetil's answer is still the best researched answer here and Ben's answer is thought provoking. The following are just my idiosyncratic brain droppings.
Beginning with a definition ... | A formal definition of a "measure of association"
I think about this a little differently than I used to, and will respond to myself here. kjetil's answer is still the best researched answer here and Ben's answer is thought provoking. The following a |
39,599 | Distribution of i.i.d. random variables $X$ and $Y$ if $XY \sim \text{Beta}(\alpha, \beta)$ | In the case of $Z=XY\sim \text{Beta}(\alpha,1)$, the moment generating function (mgf) of $-\ln(XY)=-\ln X-\ln Y$ is
\begin{align}
M_{-\ln(XY)}(t)
&= E(e^{-t\ln Z})
\\ &=E(Z^{-t})
\\ &=\int_0^1 z^{-t}\alpha z^{\alpha-1}dz
\\ &= \frac{1}{1-t/\alpha}
\end{align}
which is the mgf of an exponentially distributed random ... | Distribution of i.i.d. random variables $X$ and $Y$ if $XY \sim \text{Beta}(\alpha, \beta)$ | In the case of $Z=XY\sim \text{Beta}(\alpha,1)$, the moment generating function (mgf) of $-\ln(XY)=-\ln X-\ln Y$ is
\begin{align}
M_{-\ln(XY)}(t)
&= E(e^{-t\ln Z})
\\ &=E(Z^{-t})
\\ &=\int_0^1 z^{ | Distribution of i.i.d. random variables $X$ and $Y$ if $XY \sim \text{Beta}(\alpha, \beta)$
In the case of $Z=XY\sim \text{Beta}(\alpha,1)$, the moment generating function (mgf) of $-\ln(XY)=-\ln X-\ln Y$ is
\begin{align}
M_{-\ln(XY)}(t)
&= E(e^{-t\ln Z})
\\ &=E(Z^{-t})
\\ &=\int_0^1 z^{-t}\alpha z^{\alpha-1}dz
\\ ... | Distribution of i.i.d. random variables $X$ and $Y$ if $XY \sim \text{Beta}(\alpha, \beta)$
In the case of $Z=XY\sim \text{Beta}(\alpha,1)$, the moment generating function (mgf) of $-\ln(XY)=-\ln X-\ln Y$ is
\begin{align}
M_{-\ln(XY)}(t)
&= E(e^{-t\ln Z})
\\ &=E(Z^{-t})
\\ &=\int_0^1 z^{ |
39,600 | Why are the contours of a linear regression residual sum of squares an ellipse? | Say we are in a simple linear regression setting, so $\beta = \left(\beta_1,\beta_2\right)$ and $Y_i = \beta_1 + X_i\beta_2 + \epsilon_i$ where $\epsilon_i ~ \sim N\left(0,1\right)$ then
\begin{align}
RSS & = \sum_{i=1}^{n}\left(Y_i - \beta_1 - X_i\beta_2 \right)^2\\
& =\sum_{i=1}^{n}\left( Y_i^2 - Y_i\beta_1 -Y_i X_i ... | Why are the contours of a linear regression residual sum of squares an ellipse? | Say we are in a simple linear regression setting, so $\beta = \left(\beta_1,\beta_2\right)$ and $Y_i = \beta_1 + X_i\beta_2 + \epsilon_i$ where $\epsilon_i ~ \sim N\left(0,1\right)$ then
\begin{align} | Why are the contours of a linear regression residual sum of squares an ellipse?
Say we are in a simple linear regression setting, so $\beta = \left(\beta_1,\beta_2\right)$ and $Y_i = \beta_1 + X_i\beta_2 + \epsilon_i$ where $\epsilon_i ~ \sim N\left(0,1\right)$ then
\begin{align}
RSS & = \sum_{i=1}^{n}\left(Y_i - \beta... | Why are the contours of a linear regression residual sum of squares an ellipse?
Say we are in a simple linear regression setting, so $\beta = \left(\beta_1,\beta_2\right)$ and $Y_i = \beta_1 + X_i\beta_2 + \epsilon_i$ where $\epsilon_i ~ \sim N\left(0,1\right)$ then
\begin{align} |
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