# Tagged Questions

Multivariate refers to analyses where there is >1 response / dependent variable of interest in the statistical analysis. This can be contrasted w/ *multivariable* analyses, which typically implies >1 predictor / independent variable.

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### Expression for Sum of Multivariate Gaussian Random Vectors

Consider two multidimensional random vectors $x$ and $z$ having Gaussian distributions $P(x)=N(x\mid\mu_x,\Sigma_x)$ and $P(z)=N(z\mid\mu_z,\Sigma_z)$, respectively, together with their sum $y=x+z$. ...
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### Problem with the formulation of a gaussian copula likelihood function

I recently got to hear about copulas which to me sounded like a nice tool to model relationships between variables. I decided to try to implement the likelihood function for a bivariate Gaussian ...
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### Interpreting standardized coefficients on a natural log response variable in OLS multiple regression

I am working on a housing problem in which I use dichotomous and ratio data to predict housing production (units constructed in a year-ratio) in a 17 year time period. At this time, I am using OLS and ...
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### A measure of overall variance from multivariate Gaussian

I am performing some regression task, where I try to discover the underlying multivariate Gaussians from a set of $n$, $p$-dimensional vectors. For example, given a split of the set into $S_i$ and ...
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### Fast multivariate unimodal density estimator

I have a sample $\boldsymbol{x}_i$ for $i$ in $1,\dots, n$, from a $d$ dimensional density $f(\boldsymbol{x})$ and I would like to estimate this unknown density. In addition I know that ...
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### Backward selection in a Cox regression model

My goal is to fit a cox regression model in SAS, for which I use the PROC PHREG statement. As I am still new to regression methods, I would appreciate a little of ...
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### Understanding Naive and Multivariate Gaussian Classifier

Thank you for checking this question out. I am trying to understand how to use the multivariate gaussian classifier. To introduce you better to my problem, I will show how currently I classify data. ...
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### Categorical vs Continuous Variable

I have two variables, one continuous and one categorical which I currently both use as predictor variables in a logistic regression model. Their relationship is shown in the following plot with the ...
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### Using ANOSIM to analyze randomized complete block design data?

I've used NMDS to explore data collected in a randomized block design, involving three treatments, each applied in 10 spatial unit blocks. Is it possible to use ANOSIM to test for hypotheses of ...
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### Statistical Distance Within Multivariate Distribution

Suppose you have some multivariate normal distribution $X \sim N(\mu,\Sigma)$. Is there a good way to calculate a measure of distance between an arbitrary $X_{i}$ and $X_{j}$ of $X$ (I suppose the ...
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### Nonlinear PCA‏ ( R package homals)

I'm using the NLPCA to reduce the dimensionality of nine variables (4 nominal / 3 ordinal /2 numeric) to obtain the object-scores to be used as dependent variable in a regression model. I'm using the ...
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### Diagnostic plot for assessing homogeneity of variance-covariance matrices

Is there a handy plot for comparing the variance-covariance matrices of two (or perhaps more) groups? An alternative to looking at lots of marginal plots, especially in the multivariate Normal case?
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### pdf of multivariate normal distribution

I have a question concerning some sentences in the book Structural Equations with Latent Variables (Bollen) at page 132 (bottom) and page 133 (top) regarding the pdf of the multivariate normal ...
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### Minimize a function with respect to a matrix

I have two sets of vectors, A and B. Vectors from set A live in an m-dimensional space, ...
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### How to prove independentness of marginal/conditional (?) posterior distributions?

This is a question about exercises 4.2 and 4.3 of Jim Albert’s “Bayesian Comptutation With R” (p. 82). Note that while this might be homework, in my case it is not. We are to prove that, given two ...
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### Smoothing 2D data

The data consist of optical spectra (light intensity against frequency) recorded at varying times. The points were acquired on a regular grid in x (time) , y (frequency). In order to analyse the time ...
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### Joint PDF change of variables

I now understand how to conduct a change of variables for a marginal PDF. Now, given two functions that define parameter's spatially: $C_A(x)$ and $C_B(x)$, is it possible to construct the Joint PDF, ...
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### Pre-truncation moments for truncated multivariate normal

Suppose the random variable $Y$ has a multivariate normal (MVN) distribution, and consider truncating $Y$ in some way to create $T$. Given $T$'s mean and covariance matrix, I'd like to obtain $Y$'s ...
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### Is it normal to obtain better (smaller) P values in multivariate analysis compared to bivariate one?

If a multivariate design controls for other predictors when calculating the effect of a predictor, shouldn't it give paler P values (less significant ones, or less vivid odds ratios)? I am seeing ...
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### Find the moment generating function

Find the moment generating function of $W$, when $W=X+2Y+4Z$. $~X,~Y,~Z$ are independent normal distributions $\mathcal N(1,4),~ \mathcal N(2,9) \text{ and }\mathcal N(3,16)$.
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### PCA and varimax references?

After doing PCA it is common that the first component describes the largest part of variability. This is important in i.e. study of body measurements where it is commonly known (Jolliffe, 2002) that ...
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### Dealing with 'Don't Know' answers for a categorical outcome variable

I have a survey data with categorical outcome variable (yes, no, don't know) which reflects the acceptance of some situation by respondents. My concern is how to deal with Don't know answers, I really ...
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### Two IVs (schools) and 3 IVs (grade levels in each) where there are 2 DVs (math and reading scores)

Is MANOVA the correct test? I am looking at 3 grade levels in each of the two middle schools. I want to compare the standardized scores (reading and math) of students in each grade level to the same ...
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### Errors in Variables and Deming's multivariate regression: Assumptions

There has been extensive literature that puts forth a standard set of assumptions for the Ordinary Least Squares (OLS) estimator. I am very interested in working around the two classical problems of ...
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### How should I analyze a data set with 1 IV and 2DVs (all scale variables)?

Hello wonderful statisticians, I'm writing a proposal for a dissertation where I'd like to look at whether heart rate can predict 1) narrative coherence (as judged on a scale - but could also be ...
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### PCs scores from Correlation and Covariance matrices through matrix computations and prcomp

I'm want to get PCs scores through matrix approach. My calculated PCs scores for correlation matrix matches with prcomp results but the PCs scores for covariance ...
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### geographic distance and mahalanobis distance

I am trying to match individuals based on monthly consumption and geographic consumption in a dense metro area. Essentially I want to create treatment and control pairs with the having both geo ...
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### Is there a multivariate version of logistic regression?

Based on readings with logistic regression, it appears that you could use this analysis to make predictions about categorical variables. Does logistic regression allow you to predict multiple ...
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### Interpretation of MDS factor plot

Suppose I run Multidimensional Scaling and I got the resulting plot. Can anybody suggest me how to interpret the plot. Please find one of my result below. Here I've 5 concepts which I run the MDS ...
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### Simulated single value based on multiple chains in RJAGS

I am using RJAGS to simulate the posterior distribution of event that a certain candidate will win the presidential election. I need to find the actual percentage that one of the candidates will have. ...
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### How to find quantiles for multivariate data using R?

Quantile for a single variable is easy to implement in R. However, it is not an easy task to quantile for multivariate data. There are several papers have been proposed to quantile for multivariate ...
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### Automatic outlier detection in R

Our model processes millions of multivariate observations; manual outlier detection is impractical. I am looking for a method of automatic outlier detection. I have been trying to use R package ...
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### Sample size calculation for multivariate problems

I am interested in multivariate investigations. I have been trying to learn about designing such experiments where there is one dependent variable (a class/group) and many independent variables that ...
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### Predict 2 responses from two co-variates

I'm not quite sure how I should fit a model that has two responses. The data consists of target (x,y) co-ordinates and actual (x,y) co-ordinates. I would like to fit a model to predict a new set of ...
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### Are Product KDEs proper density functions?

I have a fairly simple question about (multivariate) Kernel Density Estimators, but I somehow don't seem to find the answer anywhere: are these estimators supposed to specify a proper probability ...
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### Ways to measure distance from multivariate Gaussian (Mahalanobis distance)

I have a cluster of p-dimensional points and given a new p-dimensional point $x$ I want to determine whether or not it is likely to belong to this cluster. The cluster is made up of $n$ ...