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I have two different algorithms that make forecasts for binary events. The observed result can either be 1 or 0 (like "rain" or "no rain"). The algorithms usually give a forecast in the 0.4-0.6 range. For measuring error I take the difference between forecast and actual result to the power of 2. So if algorithm 1 said ...
Let's say I want to generate 100 numbers. If I don't allow for any duplications it would go from 1 to 100. But I want to allow for 20% of duplications i.e. so to 20% of the sample would be non-unique -- how can I do that?
I'm trying to figure out, how to best deal with an "other" group or how to create one. I'm using R and ggplot2. Data As an example: I'm analyzing the german Bundestagswahl (general election, every four years). There are at least 38 parties, that voters could vote for in 2009 (see bundeswahlleiter.de for numbers). Let's...
Let's say that I have a friend (let's call him "George") who says that he can control the roll of dice using his mind (ie, make the dice more likely to fall on a specific number he is thinking of). How can I design a scientifically rigorous test to determine if he can actually do this? (I don't really think he can, of...
I've written Naive Bayesian classifiers before, they work wonderfully. But I'd like a classifier which will learn like a Bayesian classifier and identify new classifications when a new cluster emerges. Lets presume I have sensor data for some sort of machinery. I have training data for different conditions - too hot, t...
Is it possible to graph this? I tried doing it on a calculator but didn't have any success. If someone can and post the graph I would greatly appreciate it. $$\frac{1}{\bar{m}_{T}}\sqrt{\frac{1}{12} \sum_{h=T-11}^{T} (m_{h} - \bar{m}_{T})^2}.$$ If the equation is hard to read, it is just the standard deviation of 12 ...
I have data like this : year nb 1 1901 208 2 1902 200 3 1903 223 4 1904 215 5 1905 187 6 1906 214 And I want to specify levels, such that I can summarize the data this way : years nb 1 1901-1910 2082 2 1911-1920 6200 I had a hard time doing this either with grou...
Context: I am doing a study on lying. The independent variable was manipulated such that participants were either told to lie or tell the truth. The dependent variable is related to the amount of detail provided and is extracted from the text provided by participants(this is a standard system of deception detection ca...
I'm using the AMORE NN package to build multiple models from the same training set and i want to compare the weights between the models. I'm pretty much an R newbie, but some of the stronger R users I know can't answer either. here's the code: library("AMORE") net <- newff(n.neurons=c(104,200,104), learning.rate.g...
As I understand it, Student's t will asymptotically approximate the Z statistic at sample sizes approaching infinity (see the infinite degrees of freedom row for degrees of freedom in most introductory statistics books). However, Z tests are applicable when populations are assessed in total. Thus, when the populatio...
I'm looking at a few logistic regression issues. ("regular" and "conditional"). Ideally, I'd like to weight each of the input cases so that the glm will focus more on predicting the higher weighted cases correctly at the expense of possibly misclassifying the lower weighted cases. Surely this has been done before. Ca...
I am conducting a between groups analysis for 3 groups (N=26, one control group and two experimental groups) with 4 dependent variables. I initially planned to conduct a MANOVA, however I am not meeting normality (significant skewness and kurtosis using z > 2.58) and homogeneity of variance assumptions for 2 of the DVs...
I'm doing Phillips-Ouliaris Cointegration test with po.test function inside tseries library. I have a simple question about the "cointegration". When i do PO test I get the p-value result but I don't get the "coefficients" of the cointegration. Is it normal? I mean, the cointegration is used to know the "relathionship...
I am building a big data frame by merging the content of a few files together. These files share the same columns layout. c = read.delim('bigfile1.txt') c1 = read.delim('bigfile2.txt') c2 = read.delim('bigfile3.txt') ctmp1 = merge(c, c1, all=TRUE) ctmp2 = merge(ctmp1, c2, all=TRUE) Is the above code efficient? Should...
Lets say I have a dataset where I want to estimate the relative risk of outcome X based on a binary treatment level Y, using PROC GENMOD to fit a logistic regression model. I can use the BAYES statement to have SAS 9.2 produce nice, MCMC-based prior distributions for my data. My question is, what if I then want to samp...
Is there a package in R which implements the weighted maximum likelihood method (Warm, 1996) for estimating the person parameters in Rasch Models?
Let's say I've collected a small number (N) of observations for a hypothesis that I'd like to test. I could use the bootstrap method to produce a sample distribution for the mean result of N observations, but I'm concerned that this model could break down when N gets very small, introducing error into the sample distri...
With $y_1, \ldots, y_n$ a real valued time series and $\hat{f} : \mathbb{R} \to \mathbb{R}$ a (least square) estimate of the function $y \mapsto E(Y_i \mid Y_{i-1} = y)$ the training error $$\text{err} = \frac{1}{n-1} \sum_{i=2}^n (y_i - \hat{f}(y_{i-1}))^2$$ will typically underestimate the expected prediction error o...
Apologies for this vague and unclear question, I have no background in statistics. I have two vectors of time series data, covering a six month period. The data is in daily intervals (except for weekends). The first vector contains the stock volume for a company on each of the days. The second vector contains an ex...
EDIT: After doing some more research, it seems slice sampling could be the way to go. I've seen it mentioned a lot in the context of how to sample the univariate distributions required for Gibbs Sampling. Any thoughts/opinions on this? Any other algorithms that might work better? This is a half statistical and half met...
I have a dataset with responses coded as 0 and 1. I am trying to specify 3 models of responses and compare it to the observed results. I would therefore like to make single comparisons between two binary distributions. Is there a way to do this? Basically what I want is to compare observed results for 16 question per p...
What would be the common way of estimating MC transition matrix given the timeseries? Is there R function for doing that?
I'm struggling getting a greater than sign (>=) into a forestplot. The expression should embedded in some kind of matrix. This should be simple and straight forward but I just can't find the right formula, here's my debug code: library(rmeta) row_names <- matrix(list("variable a", expression(test >= 2))) test_data <- d...
I'm trying to minimize function f, firstly I was using fminsearch but it works long time, that's why now I use fminunc, but there is one problem: I need function gradient for acceleration. f = @(w) sum(log(1 + exp(-t .* (phis * w'))))/size(phis, 1) + coef * w*w'; options = optimset('Display', 'notify', 'MaxFunEvals', ...
Waiting line : M/M/3 with $\lambda = 24/u$ and $\mu = 10/u$ vs M/M/1 with $\lambda = 24/ u$ and $\mu = 30/u$ I'm doing some exercises on waiting line theory, now I've got a question to which I did not note an answer during class. Will the waiting line increase ? The question is : a company can do 24 jobs / hour at an ...
Prologue I have a matrix $N$ with dimensions $I\times J$, $I >> J$, and $n_{ij}$ is assumed to follow a Poisson distribution with mean $\lambda_{ij}$. Using a method (say NtoM), I reduce $N$ to a matrix $M$ with dimensions $I \times K$ (rows correspond to that of $N$, however columns are not representing the same quant...
I have data for the population of a number of different fish, sampled over a period of about 5 years, but in a very irregular pattern. Sometimes there are months between samples, sometimes there are several samples in one month. There are also many 0 counts How to deal with such data? I can graph it easily enough in ...
I'm looking for a R package to compute sample size for the differences of two proportions via confidence inetrval (CI). Note that there are several methods to compute CI for the difference in proportions, and for some of these methods one can compute sample size with pencil and paper, but I was wondering if there is pa...
I have 4 sample pairs, let's say (x1, y1),...,(x4, y4). What is the minimum sample size for a paired t-test? Which assumption should I check for paired t-test? If my data is non-normal, what is an alternative non-parametric test?
Formulating a mathematical model for a problem is the one of the most subjective aspects of statistics, but also one of the most important. What are the best references dealing with this crucial but often underlooked topic? And which famous statistician said something along the lines of, "Let the data guide the model...
I am trying to understand what statistical measures I can use to compare three groups having varying populations to understand which group is bad (highest probability of death or most vulnerable or weakest or whatever measure of strength is suitable) and which group is good. Total Population ------------------ Group A...
Say I have fitted a model using proc reg data = data; model a = b; run; How do I test if the coefficient of b is, say, less than 1?
The aim is to estimate an error on a stochastic event rate dynamically. This Question points in the same direction, I am interested in a theoretical extension. I read out the event counter second-wise, every black $1$ is a counted event (new events over time, see the plot below). During the measurement I am estimating...
In social science it is comon to use sample weight to post adjust the sample so that it fits to a given basci population. There are algorithms to calculate how many cases you need to have a representive sample of the population. But often we would like to analyse a bit deeper than just the sample as a whole e.g. male v...
I see a similarity between a problem I'm working on and Linear (or Quadratic) Discriminant Analysis when the sample size is smaller than $p+1$. I'm interested in theory bounding the generalization error of either classifier when the data can be assumed to be dense (i.e. all of the data parameters are potentially inform...
For my microsimulation, I want to use R to predict values and draw a random sample based on this prediction. To clarify my point: I want to simulate the number of chronic conditions people suffer from ($y_t$) at a certain point in time. I have a few waves of panel data available to estimate a relation between age, sex,...
Model: A vector $X=(X_1, X_2, X_3)$ that follows a trinomial distribution with parameters $p=1/3$ and $n$. (I have a coin with three sides $S1$, $S2$, $S3$). I flip the coin $n$ times. The coin has a probability $p=1/3$ to be flipped to the side $S1$, and similarly with $S2$ and $S3$. $X_1$ counts the number of times t...
Could you suggest more recent reviews or book on the methods for handling missing data (i.e. multiple imputation)? I want to know the challenges in this field.
I have 9 categories of response variable, and facing interpretation problems. Could I use this ordinal data as continuous data? If not then please refer me to some example with more than 5 categories. Thanks!
My understanding is that a hazard ratio from a Cox proportional hazards model compares the effect on the hazard rate of a given factor to a reference group. How would you report that to an audience that doesn't know statistics? Let's try to phrase an example. Say we enroll people in a study of how long before they buy...
Mathematics and Statistics are quite far behind in my educational curriculum, and yet now I seem to need them again, so this set of questions is very basic I suppose: What is a trend line? What various types of trend lines are there? And what are their respective use or relevance? Background: I'm working on a thesis an...
My understanding is that a hazard ratio from a Cox proportional hazards model compares the effect on the hazard rate of a given factor to a reference group. Does that actual group have to exist in the data? Say we enroll people in a study of how long before they buy a couch. We right-censor at 3 years. For this exampl...
As science must be reproducible, by definition, there is increasing recognition that data and code are an essential component of the reproduciblity, as discussed by the Yale Roundtable for data and code sharing. In reviewing a manuscript for a journal that does not require data and code sharing, can I request that the ...
I'm working on a couple of problems where I use pseudo-likelihood (a.k.a. composite likelihood) as an estimation method since full maximum likelihood is not feasible. To give some background without getting into very specific details, in both projects the data are iid samples of clustered binary data such that there ar...
Suppose I have a multivariate predictive distribution (dimension N). The distribution cannot be described in closed form with a mu vector and associated covariance matrix. However, I can sample from the distribution various scenarios with associated probabilities. One can imagine sampling 100,000 scenarios to construc...
Let's say I build a Generalized Least Squares model. I follow the standard procedure and first estimate a LM model. Then I create an error-response covariance matrix based on the residuals of this model. Now I build an LM model again only this time I specify weights based on the error-response covariance matrix. Now su...
I have a regression where I am trying to predict Y, using several variables. My variables are A, B, C. I'm using R for my analysis. My equation is as follows: mod <-lm( log(Y/B) ~ log(A/B) + log(A/C), data = dataframe) and a summary of the model is as follows: Coefficients: Estimate Std. Error...
I've poked around a bit in the Cross Validated archives and haven't seemed to find an answer to my question. My question is the following: Wikipedia gives three assumptions that need to hold for the Wilcoxon signed rank test (slightly modified for my questions): Let Zi = Xi-Yi for i=1,...,n. The differences Zi are ass...
Anybody have any experience with software (preferably free, preferably open source) that will take an image of data plotted on cartesian coordinates (a standard, everyday plot) and extract the coordinates of the points plotted on the graph? Essentially, this is a data-mining problem and a reverse data-visualization pro...
I am wondering is there any straight forward approach to convert a Gauss-Markov process, i.e., a First order autoregressive process with i.i.d. Gaussian input, with the covariance matrix $K=Toeplitz(1, \rho, \rho^2, \ldots, \rho^{N-1})$ where $0 \leq \rho < 1$ is the normalized correlation coefficient, to i.i.d. Gaussi...
How can one easily and quickly grasp the idea of Bayesian statistics and modelling? I can understand the Bayesian theorem on conditional probabilities, I understand how frequentist statistics works (test statistics, p-values, hypothesis testing...), I understand some ideas of Bayesian statistics, but how does Bayesian ...
Here is the structure of my data.frames: > str(c) 'data.frame': 21633 obs. of 20 variables: $ Trade : num 7e+12 7e+12 7e+12 7e+12 7e+12 ... $ New : Factor w/ 2 levels "N","Y": 1 1 1 1 1 1 1 1 1 1 ... $ Amended : Factor w/ 2 levels "N","Y": 1 1 1 1 1 1 1 1 1 1 ... $ Unwound : ...
I have a dataset with four within-subject conditions. Participants gave binary answers to 8 questions in each condition, and these were averaged to form a proportion for each condition. I would like to compare the mean proportions of people choosing a particular answer between conditions. For example 80% chose a partic...
When performing model validation and we are dropping the least significant explanatory variables until we find the optimum model where all remaining variables are significant, how does one go about dropping a particular "unimportant level" within a nominal variable? In my output below I have run a Neg. bin. GLM inorder...
I am facing the following dilemma. I am aware of how to handle the one-sided Chi-squared distribution, but I am falling victim to how to handle degrees of freedom. Let me clarify with an example what I mean. I have the following obseverd and expected values: [Observed Data] #Periods CountryI CountryII Count...
I'm in the process of designing a system. So basically, every day users on my site rack up points based on their activity on my website. So whatever they do on my website, they rack up points. So on 8/3, a user might do multiple things on my website so that they rack up 10 points. Every day, I figure out the number of...
Just want to know the ways to remove skewness from the skewed population. I am working on logistic regression (in the insurance domain) for finding out the repurchase propensity of existing users. Income data is right skewed. Will it cause any problem for runing logistic regression? If yes then how to remove it (dele...
I need to make inference about a positive parameter $p$. To acomodate the positiveness I reparametrized $p=\exp(q)$. Using MLE routine I computed point estimate and s.e for $q$. The invariance property of the MLE directly gives me a point estimate for $p$, but I am not sure how to compute s.e for $p$. Thank in advance ...
We're planning a case-control study, in which we assign subjects to be either cases or controls (based on normal vs low birth weight) and then measure a continuous outcome variable (% body fat) subsequently. Can anyone point me towards a method for calculating how many cases vs controls we will need. We have an idea o...
I'm wondering if anybody knows of a compendium of cross-validation techniques with a discussion of the differences between them and a guide on when to use each of them. Wikipedia has a list of the most common techniques, but I'm curious if there are other techniques, and if there are any taxonomies for them. For exampl...
I have data on results of surgical operations: date of operation (in YYYY-MM-DD format) result of operation (0 for successful operation, 1 for unsuccessful operation) Date is usually used only for case ordering. I need to plot a learning curve. (I had found that the resulting curve called cumulative average.) x s...
I have information on the distributions of anthropometric dimensions (like shoulder span) for children of different ages. For each age and dimension, I have mean, standard deviation. (I also have eight quantiles, but I don't think I'll be able to get what I want from them.) For each dimension, I would like to estimate ...
Has anyone attempted time series prediction using support vector regression? I understand support vector machines and partially understand support vector regression, but I don't understand how they can be used to model time series, especially multivariate time series. I've tried to read a few papers, but they are too ...
Suppose $X$ is a random variable with pdf $f_X(x)$. Then the random variable $Y=X^2$ has the pdf $$f_Y(y)=\begin{cases}\frac{1}{2\sqrt{y}}\left(f_X(\sqrt{y})+f_X(-\sqrt{y})\right) & y \ge 0 \\ 0 & y \lt 0\end{cases}$$ I understand the calculus behind this. But I'm trying to think of a way to explain it to someone who...
Cross-posted from Biostar I'm stuck in a step for calculating Normalized intensity ratio for i-TRAQ reporter ions, used in quantitative proteomics. Here's the worked out example of how it's calculated and the description is as follows. Medain adjusted normalization is used in quantitative proteomics. The reporter ion...
Suppose my CSV file has time and various columns of data vs time. I want to be able to automate plotting. To a file at least; multiple formats or to the screen as well is a plus. There will be lots of plots. Multiple plots on same axes, e.g. like a spreadsheet scatterplot with multiple columns. Changing the plot com...
My multiple regression analysis model has a statistically significant F value however all beta values are statistically non-significant. All the regression assumptions are met. No multicollinearity was found. Correlations among all predictors are all less than 0.60. What else might be the cause of the insignificant p...
Question I have a vector of data, and I want to test if it came from a normal distribution with mean zero and unknown variance. Do you know if there is matlab function or simple script for this? If you don't know anything matlab specific, then a name and reference for the specific test is fine and I will just implement...
Assume that I have decomposed a data set using Symlet Wavelet with six levels. How can I estimate the approximate frequency interval of each level? That would be great if you consider your answer in the Mathematica environment. If the above dataset describes turbulent velocity field, how I can decide up to which level...
I have some physiological measurements which consist of 4 events measured in a "during task" condition and preceded and followed by a rest period. I want to test that the data points immediately preceding the 4 events do not differ from the rest baseline, calculated as the average of the values in the start and end res...
I am currently reading about fractional integration in the context of error correction models. Does anyone know of a package in R that has a function for Sowells maximum likelihood estimator of d?
I know that correlation of lab to lab test results for clotting times of patients on anticoagulation treatment is not great. Clotting times are measured in INR (international normalized ratio) and a research paper I am reading asserts For the larger hospital laboratories analysing external controls with INR > 2, th...
I think I understand how the fundamentals of bootstrapping work, but I'm not sure I understand how I can use bootstrapping for model selection or to avoid overfitting. For model selection, for example, would you just choose the model that yields the lowest error (maybe variance?) across its bootstrap samples? Are th...
I was wondering if there is an R package to perform incidence density sampling for a case-control design. That is, for matching in a case-control design; accounting for multiple matching covariates.
Suppose that, in a study of 15 subjects, the response variable (res) is modeled with two explanatory variables, one (level) is categorical with 5 levels and the other (response time: RT) is continuous. With lmer in the lme4 package of R, I have: fm1 <- lmer(res ~ level * RT + (level-1 \| subject), data=mydata) anova(fm...
Given a set of points (x,y), I would like to create K clusters of these points similar to the k-means algorithm. The difference is that I would like to define the number of points contained in a cluster, in my situation I would like them to all be equal. For example, take 30 points and put them into 3 sets of 10 points...
Using the following code, I tried to draw four plots on a graph in R. I am not happy with the figure because there is a lot of space between the plots, therefore the width of the plots are not sufficient enough to analyze the plots. Could someone help me to produce a nice graph having four plots? How can I keep x-a...
I have a tobit model the looks like Y = cons + B*(X) + error. This model is estimated twice on two different samples. I want to be able to test if, say, B is different across the two models (the sample A model vs the sample B model). I have done this before for logit models using two approaches that yielded the same...
I'm considering circular regression and elliptic regression on a computational and conceptual basis. If we fit an ellipse to our data then we deal with the principal components as reference for the main and for the secondary axis; we set the lengthes of the axes according to the sqrt of the eigenvalues. The idea b...
I read in the book The basics of S and S-plus that "A:B" functions as "Interaction between A and B". However, in other book I read "There is never an interaction effect for two factors when one is nested within the other". But aov(y~a/b) would have the same results as aov(y~a+a:b). So it seems to me a:b could mean i...
Let $X$ be an $n \times l$ matrix, and $F$ an $n \times p$ matrix, with the rows of $X$ and $F$ drawn i.i.d. from multivariate Gaussians. (The independence applies to rows: the $X$ and $F$ may be correlated.) Let $\Sigma_X, \Sigma_F, \Sigma_{XF}$ be the covariances of the two Gaussians and the covariance of the two Gau...
I know that with fixed breakpoints (for the x variable), piecewise linear regression is easy and linear. However, for a variety of reasons, I would like to fix the breakpoints for the y variables. One reason is that there are natural candidates for the breaks for the y variable, but I have no clue about the x. Becau...
I am using R for a simple hierarchical clustering method for finding protein sequence similarities. I already have a distance matrix computed. I am using the hclust method to run it (thus I dont want to use dist method). Could anyone tell me what format does my distance matrix need to be for hclust to run? I used the r...
What is the default significance level for the chisq.test() function in R? I have been trying to figure that one out but couldn't. The documentation seems really poor on these specifications.
I have run the following logistic regression: glm(formula = DecisionasReceiver ~ L1 + L2 + L3, family = binomial("logit"), data = lue) where L1 L2 and L3 code for differences in condition of no.GREEN. L1: 1,-1,0,0 : is there a difference in DecisionasReceiver as no.GREEN changes from 1 to 2? L2: 0,1,-1,0: is there ...
I'm check the residuals of a linear regression with Zivot & Andrews unit root test. This is the plot: And the results are: > z <- ur.za(resid(mod), model='intercept') > summary(z) ################################ # Zivot-Andrews Unit Root Test # ################################ Call: lm(formula = testmat...
I have data on a dependent variable y and an explanatory one, x, and want to find out if there is a non-linear relationship between theses by running regressions where the data is divided in quartiles from the lowest to the highest value of x. So for example, what is the slope of x when x lies in the first quartile, sa...
This is something I've always wondered. Consider the Kinect. It takes its 3d image data and manages to recognize that a human is contained at a given boundary. Are these types of technologies exclusively machine-learning driven?
Is there a name for this data visualization? It's almost like half a pie chart. In this case, it was animated like a speedometer you would see on a car dashboard; the divider (the needle) pointed left fully horizontal at first.
Is it possible to specify that one parameter must be larger than another parameter in an nls call in my R script? Here's my nls call: fit <- nls(y ~ ifelse(g, m1 * (x - x0) + y0, m2 * (x - x0) + y0), start = c(m1 = -1, m2 = 1, y0 = 0, x0 = split), algorithm = "port", lower = c(m1 = -...
I'm using KPSS unit root test with a vector of 700 observations. The test return a p-value of 0.1 (so it seems stationary), but if I reverse the vector the KPSS test tells me the vector is not stationary. With "reverse" I mean 1, 2, 3, 4 becomes 4, 3, 2, 1. (Obviously those are not the numbers I have.) So the questions...
I have a very strange problem. I don't think it's a bug because I've tried it a few ways with similar results. I have three sets of data that are all related to each other. When I make density plots of them individually (with the sm package), like so: sm.density(sim$V2) I get this curve: And the other two curves loo...
I am trying to interpret the coefficients on the year dummies in an ordered probit regression. My data is a panel with 20 years. I have included 19 year dummies with the exclusion of the first year. This enables me to interpret the coefficients of each dummy in relation to the year that was dropped. Now I have to inclu...
I'm currently on a project where I basically need, like we all do, to understand how output $y$ is related to input $x$. The particularity here is that data $(y,x)$ is given to me one piece at a time, so I want to update my analysis every time I receive a new $(y,x)$. I believe this is called "on-line" processing, as o...
I have measured the following variables on 200 individuals. Independent variables: Measures of personality Extraversion Conscientiousness Leader Member Exchange (LMX) quality Dependent variable Measures of sales performance Sales achieved Repeat sales Should I use Multiple regression? I seem to have 3 IVs a...
In four different experiments, I ran two programs A and B with different parameter setteings a, b, and c. Target variable is kind of time -- lower Target value means higher performance. I know the reasons why program A is better than B or vice-versa. Currently I am representing this data as tables in my latex document....
I am beginner to data mining. This is my understanding, regression is used to predict continuous values. It is a type of classification. Classification is Supervised and Clustering is unsupervised. In classification we have predefined classes, whereas in clustering there are no classes defined. What does this exactly m...
How does one prove that a separating hyper-plane that can be represented as a linear combination of the training samples exists for a linearly separable pattern? Although, it looks pretty obvious physically, I was interested to know if it could be proved mathematically.
I'm currently working on my thesis, more specifically I'm analyzing some data collected from researchers about the project's they're working on. In the end, I have performed a multiple linear regression to verify which determinants (budget, team size,...) significantly influence the external impact of a research projec...
Are there any tools for remote collaboration in prediction or machine learning settings? I am looking for a computing environment that includes appropriate source control, keeps track of how different datasets are being matched to different algorithms, and facilitates blending of various predictions. What tools would...

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