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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R: how to do statistical inference on multiple dependent and independent variables?

In the past I've run separate multiple regression models for many correlated independent variables and one dependent variable. For this I've been using the R package multtest ...
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10 views

How to calculate Focused Information Criterion in R for Cox proportional hazards models? [migrated]

I am utilising R to perform a multivariate Cox survival regression for a research project. As I have many possible interchangeable variables in the model, I was wondering how to apply the Focused ...
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12 views

Inference in bivariate continuous distributions

We have two nodes in different positions, which are represented by two random variables X,Y, with two prior bivariate continuous distributions, p_X , p_Y. f(X,Y,U,V) is a constraint on both ...
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18 views

Double Repeated Measures in SAS

Given: The data is balanced; there are no missing values. main effects A 2 levels urban, rurual F 17 families- 10 urban, 7 rural repeated measures ...
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1answer
24 views

Identities in a VAR model

I am working on a VAR model where one of the equations is an identity. For example: $$ \begin{cases} A_t = \alpha_{11} + \alpha_{12} A_{t-1} + \alpha_{13} B_{t-1} + \alpha_{14} C_t + ...
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85 views

A Book for Multiple Regression and Multivariate analysis

I have done a course in Simple Linear Regression and I am aware of linear statistical models (I follow the book by C.R. Rao). Keeping this background in mind, please suggest some good book(s) for ...
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22 views

Clustering MVT response data by audience

We are doing multivariate testing 4 possible values for each of 3 variables on a landing page: (a) offer presented, (b) product claim message displayed and (c) image used. So, 12 dummy variables, 64 ...
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15 views

Analyzing Social Behavior in Bats

I had a question about what might be the best way to approach one of my datasets. I had been using one method, but a recent talk with one of my professors made me think that perhaps it wasn't the best ...
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24 views

Can I compare Mahalanobis distances from different distributions?

I have a multivariate dataset representing multiple locations, each of which has a set of reference observations and a single test observation. For each location, I would like to measure how anomalous ...
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22 views

Adjusting Monte Carlo estimates to generate correct even moments - improving on antitthetic draws

If I want to generate a matrix 10,000 (row) samples of 3 uniform (uncorrelated) variables it is trivial to use antithetic draws to ensure the odd moments such as the mean equal their "true" value. ...
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11 views

Chi square test of independence with multivariate nominal data

I used a list-type open-ended question to collect responses, in which respondents can list up to 6 items. After coding the items, I have the multivariate nominal data. I want to check if my IV ...
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26 views

Using Non-Euclidean Distance Matrix in Multi-Dimensional Scaling

I'm trying to use a non-euclidean distance matrix in MDS. Specifically, I'm using cmdscale in R. The resulting eigen vector appears to have huge negative values. From what I've read it appears that ...
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9 views

VARMA with t-student innovations

I'm wondering if there is a possibility to estimate VARMA model with t-student innovations in R. I found package MTS, but all models here seem to be estimated assuming multivariate normal ...
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1answer
61 views

Whitening transformation for skewness?

Let $X$ be an $(m,n)$-matrix interpreted as a two dimensional array with each column representing $m$ samples from a random variable, with known covariance matrx $M$ and mean equal to $0$, it is ...
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0answers
23 views

Goodness of fit for multi dimensional scaling

What is considered to be an acceptable value for goodness-of-fit in multi-dimensional scaling (MDS). I tried to run an MDS analysis on my data with four dimensions in R. The goodness of fit comes ...
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16 views

Multivariate Gaussian, rearranging means

Looking through the the matrix cookbook, a collection of matrix identities, I came across this one called "rearranging means" in the multivariate Normal distribution (Sec. 8.1.5 or Eq. #356, also ...
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7 views

Generate Correlated Outcomes Between Groups

For a simulation study, I want to generate an outcome (Y) for 3 groups (Control, Treatment1, and Treatment1). The outcomes for Control and Treatment1 are correlated by .50; the outcomes for Treatment1 ...
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21 views

Non parametric version of Hotelling's $T^2$

Is there a non parametric version for Hotelling's $T^2$ test? Namely, the one group test for location (not the two group).
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16 views

evaluate the similarity between two time series

I have two time series, $\mathcal{T}_1$ and $\mathcal{T}_2$, each time series is of two dimensional. One time series is collected from two sensors (SA, SB), and the other is collected from other ...
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10 views

Volatility, Spillover and Shocked

What are major difference between Volatility, Spillover and Shocked in context of Multivariate GARCH Financial modeling? or What is difference between Multivariate GARCH models of volatility, ...
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9 views

Test of Ordered, Multivariate Correlation

This should be a simple question: I have an ordered series for which I have measured three variables. Some appear to have positive correlations and some have negative correlations. Here's an example ...
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2answers
50 views

Tweedie distribution GLM for manyany() in {mvabund} package

My data follow a Tweedie distribution, and I'm working with multivariate abundances. So I'm trying to use the manyany() function in the ...
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21 views

How do I analyse data with one independent variable and two dependent variables? [on hold]

I am currently working on my research thesis and my topic is "Foreign Direct Investment (FDI) and Capital Structure in Power Projects". From this topic, I have one independent variable (i.e., FDI), ...
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1answer
50 views

How to interpret this PCA biplot?

I am approaching PCA analysis for the first time, and have difficulties on interpreting the results. This is my biplot (produced by Matlab's functions pca and ...
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22 views

Binary outcome prediction based on multivariate time series in R

everyone! I have some monitoring dataset for 90 patients. It consists of about 10 parameters (continuous variables) that were recorded each 1 minute 3-4 days for every patient. I know the binary ...
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9 views

What models allow the study of the relation between a set of response variables and a set of covariates?

A first technique that comes to mind is Canonical Correlation Analysis. Bayesian Networks and other graphical models, I guess, can also be used to analyse such things. Any else that I should be aware ...
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51 views

Find an unbiased estimator of $\Sigma^{-1}$

Suppose $ X_1,\dots, X_n$ be a random sample from $N_p(\mu, \Sigma), \Sigma > 0$. Find an unbiased estimator of $\Sigma^{-1}$. I know the unbiased estimator of $\Sigma$ is $\dfrac{1}{n-1} ...
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Proving the given quadratic form is chi-squared $k$

Suppose $\underline{X}$ is an $m$-dimensional vector following multivariate Normal distribution i.e. $\underline{X}$~$N_m(\underline{\mu},\Sigma)$ where $\Sigma$ is positive definite. Let $B$ be a ...
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26 views

Can I run a multivariate quasi-binomial analysis of proportion data?

I am trying to best analyse a set of foraging ecology data with >10 behaviour categories (DVs) and 3 levels of IV (season, sex, age). The time which an animal spent engaged in a behaviour was recorded ...
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11 views

Multivariate Mahalanobis Distance Vector Normalization

I have a vector including different variables with different scales. For instance ''a'' presents ''dollar value'' in billions.''b'' is a ratio, presents value divided by quantity and it ranges 0 to 1 ...
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1answer
60 views

LDA, PCA and k-means: how are they related?

I am trying to understand how linear discriminant analysis (LDA) is related to principal component analysis (PCA) and k-means clustering method. As an example, here is a comparison between PCA and ...
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33 views

Statistical meanings of some matrix vector operations

These questions may be too elementary, but I'm new to statistics and just trying to grasp new concepts, so please be patient with me. Suppose I have data on a single variable, expressed as ${\bf{y}} ...
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17 views

Multivariate discrete distribution

Let $\mathbf{x}=(x_{1}, \dots, x_{m})$ be a vector of discrete variable; $x_{j} \in \mathbb{Z}^+$. Which distribution can I use over $\mathbf{x}$ that allows to have dependence between each couple ...
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A Conditional Probability Question

Assume we know $$p(w) \sim N(0, \Sigma)$$ $$p(e) \sim N(0, 0.01)$$ $$y=w^\intercal x$$ $$o = y + e$$ Where w/x/o/y/e are all vector How do we calculate the distribution of $$p(y|o,x)$$
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92 views

Variance estimation in a one-factor linear model

I was given a dataset (a mat file) of $100\: 000$ observations, each with $50$ dimensions (coordinates). Denote matrix $X$ a $50\times 100\:000$ matrix in which each column was generated according to: ...
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16 views

Conditional Probability in Multivariate Normal

Given a tri-variate Normal, the conditional probability of an element given others truncated information is Now if I know that the mean vector u is (-0.91,-1.31,-1.39) and R is ...
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26 views

Mulitvariate normal truncated conditional expectation

There is three-variable multivariate normal distribution. Denote 3 variables with $X_1$, $X_2$, $X_3$. Let $\mu_i$ be means, and $\sigma_i^2$ variances of respective variables, and let $\Sigma$ be ...
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Logistic regression and IV that depends on another IV value

I am modeling the effect of aspects of house change and marital status change on a (binomial) DV. Each observation in my data is a 3-year period in someone's life. Thus, for family change, I have a ...
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10 views

Adding a new factor to an existing factor model for stock returns

Let's assume I have a three factor model of stock returns (Cross-sectional model): $R_i = \alpha + \beta_{1,i} X_1 + \beta_{2,i} X_2 + \beta_{3,i} X_3 + \epsilon_i$ for $i =1,..,N.$ where ...
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1answer
17 views

Multivariate analysis - creating a classification index

I have the following problem I would like to tackle, I thought it would be useful to get some help for determining the best possible workflow. I have data for some 200 biological observations. 1 of ...
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57 views

Mahalanobis distance

I have two vectors. I want to evaluate Mahalanobis distance between them. None of software packages are able to evaluate the distance producing a warning that the number of rows should be greater than ...
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1answer
58 views

Simple Multivariate Bayesian Method in Python

I am trying to follow the Bayesian method described in this text. The python notebook goes through the example of creating two Poisson functions describing a change in SMS frequency at some point tau. ...
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1answer
22 views

Can I use HCA-Ward's cluster-centers to run a K-means including a new item, to see to which cluster is more similar to?

Thank you for reading my question. I have an archaeological case-study, that we can call "Site1", that I want to compare with 9 others "Sites" studied by other scholars. For all of them I have 8 ...
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12 views

Mixed within-between ANOVA or MANOVA? [duplicate]

I am doing a research, the instrument of which is an English proficiency test that consists of two parts: one part is related to the test-takers' field of study and one part is unrelated. my ...
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46 views

Meta analysis of multiple-treatment-multiple-endpoint studies

I have read some things about Meta Analyses for stochastically dependent effect size (e.g. Gleser and Olkin (2009) in The handbook of research synthesis and meta-analysis (2nd ed.). I understood ...
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1answer
40 views

Does MCD estimator suffers from swamping effect?

If there are multiple outliers in the data set, the Mahalanobis distance suffers from masking and swamping effects. In order to rectify this problem, robust estimation of location and scale, such as ...
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29 views

How to calculate the conditional probability $p([x,y]|x=y)$?

How do you find conditional probability in a Multivariate Normal subject to the conditions of relationships in the individual variables? To write it mathematically, Given the fact that, How can we ...
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13 views

How to evaluate differences in spp richness between two comunities

I am trying to assess if there is a difference between ne number of species between two communities, that share some species. any suggestions??? Maybe a multivariate analysis??
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30 views

what are the moments of a multivariate distribution?

For a random variable $X \sim f(x)$, the n'th moment is defined to be $E_f[X^n]$. But for a multivariate distribution, $X$ is a vector so this definition doesn't make sense since you can't raise a ...
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31 views

Help with cluster analysis. Is this possible? [duplicate]

I'm working with the productivity of various government documents. In my data I have two variables (annual frequency and time of resolution) and each document gets its position in a Cartesian plane ...