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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Derivative of multivariate gaussian wrt to covariance

The derivative of the logarithm of a multivariate Gaussian distribution wrt the covariance matrix is: $$ -\frac{1}{2}\Sigma^{-T} + \frac{1}{2}\Sigma^{-T}(x - \mu)(x-\mu)^T\Sigma^{-T} $$ The derivative ...
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12 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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24 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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9 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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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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1answer
41 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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58 views

Multivariate Normal Distributions & chi-squared

With a table of data with multiple variables (lets say 2 for ease) and multiple samples how can one calculate the chi-squared test statistic? That is, given $x\sim N(\mu,\Sigma)$, the chi-square ...
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1answer
50 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
9 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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14 views

Multivariate normal distribution [closed]

Could somebody help me with this problem please? Let X = (X1, X2, X3)′ denote a random vector with distribution N3(μ,Σ),whereμ=(2,1,2)′ and  Σ= 2 1 1 1 3 0. 1 0 1 b) Find the ...
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34 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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33 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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24 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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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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1answer
28 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 ...
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19 views

Statistical technique for data when three interventions are administrated and multiple responses measuring different constructs are measured

I have a data where three interventions were administrated on subjects and different response variables (say 15 variables) on Likert Scale were observed. These response variables measure three ...
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1answer
37 views

Example of dependence with zero covariance

This is a constructivist question. Please provide a bi-variate distribution or density/mass function of two absolutely continuous/discrete (but not mixed-type) random variables, which (may) have ...
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23 views

Two univariate vs. multivariate analysis

Suppose I have 2 response variables $Y_1,Y_2$ and some predictor variables $x_j$. Is it the same if I use 2 separate linear models, one for each of the response variables, vs. using a multivariate ...
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34 views

Modeling a national dataset at a lower level of census geography

I want to build a model from a set of a over 100000 individual survey responses. Then, from the distribution of new responses (not found in the training set) on a subset of questions from the survey, ...
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multiple imputation: contrasts can be applied only to factors with 2 or more levels [migrated]

I am using the data available here: http://www.ads.org.pl/pobieranie-zbioru-danych.php?id=91 which is a survey with 17497 observations of 1681 variables. I am interested in variable q32, which is a ...
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12 views

Distribution of the probability density values in a multivariate normal [duplicate]

Good day, I'm having trouble with the following question. Suppose i have a random vector following a multivariate normal distribution i. e., $$ \textbf{X}=\{X_1,\dots,X_k\}\sim N_k ( ...
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1answer
25 views

adjusted odds ratio vs odds ratio

In multivariate regression analysis, it seems that people use different definitions of adjusted odds ratios. Could you please clarify for me what an adjusted OR is and how it differs from a ...
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Interpretation of confidence interval from multivariate analysis

Could you help me interpret the predictive variables from the table below taken from an article on preterm labor? I am trying to understand whether it is accurate to call 'non-significant' the ...
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Composition of Multivariate Gaussians

This question is teasing my intuition for a moment : $X \tilde{} N(0,S_1)$ $Y|X \tilde{} N(X,S_2)$ Does $Y \tilde{} N(0,S_3)$ with some $S_3 = f(S_1,S_2)$ like (for instance) $S_1+S_2$ ? What I ...
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Sample size for mvtest in Stata for MANOVA assumption test [migrated]

I am looking for advice on a specific Stata command - I am analyzing simulation output with MANOVA (in STATA) and want to test the assumptions - specifically (1) the Homoscedasticity and (2) ...
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JAGS: multivariate normal with both, unobservable and observable variables? [migrated]

I have a "simple" problem with JAGS that drives me crazy. In essence, consider the following example that works: ...
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3answers
60 views

Multivariate GARCH with respect to Value at Risk

For the last few weeks I studied GARCH with respect to individual assets. Now I want to combine assets and execute a multivariate (DCC) GARCH test. Let us say that I have a portfolio containing four ...
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120 views

What can be inferred from a short multivariate time series?

I have annual observations of 24 variables over 10 years, and I would like to identify evidence of structural change (regime shift). The data pertain to university enrollment & spending, so I ...
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Multivariate Bernoulli, Covariances for Categorical Data

I need to find outliers in multidimensional, categorical, 1-hot encoded, binary data. Data might look like, 0,1,1,0 1,1,0,0 1,1,1,0 0,1,1,1 0,0,1,0 I toyed with ...
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Conjoint analysis

I am planning to conduct a conjoint study, but am having problems in terms of the number of product profiles to include. I will have to interview respondents in the markets and hence wanted that the ...
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algorithms for color image edge enhancement using potential function

I want to use the method based on the use of weighting function also known as Parzen Kernels and form estimation of the probality density function (pdf) based on ...
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Learning from sparse label products

Consider the following binary classification problem $f(\mathbf{X})\rightarrow\mathbf{Y}$ where: $\mathbf{X}$ = Feature matrix $\mathbf{Y}$ = Product of several label (binary) vectors, i.e. ...
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Does diagnolizing higher-order cross-moment matrices lead to independent variables?

Diagonalizing the covariance matrix transforms multivariate data into uncorrelated variables, but does not make them independent necessarily. Does it follow from this that if I were to diagonalize ...
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Anomaly detection: multivariate Gaussian distribution

I am trying to do anomaly detection on a heterogeneous dataset (There are unknown groups present in the dataset). I want to try multivariate Gaussian distribution based approach, but I was thinking of ...
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52 views

Product of two gaussian processes

Given, $\ {y}_{i} = N({\mu}_{i}, {\Sigma }_{i}) $ If we go by the link http://www.tina-vision.net/docs/memos/2003-003.pdf then we can understand that the product of many multivariate gaussians can ...
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116 views

How can MANOVA report a significant difference when none of the univariate ANOVAs reaches significance?

I would just like to ask if it is normal for the values from my multivariate tests to be significant but for the values from my univariate tests of between-subjects effects table to be insignificant. ...
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21 views

Significance of multivariate models and correction for multiple comparisons

I have performed a multivariate binary classification using a number of features (or variables), I will call them features from sets (A), (B) and (C). I have calculated the P value of this ...
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17 views

Generalized Estimating Equations- How many predictor variables are too many based on sample size?

I am conducting analyses on wild animals, on how diet of an individual changes based on environmental changes. I will list the setup of my dataset below. Until now, I have been running independent ...
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Need help understanding hypothesis tests in multivariate statistics

I'm not really sure where to begin with this question, and I'm not sure if I am supplying all the resources necessary to answer this question, so just let me know and I will update. I'm going to copy ...
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34 views

When to use a bootstrap in MLE

Suppose I have a data set of $n$ observations with the dependent variable sample $\mathbf{Y} \in \mathbb{R}^{n \times k}$, and independent variable sample $\mathbf{X}\in \mathbb{R}^{n \times l}$ such ...
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What criteria to use for separating variables into explanatory variables and responses for ordination methods in ecology?

I have different variables that interact within a population. Basically I have been doing an inventory of millipedes and measuring some other values of the terrain, like: The species and the amount ...
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19 views

How to add one covariate at a time, for neural network, lm, or tree models

I have about 26 dependent variables and 400 to 1200 independent variables with 18000 observations. Is there an R package for adding one variable at a time to identify the variable(s) that reduce the ...
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45 views

How can I verify that variance(factor)=1 from Exploratory factor analysis results?

I am reading upon Exploratory factor analysis. One of the assumptions of the Orthogonal factor model is that $$ \sigma^2(factor)=1 $$. Reference via "Applied Multivariate Statistical Analysis-by ...
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Understanding Multivariate Normal Distribution in simple terms

While reading about the proc Tcalis procedure in SAS for SEM, I came across the statement: "For maximum likelihood (default) and generalized least squares ...
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43 views

Extend bivariate to multivariate convolution formula?

In reference to this post, the pdf for dependent random variables $X_1+X_2$ is given by: $$f_{X_1+X_2}(z) = \int_{-\infty}^{\infty} f_{X_1,X_2}(x,z-x) \mathrm dx$$ How does this formula extend to ...
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25 views

Formulas for generalized Mahalanobis distance

I've been trying to calculate Generalized Mahalanobis distance (the Mahalanobis distance between two multivariate distributions) using some formulas, I believe at least one of them is wrong though: ...
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Need help with multivariate multiple regression models [duplicate]

I want to predict more than one dependent variable by running one model, I thought that we can use Multivariate Multiple Regression Model. But I don't know how to do it with Excel or R. Can anyone ...