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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PLS Regression and collinearity

From what i know PLS regression is used when there is more variables than observations and when there exist multicollinearity between the independent variables. I have data for a regression model that ...
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13 views

group differences [on hold]

Assume that you have been provided with data on 12 conceptually distinct variables that are moderately correlated with one another at the empirical level. The data are from students in four different ...
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22 views

Importance of multivariate normality assumption for BIC-like sparse model selection inference with PCA

I am reading a paper for robust, sparse PCA in which they propose a BIC-like criterion for selecting the appropriate value of the sparsity parameter $\lambda$. They define this as: ...
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24 views

Difference-in-difference more than two periods [closed]

I try to use a difference-in-difference design in my study. But I have three periods. So I would like to know how I could run my difference-in-difference analysis on Stata with more than two periods.
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1answer
32 views

Learning multivariate techniques to analyze the gut microbiome

I would like to start learning some of the basics regarding data processing and analysis of microbiome data using R. Can anyone recommend a tutorial on some of the core/basic approaches that also ...
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11 views

Homogeneity of Variance, 2 Way Completely Crossed Design

I am looking for some advice as to how I might handle having an unfavorable Levene's test outcome, that is to say a highly significant value. DOE Various containers with water were microwaved for ...
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15 views

The distribution of sample means conditioned on the sample correlation coefficient

Consider the $(X_{i1}, X_{i2}), i=1, \ldots,n $, where $X_{i1}, X_{i2}$ follow bivariate normal distribution with correlation $\rho$. Define the sample means as $\bar X_j= \dfrac{1}{n}\sum_{i=1}^n ...
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18 views

Limited Dependent Variable Analysis

I am using a dependent variable that is the average of a rating. Customers use a one to ten scale regarding how much they liked a meal. I have the average rating (each meal is rated by 22 to 129 ...
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18 views

Statistics for catch of tuna longline

I have study on catch for tuna longline. In here I have 3 independent variables (number of hooks, length of branch line & baits) and 3 dependent variables (catch of tuna, catch of marlin & ...
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31 views

multivariate distributions bounded on [0,1] where parameters can be solved for from known mode

I need some kind of multivariate distribution which has the following properties support is $x_1,$ $x_2$, ..., $x_K$ where all $x_i \in [0,1]$ Though not required it is true that elements of the ...
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16 views

Extreme value distribution for multivariate normal

I have a series of data sets. Each data set represents a measurement in 3D space relative to a global origin. I want to model the extreme values of my data. If I were to calculate the extreme radius ...
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1answer
25 views

Approximation of Pr(X > a), with X a multivariate normal rv

Let $X = (X_1, ..., X_p)$ a random variable with a $N(\mu, \Sigma)$ distribution. $$ $$ $$ \Pr(X_1 > a_1, ..., X_p > a_p) \\ =\int_{a_1}^\infty ... \int_{a_p}^\infty (2\pi)^{-p/2} ...
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16 views

Multivariate multiple regression in SAS [migrated]

Suppose I want perform a multivariate multiple regression analysis and test (using a single test) the hypothesis, that the regression parameters for two explanatory variables are 0. In ...
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40 views

Visualizing many left-skewed distributions

I have a series of left-skewed/heavy tailed distributions that I would like to show. There are 42 distributions across three factors (labeled as A, ...
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20 views

PSD estimation from multivariate data

Assume a multivariate dataset $\mathbf{x} = (x_1, ..., x_n)$ where $x_{i}$ are for example different sensors. Now, there are several techniques (e.g. Welch's method) to calculate the power spectrum of ...
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1answer
82 views

Are the marginal distributions of a multivariate distribution the corresponding univariate distributions?

Are the marginal distributions of a multivariate distribution necessarily the corresponding univariate distributions? For example: Every marginal distribution of a multivariate normal distribution ...
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39 views

How to analyse data with multiple dependent and independent variables

I have two dependent variables, Abundance and Richness of moths, and 12 independent climate variables. These are ...
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23 views

extract residuals from adonis function in vegan

I am using the adonis function in the vegan package to determine effects of different environmental factors in forest plant community composition in different regions. I would like to first use adonis ...
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4answers
66 views

Statistical videos to learn regression analysis and multivariate analysis?

I'm having a tough time to understand concepts of Regression Analysis and Multivariate Analysis. I'm following the books of Johnston and Anderson, but some video lectures would help me learn it ...
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26 views

Is the multivariate Gauss the only pdf incorporating covariances?

I am wondering whether there is another probability density function known to literature which is similar to the multivariate normal distribution in the respect that the pdf incorporates the ...
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14 views

How to find probability distribution of a multi-attribute datapoint in a dataset

I have a dataset with certain number of multi-attribute tuples. Each of the attribute values is a continuous random variable. I want to model each tuple (rather each attribute of the tuple) by a ...
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34 views

Keywords to find academic lectures on multivariate time series analysis on youtube

If I search for "HOTT homotopy type theory" on youtube, I find numerous (advanced/state-of-the art) academic lectures on the topic. For instance the following lectures are found on youtube: ...
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2answers
63 views

If x = y*y, and you know var(y), var(z), and cov(y,z), do I know cov(x,z)?

If I know that x = y*y, and I know a whole of statistics pertaining to y, such as the variance and its covariance with other variables, can I analytically solve for the variance and covariance of x? ...
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53 views

Principal Components, Canonical Correlation and Eigenvalue problems

It is well known that the solution to the optimization problems proposed in Principal Components and Canonical Correlation Analysis are given by the solution to eigenvalue problems and generalized ...
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2answers
65 views

Principal Components and Noise

When doing principal components it is intuitively clear that noise accumulates more towards the last components. What would be the formal explanation of how and why this happens?
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1answer
44 views

Binary logistic regression with 3 similar outcomes

I was given three binary dependent variables, which are the following: ...
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79 views

Multivariate logistic distribution

The normal distribution can be generalized into the multivariate normal distribution. Can the logistic distribution also be generalized into a similar multivariate distribution? Is there a ...
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69 views

What exactly is the vector fitting on a nMDS plot telling me about community structure?

I think I have a basic misunderstanding of what the vectors typically plotted over an nMDS (non Metric Multidimensional Scaling) plot are telling me. I understand the direction of the vectors point to ...
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81 views

Fitting a multilevel multivariate model in R with `glmer`

Background I have a large dataset that contains three binary outcomes for individuals belonging to groups. I am interested in jointly modeling these binary outcomes because I have reason to believe ...
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41 views

Multivariate Beta distribution (no Dirichlet!)

What is a multidimensional generalization of the Beta distribution, in compliance with the following specification? I am not looking for the Dirichlet distribution. I am looking for a generalization ...
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91 views

Estimating variance from sequence of random variable

Given $X\sim N(0,\Omega)$. Suppose that we can construct a sequence $\{X_n\}$ based on the observation such that $\{X_n\}\to X$ in distribution. My problem is to estimate $\Omega$ consistently using ...
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51 views

Is this multivariate normal? 2 time series linked by a common process

Summary: Consider a scenario where you observe the inputs ($X$) to and outputs ($Y$) from a process ($B$). If I have a model describing how $X$ evolves over time, and a similar model for $Y$, how do I ...
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1answer
94 views

dimension reduction of discrete numerical data

I have a bivariate discrete numerical dataset and would like to reduce its dimensions to a single variable. A 9 x 8 table of counts of the (x,y) data values is: ...
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21 views

A model for multiple nested proportions?

I think this is more of a stats advice than code question so I've posted here rather than SO. My data looks like this (~300 more sample rows). ...
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22 views

Estimating a joint probability distribution with antimode

I am looking for a certain multivariate probability distribution function to fit to my data, but the usual multivariate normal distribution is unfit, since my data has a dent (antimode) instead of a ...
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1answer
39 views

Left-censoring in time series data

This is from a Bayesian problem I'm working on. I have worked out \begin{align} f(y_1,...,y_T|\varphi)=f(y_1|\varphi)f(y_2|y_1,\varphi)...f(y_T|y_1,y_2,...,y_{T-1},\varphi), \end{align} and all terms ...
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53 views

Multivariate multi-level analysis in nlme

The question I have a dataset which I think requires a multivariate multilevel analysis. I am unsure both of the appropriate model and of how to fit it with R. I ...
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2answers
43 views

Multidimensional Differential Entropy

I am looking for a measure of entropy over multiple random variables, each with values between 0 and 1. Intuitively, it seems possible to talk about the expected value of information of several ...
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45 views

Dimension of a distribution

I have a distribution that can be written as follows: $$ q(w, \lambda, \phi) = q(w) \times q(\lambda) \times q(\phi) $$ Here the $q$'s denote densities. $q(w)$ is a multivariate normal distribution ...
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How to understand complex social relations in huge populational data?

I have 20 years of data from observing dolphins. When a group is seen, it gets an unique number identifying it, and all identified (marked) dolphins were also registered. So I had a table like ...
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How to characterize the distribution of the intersection of 2 bivariate normals

I have two 2-dimensional Gaussian distributions: $$ D_1 := \mu_1=\pmatrix{x \cr y}, \quad \Sigma = \pmatrix{{\rm var}(x) &{\rm cov}(xy) \cr {\rm cov}(yx) &{\rm var}(y)} \\ D_2 := ...
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1answer
47 views

Detecting 'causality' in Likert-time series data

[Note] I've decided to re-write my question for the sake of brevity. The original question can be found below. Suppose a number of individuals fill in a questionnaire at a multiple number of time ...
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139 views

Multivariate meta-analysis in R: how to investigate network of variables

I would like to conduct a meta-analysis to investigate the interaction of three variables:hair color (dark/light), gender (male/female) and size (continuous). I have three studies reporting effect ...
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211 views

Sampling distribution of the radius of 2D normal distribution

The bivariate normal distribution with mean $\mu$ and covariance matrix $\Sigma$ can be re-written in polar coordinates with radius $r$ and angle $\theta$. My question is: What is the sampling ...
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19 views

Getting residuals from (kernel) canonical correlation analysis

I'm playing around with kernel Canonical Correlation Analysis, as implemented in the R package kernlab. Is there a simple way to extract the residuals after fitting? (Is this a well-defined quantity?) ...
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1answer
133 views

How to work out Effect Size for a MANOVA using G*Power

I'm using G*Power to work out how many participants I need. I'll be using a MANOVA, I have two independent variables (Male and Female) and they will be answering 13 different questionnaires so 13 ...
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91 views

Nested design — adonis function in vegan R package

I am using the adonis function in the vegan package to determine differences in dissimilarities in a community (PCB congeners) between several different factors. ...
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49 views

Canonical Correlation Analysis for different data types

I have to do canonical correlation analysis between two multivariate datasets X and Y. One dataset contain numerical data and the other binary data. I would like to know what features are highly ...
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32 views

Steps to follow for correspondence analysis when each brand is not shown to every respondent

I want to understand the steps followed for correspondence analysis when each brand is not shown to every respondent. Till now I used to assign a number (proportion) to each brand for each attribute ...
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389 views

Can the scaling values in a linear discriminant analysis (LDA) be used to plot explanatory variables on the linear discriminants?

Using a biplot of values obtained through principal component analysis, it is possible to explore the explanatory variables that make up each principle component. Is this also possible with Linear ...