instruction stringlengths 9 38.7k |
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I'd like to measure the duration of a function call. The function call has one parameter, n. If I were to graph an average of the function call's duration, with n on the x axis, I would also provide the standard error for each n.
The function call duration is, however, extremely short. It seems more appropriate to time... |
For simple ordinary linear regression $y=a+bx$, if I want to use the reduced model $y=bx$, i.e. passing through the origin, how to do statistical tests on the validity of such a linear model?
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In probabilist statistics, the properties of a discrete Pearson's chi-squared test hold that:
\begin{aligned}
\chi^2 = \sum_{i=1}^{r} \sum_{j=1}^{c} {(O_{i,j} - E_{i,j})^2 \over E_{i,j}}
\end{aligned}
Where $\chi^2$ is our (Pearson's) cumulative test statistic, $O_{i,j}$ is an observed frequency in a given contingency ... |
I am trying to find out if there is a relation between 5 different stock markets rates over a period of 5 years.
I was advised by my supervisor to use the Concordance Correlation Coefficient which unfortunately I have not studied and I am unsure how to proceed. I was also advised to use Timeseries on the data.
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What would be the simplest, straightest-forwardest way to determine the following:
Whether A,B,C is non-randomly distributed in each single group (IE: are there more A's in group 1 than random chance would predict?)
Whether the distribution of A,B,C is different between the groups. (IE: Group 1 is has more Cs than Bs... |
This is a very simple question but it has been years since I have done statistics. I am also new to this website (was recommended by a friend) so apologies if this question has been done 'wrongly'.
I am comparing several criteria between two different treatment methods of a certain disease. I have the following table a... |
I have a variable which is a linear combination of two other variables, each one following an N(0,1) distribution.
I need to compute the threshold of the distribution of this combination variable (to compute the Z for a specific probability).
Does anyone know which function should I use, i.e. which package is available... |
Introduction
In forecasts combination one of the popular solutions is based on the application of some information criterion. Taking for example Akaike criterion $AIC_j$ estimated for the model $j$, one could compute the differences of $AIC_j$ from $AIC^* = \min_j{AIC_j}$ and then $RP_j = e^{(AIC^*-AIC_j)/2}$ could be... |
Most coefficients (e.g., odd ratios, mean differences, etc.) can be converted into a (Pearson-like) correlation coefficient.
Q: Is there a conversion from probit coefficient --> correlation coefficient?
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I'm trying to reproduce an existing prediction algorithm, handed down by a retired researcher. The first step is to fit some observed data to a Weibull distribution, to obtain a shape and scale which will be used for predicting future values. I'm using R to do this. Here's an example of my code:
x<-c(23,19,37,38,40,36,... |
I'm running a predictive model to predict the probability of winning a certain item based on the price that I bid (other factors also). After running the model (ols) in R, I wanted to account for all the variables in my model and develop a graph highlighting the 'predicted probabilities' regarding the primary variables... |
Some guys, decided to make some money, by selling lemonade in different public places. Each guy has a fix spot on which she sell the lemonade. In every morning, they go to a lemonade maker warehouse and buy the stock for the entire day, based on their forecasts. At any moment of the day, they can ask for an instant del... |
I have data from a 24-item (each item ordinal) scale used at two time points in 2 groups - before and after treatment with treatment A and treatment B. I want to capture a core group of symptoms that are related and might respond to one treatment but not another, i.e. I want to see if the magnitude of the change in eac... |
Does the sign of the vectors returned by PCA have any significance after I center my variables?
|
I'm interested in fitting a linear mixed model with this special variance structure on the random effects $\mathbf{u}$:
$\begin{eqnarray*}
\mathbb{V}\left(\mathbf{u}\right) & = & \mathbf{A}\mathbf{G}\mathbf{A}^{\prime}
\end{eqnarray*}$
This variance structure is very similar to Cholesky and Antedependence structures ... |
I know just enough about lme() and lmer() to get myself by with simple models, and to get myself into trouble with more complex ones. I'm really confused about the proper way to model some data I'm currently working with, and would be grateful for some help.
The question: do people give different estimates of a distan... |
I want to fit a regression model to see whether these is changes in the proportion of First-year students over years. I have count data for the total count of First-year students (FirstTimeStudents) and total count of all students (TotalStudents). I want to fit a GEE model with this data and wrote the following code... |
Currently working in Octave, but due to the poor documentation progress is very slow.
What language is easy to learn and use, and well documented to solve machine learning problems? I am looking to prototype on a small dataset (thousands of examples), so speed is not important.
EDIT: I am developing a recommendation en... |
There are three misspecification tests that I would like to perform on my model for a Johansen test before continuing with the cointegration tests themselves. Following Johansen's advice in Likelihood-based inference in cointegrated vector auto-regressive models, I would like to use the Ljung-Box test for autocorrelati... |
I am doing a simple marketing project that has the following types of variables:
X1 - continuous (e.g. income)
X2 - categorical (e.g. gender)
Y - continuous (e.g. number of a product type purchased such as tubs of ice-cream)
I am interested in the relationship between income (X1) and product purchase (Y) but also th... |
Consider the following little problem:
Roll an $m$-sided die $n$ times. What is the probability that all and only indices from $1$ through $k$ appear? ($k\leq n,m$)
Here's my thought (you can check if it's correct). I want to know if there's a simpler approach available (which doesn't invoke recursive formulae, for e... |
I've run an ordered logistic regression model in R with Zelig and am looking to calculate predicted probabilities. Zelig has a series of simple one line commands to generate the information I want on first differences and so forth. Unfortunately, I keep getting an error when running the zelig function and was wondering... |
I am looking for a R package that implements Incremental PCA (online version of PCA)
Is there anybody that knows a piece of code that implements such algorithm?
|
If I use radial basis function networks (RBFNs) for probability estimation by plugging the output of the RBFNs into the Logistic function are weights between 0 and 1 sufficient?
|
In the post here, a contributor (dmk38) makes an interesting, and may I add a very commonsense observation, that to include or not to include the main effects in an interaction model containing the product term should be guided by theory and hypothesis that is being tested.
I have a similar situation where the produc... |
Does RSS + ESS = TSS all the time?
I am thinking - does it hold if there is no intercept?
Does this apply for all regressions, or are there certain conditions that need to be met?
|
How do we find out the long term and short term effect of estimators on AR model?
|
I am looking at patient data where the main outcome of interest is mortality within 30 days following hospitalisation with an emergency condition. I am working on data from 2003-2017, with approximately 100,000 observations per year. I had previously understood that this was to be a "simple" multilevel logistic analysi... |
I need to be able to find outliers in my data. I thought it best to test for this using the Kolmogorov-Smirnov Test.
I have over 800,000 points so I wanted a way to filter the data first to only test those that are on the edge of my sample. By eye I can fit an exponential decay (red line) but I was wondering if there ... |
I am seeking advice on programming a new random effects variance-covariance matrix/structure (pdmat) in R for use in lme()? I've checked out the lme source code (as suggested if you want to program your own pdmat), but remain confused. Does anyone have a good reference? Thanks in advance!
|
In a sequential (on-line) tree algorithm, I'm trying to estimate class label densities using a histogram. The algorithm grows a tree by generating test functions at each decision node, which correspond to the features in the data set. That is to say each feature is used to create a test in the form of $g(x) > 0$ that's... |
A design has two predictor variables (both continuous). The response is pass/fail. I would like to know how to use Binary Logistic Regression to know what value of each variable will give me a failure rate of 0.000001 with 95% confidence.
With one predictor variable, it's clear - but not with two. I usually use Mini... |
I am learning some image processing stuff and equalizing a histogram comes up as an important topic. I have followed the procedure listed on Wikipedia but the resulting equalized histogram does not look much better to me.
Let's say I have the following histogram where values only range from 0 to 7:
0 | 2
1 | 6
2 | 12
... |
I have a population - in this case they are phone calls into a call center.
Each call can be one of approximately 200 'Problems'. (an example of a Problem is 'I cannot connect to the internet').
I would like to predict the top 10 most common problems across the entire population based on analysis of a sample set of ph... |
I've obtained 2840 observations of a stochastic process with large Gaussian noise. The process parameters change at one point around the 1500th observation. I've ensemble-averaged these into sets of 10, 40 and 284 observations and would like to present those three sets to the readers of my report, but I can't figure ou... |
I'm reading Steffen L. Lauritzen's "Graphical Models" and I'm having trouble fathoming the meaning behind the concept of a perfect sequence. Here's how it's defined in the book (page 14/15):
Given an undirected, marked graph $\mathcal{G} = (V,E)$. Let $B_1,\ldots,B_k$ be a sequence of subsets of the vertex set V. Let ... |
Following the advice here regarding statistical significance versus substantive meaning of a model, I did a scatterplot with 'fit line at subgroups'.
My graph clearly shows that there is an interaction between X1 and X2 on Y. However, the F test of the X1*X2 interaction is insignificant. I am using SPSS GLM. X1 is sign... |
I have an experiment where observations are one of eight different treatment combinations and are then either one of two different heights. There are 4 blocks, with 8 plots for each block, and the two heights are thought of as split-plots.
I.e. the data table resembles:
I don't know how to set up the anova table, i.e... |
I found that it is possible to look at adjusted residuals and treat them as a z-score and then use a two-tailed test to find a p-value. The problem is how do you calculate adjusted residuals on what I realise is a 1xr table (as it is a goodness of fit test)?
In addition if anyone is interested in seeing what I was doi... |
Let's say in linear regression, I got a fit and I can plot residuals to see whether there is any systematic trend in such a plot. How to quantitatively determine whether the residues are really random? Is Durbin-Watson test used for this purpose? How to interpret such test if so?
Please provide an example, preferably i... |
I know that if
$$X\sim N(\mu_X, \sigma^2_X), \hspace{1em} Y \sim N(\mu_Y, \sigma^2_Y), \hspace{1em} Z = X + Y, \hspace{1em} X,Y \text{ independent}$$
then
$$Z \sim N(\mu_X + \mu_Y, \sigma^2_X + \sigma^2_Y).$$
But what would happen if $X,Y$ were not independent? i.e. if
$$
\begin{pmatrix}X\\Y\end{pmatrix} \sim N\left( \... |
What are the best methods for fitting the 'mode' of data sampled from a continuous distribution?
Since the mode is technically undefined (right?) for a continuous distribution, I'm really asking 'how do you find the most common value'?
If you assume the parent distribution is gaussian, you could bin the data and find... |
Edit: I think the data was poorly given, varables coke, pepsi, and sprite were just given in 2 columns when I got it, but it has nothing to do with before and after treatment?
here's the original questions since someone asked
For the study, 2 males and 2 females are picked randomly from NYC, and a random sample of 2 ma... |
I want to estimate the parameter $\mu$ using the difference between two Poisson distributions with the same parameter, i.e. a Skellam distribution with $\mu_1=\mu_2 = \mu$.
I can calculate the variance of the Skellam distribution as the average variance over multiple samples, however, depending on sample size and som... |
In a simple experiment I asked participants to make acceptability judgements (9-point Likert scale) when they observed different animated virtual characters. I have two factors: character (7 levels) and motion (5 levels).
Two-way ANOVA showed significant interaction between the above factors, so I want to explore this... |
Do you know how can I compute out the p-value in LM statistics? (What is the command in stata?)
I know that to implement the LM computing procedure I have to do the following steps:
Obtain the OLS estimators of the restricted model;
Obtain the residuals regression;
regress the residuals on all independent variablesof ... |
Possible Duplicate:
Should I run separate regressions for every community, or can community simply be a controlling variable in an aggregated model?
I have a SPSS model output with fixed effects. The dependent variable is pay, and I'm testing for the difference between males and females including several variables a... |
... where the significance of the results has been checked with statistical tests.
If no, then why?
side note: The data is generated based on specified prior probabilities.
|
I found documentation at: http://hosho.ees.hokudai.ac.jp/~kubo/Rdoc/library/SuppDists/html/maxFratio.html
I am not sure how really to use this though and am coming up short finding help online.
If anyone has a link or tutorial on this in R please let me know.
|
I separate my plants into four groups of 16, and I spray them to keep the bugs away:
group 1: I spray daily
group 2: I spray every 2 days
group 3: I spray every 3 days
group 4: I spray every 4 days
at the end of the 12 days, I check number of plants that's bug free
group 1 is: 12
group 2 is: 10
group 3 is: 7
group 4 i... |
I was trying to help my colleague with fitting a distribution curve to some empiric data (these are sea water level observations at different time points). However, I haven't succeeded since it's my first experience in approximating an empiric distribution with a theoretical one.
The mean value of $Y$ is 0.32688.
$\si... |
I have the following experimental design :
Sampling is carried out on three random sites (Factor Site is coded : Site1, Site2, Site3).
Within each site, sampling is carried out in a dry plot and in a wet plot (Factor Hydrology is coded : Dry/Wet)
Within each of the previous plot, sampling is carried out at two Depths (... |
I've been asked to analyse the distribution of a set of data, essentially a single column of random samples of a physical parameter which cannot be negative. The standard deviation that I usually calculate assumes that data are normally distributed, which in this case cannot be true.
Since I'm used to being asked to pr... |
I have come across a needed condition on a continuous probability distribution defined over $[0, \infty]$ and wonder whether it has a name. For a distribution with CDF $F$ and pdf $f$ I need that the quantity:
$$\phi(x) \equiv \frac{f(x)}{F(x)+xf(x)}$$
be monotonically non-increasing. Putting the condition in another f... |
I am analysing a dataset composed by three groups of individuals: unemployed, unstable workers and regular workers. These three groups are numerically equal (400 individuals in each category). I am running a logit analysis to test the effect of occupational status (regular worker, unemployed and unstable worker) on a b... |
I'm currently taking a data mining class, and for one our projects we're required to predict the class label for an unknown data set by first building a classifier on a training data set which already provides the class label.
We're only required to get an accuracy of 80% to get a full mark on the assignment. I have a... |
I have parameter estimates fitting a particular nonlinear model for thousands of experimental cycles. My goal is to find a nice way to tag those cycles which didn't fit the model very well. Currently I am comparing RMSE values for this. I have a huge list of RMSE values and am looking for a cutoff RMSE past which to f... |
I am trying to cross validate a logistic regression model with probability sampling weights (weights representing number of subjects in the population). I am not sure how to handle the weights in each of the 'folds' (cross-validation steps). I don't think it is as simple as leaving out the observations, I believe the... |
I was always under the impression that regression is just a more general form of ANOVA and that the results would be identical. Recently, however, I have run both a regression and an ANOVA on the same data and the results differ significantly. That is, in the regression model both main effects and the interaction are s... |
Suppose we have someone building a predictive model, but that someone is not necessarily well-versed in proper statistical or machine learning principles. Maybe we are helping that person as they are learning, or maybe that person is using some sort of software package that requires minimal knowledge to use.
Now this ... |
More recently, I read two articles. Speed's article is about the history of the correlation, and the article by Reshef, et al. is about a new method called maximal information coefficient (MIC). I need your help to understand the MIC method to estimate non-linear correlations between variables.
Moreover, instructions f... |
I have a question on selecting the appropriate statistical test as below:
I have a group of people attending a training course, in order to measure whether the training course is effective in improving attendees' knowledge. We did the following:
attendees will complete a pre-test (TRUE or FALSE only) before the traini... |
What I want is some tool that will test an ordinal, discrete variable against a specific probability distribution, say the variable might take 4 values, 1, 2, 3, 4, and my expected probability distribution is that 10% will be 1, 50% will be 2, 30% will be 3 and 10% will be 4.
What program, or application, need I use t... |
Does anybody have good documentation for discriminant analysis? I have 9 variables (measurements), 60 patients and my outcome is good surgery, bad surgery. Also, is my sample size too small?
Thank you
|
I have two variables A and B of interval scale type.
A is the birth year of a person and B is the number of years spent at university.
What method would you recommend to measure the correlation?
|
I have two variables A and B.
A is of nominal scale type and B is of interval scale type.
A is the brand of the car a person drives.
And B is the person's mean salary per year.
What method would you recommend to measure the correlation?
|
I'm familiar with post-hoc testing with ANOVA for exploring differences between a sequence of groups, but recently I've been reading about Change Point Analysis (especially the R packages bcp, changepoint and strucchange).
It looks like those packages only handle data where there is one data point per unit of time. I'... |
Is there any way to calculate an ordered logistic multilevel regression in an imputed dataset? I have tried Stata’s GLLAMM (Generalized Linear and Latent Mixed Models), but that won’t work with the mi estimate, post:command prefix. Should I “estimate anyway”, or is there a better way to do it, preferably R or Stata?
> ... |
Possible Duplicate:
Effect of moving average parameter on variability and variance of demand
What is the effect of Theta on MA(1) process, when we move from zero to 1 and from zero to -1, how the process will be affected?
the same question for AR(1)
|
I wish to better understand the pros/cons for using either loess or a smoothing splines for smoothing some curve.
Another variation of my question is if there is a way to construct a smoothing spline in a way that will yield the same results as using loess.
Any reference or insight are welcomed.
|
I have been watching Tom Mitchell's lecture on Bayes Nets:
http://cc-web.isri.cmu.edu/CourseCast/Viewer/Default.aspx?id=bc507778-7a18-4121-b345-
83d9bab72f55
He states the following by way of the chain rule. I'm being dense I am sure but don't recognize this quickly. Is it a straight application of the chain rule?
$$... |
I am trying to implement an algorithm for calculating $p$-values of $F$-tests and I need this method to be highly precise. It is easy to implement this with $z$- or $t$- tables, however I don't know how to do this with $F$-values. I have seen some online calculators that do this job, what method do they use? Interpolat... |
Consider an MA(1) process, $d_{t}=e_{t}-\Theta e_{t-1}$, when $d_t$ is the demand at time $t$ and $e_t$ is error term and $\Theta$ is moving average parameter. Now if $\Theta$ equal to zero so we have a white noise process, if $\Theta$ gets positive values, process is more irregular than white noise, and when the is ne... |
Possible Duplicate:
Machine learning cookbook / reference card / cheatsheet?
I wonder if there is a good self-learning textbook for machine learning? I am particularly looking for those in application-level, not so much theoretical. I wouldn't mind a math-heavy book, as long as you guys think it is suitable for self... |
I have a database of users with a field of the last time they logged in. Would this kind of data be considered "censored", and if so is there anything I can do with it beyond a histogram/density of how many people logged in within the last month, two months, etc? (To be clear: I only know the last time they logged in, ... |
I am working in a genomics project and I ended up having a huge table with around 800 measurements (cases/rows), around 200 channels (columns/continuous variables) and 5 categories (one categorical column)
I would like to do two things:
Try to find sub-groups in the different levels of the categorical variable that I... |
I have our company's daily revenue data in multiple markets. The essence of the project is to see how different markets compare to each other based on a few variables, namely the age of the market and its population.
I've created 30 day rolling means for each market and plotted them,
What my boss wants is a way to in... |
As the title states, is there a closed form formula for the expectation of the square root of a hypergeometric variable.
Edit:
Closed form approximate solutions based on related distributions or expansions are also welcome.
|
I was was wondering about where to track down implementation details for SAS: I have certain outputs (depending on small amounts of data) which I would like to understand better by trying to check against a theoretical solution. I'm looking at something pretty specific (how standard errors on predicted probabilities fr... |
I have seen the terms "frequent pattern mining", "subspace clustering", and "biclustering". They all pertain to finding clusters using subsets of the data attributes. What's the difference?
|
To strengthen my understanding of fundamental probability theory, I am working my way through Professor Aaron Hertzmann's Introduction to Bayesian Learning course notes. Section 3.8 of these course notes includes the following exercise.
Original Problem
Derive a formula for $P(\mathbf{A})$, assuming you know $P(\mathbf... |
I want to sample from mixed normal distribution, first one is $N(1,2)$, second one is $N(5,4)$. I used rnorm(100, c(mean=c(1,5), sd=c(2,4))). Is this correct?
The problem I am trying to solve is sampling from the 2 distribution above, first one with 75%, second one with 25%. Am I on the right track?
Edit: I will rewr... |
Let's say I'm running a model to look at questions asked on a form. My model looks like:
Price = B0 + B1(Gender) + B2(Age) + B3(Credit Type) + B4(Home) ...
I'm trying to calculate expected price for every possible scenario.
So price for gender = 0, age = 18, home = 1, etc.
Price for gender = 1, age = 18, home = 1, etc.... |
I have a SPSS data file, which i am trying to reduce. However the data which belongs together is spread within multiple columns. I.e. I have one row per subject, but each subject has done multiple different conditions as well as procedures. The conditions are in columns condition_1, condition_2 etc. The procedures are ... |
I am analyzing data with a binary outcome and a variety of continuous and categorical (including dichotomous) predictor variables. My approach is to perform a binary logistic regression and to treat any predictor with more than 20 unique values as continuous. Several arguments against categorization, especially well-do... |
I have a set of positive and negative samples in 2D $(x, y)$, and I would like to fit a curve $f$ to this data set so that $f(x, y_c)$ is increasing in $x$ and $f(x_c, y)$ is increasing in $y$. The function $f(x, y)$ can be thought of as the probability that a new random sample from point $(x, y)$ is positive. The func... |
The question I want to ask is this: how does the proportion of samples within 1 SD of the mean of a normal distribution vary as the number of variates increases?
(Almost) everyone knows that in a 1 dimensional normal distribution, 68% of samples can be found within 1 standard deviation of the mean. What about in 2, 3, ... |
I have a data that looks like this
City Sex Rater drink response
1 NY M 1 coke 77
2 NY M 2 coke 72
3 NY F 3 coke 78
...
There are 3 different cities and 3 different types of drinks, and n=48.
How should I do ANOVA on this?
Here's the data.
structure(list(Ci... |
When computing the Pearson correlation coefficient between a vector $X = \{x_1,...,x_n\}$ and a vector $Y = \{y_1,...,y_n\}$, we need to compute it as
$$\frac{1}{n}\sum_{i=1}^{i=n}(x_i-\bar{x})(y_i-\bar{y}).$$
Here $\bar{x} = (1/n)*\sum_{i=1}^{i=n}x_i$.
My question concerns the case where $x_i$'s, $i=1\dots,n$, are in... |
I recently received this email from a graduate student, and I get similar questions often enough, that I thought I'd post it here:
I'm using factor analysis, multiple regression, and SEM and currently
checking statistical assumptions. I have found numerous univariate
and multivariate outliers. If I deleted them ... |
I compared ?prcomp and ?princomp and found something about Q-mode and R-mode principal component analysis (PCA). But honestly – I don't understand it. Can anybody explain the difference and maybe even explain when to apply which?
|
Gradient tree boosting as proposed by Friedman uses decision trees with J terminal nodes (=leaves) as base learners. There are a number of ways to grow a tree with exactly J nodes for example one can grow the tree in a depth first fashion or in a breadth first fashion, ...
Is there an established way how to grow trees ... |
Please, prove that if we have two variables (equal sample size) $X$ and $Y$ and the variance in $X$ is greater than in $Y$, then the sum of squared differences (i.e., squared Euclidean distances) between data points within $X$ is also greater than that within $Y$.
|
The cumulative distribution function (CDF) for a truncated log-normal distribution is represented as shown below. How can I find its inverse in Matlab?
CDF_truncated_lognormal_distribution = lognormal_cdf(r)./(lognormal_cdf(rmax) - lognormal_cdf(rmin))
Where, lognormal_cdf() in above equation is a CDF of the standard l... |
I have a series of data to which I want to fit my model. The model predicts the probability of success at a given value of x. I have a single data point at a number of points in this space. As I have a single point which is either pass or fail with a certain probability I believe I should fit using a Bernoulli maximum ... |
Can someone help me find a way to estimate the variance of the Kaplan-Meier estimate with dependent observations? Specifically, I have failure time data from patients with several different observations for each patient (and different patients may have different number of observations). The observations for different p... |
I've got some data on the time between heart beats of a human. One indication of ectopic (extra) beats is that these intervals are clustered around three values instead of one. How can I obtain a quantitative measure of this?
I'm looking to compare multiple data sets, and these two 100-bin histograms are representative... |
I have a situation that seems trivial but I can't figure it out. I have a dataset in Matlab that has categorical values. For example:
Outlook,Temperature,Humidity,Windy,Play
sunny,hot,high,false,no
sunny,hot,high,true,no
overcast,hot,high,false,yes
rainy,mild,high,false,yes
rainy,cool,normal,false,yes
rainy,cool,normal... |
pls correct me if i'm wrong. of the econometrics' literature i've read so far, most mentioned heteroskedasticity is not a major problem empirically but multicollinearity would pose a greater concern to researchers and that data transformation would improve empirical results but not completely remove heteroskedasticity.... |
In a traditional filtering context, you'd analyse polls coming in with something like
mu[i] <- alpha[date[i]]
prec[i]<- SampleSize[i]/(alpha[date[i]]*(1-alpha[date[i]])
y[i] ~ dnorm(mu[i],prec[i])
If the surveys are observed with rounding, this usually won't make a difference. But I'm in a situation where it does. Wha... |
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