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Questions tagged [multivariate-analysis]

Analyses where there is more than one response or dependent variable of interest. This can be contrasted with "multiple" or "multivariable" analysis, which typically implies more than one predictor or independent variable.

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Interpreting Multiple Correspondence Analysis Output

I have the following data for Maryland and Virginia with six different capacity types along with what score (1, 3, or 5) each person grades that capacity type. Essentially what I want to do is see if ...
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Multivariate analysis for data concerning lake chemical profiles

I am trying to compare two different watershed's chemical profiles to determine which is less contaminated. I have data from four different lakes in each of the two watersheds, and alkalinity, ...
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Dependency of variable P on multiple factors, and factors interactions

In my data, I have a variable/vector P which is dependent on variables X, Y, Z, K and gender. The factors X, Y, Z are interacting. What kind of statistical tool/method I can use to explore dependency ...
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How to combine exposure measurements with a job exposure matrix

In order to better estimate occupational exposure to chemicals in the general worker population, I'd like to combine a job exposure matrix (JEM) with chemical exposure measurements. A generic JEM is ...
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Simplification of an expectation

While attempting to simplify a combination of expectations, I'm stuck at a particular term whose simplification I'm unable to deduce. The term to be simplified is: $\mathbb{E}[X^{T}F^{T}FX]$ where $...
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Coding a BEKK mutlivaraite GARCH model

I have the code, but I am struggling to determine which specific BEKK model it is for... Any advice would be appreciated, ...
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Checking equality of covariance matrices using Box's M test in multifactor MANOVA

With only one factor (independent variable) in multivariate analysis of variance (MANOVA), Box's M test can be used to check the equality of covariance matrices. ...
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20 views

How to use derivatives of a function to better estimate its variance over the domain?

How to use derivatives of a function to better estimate its variance over the domain? I have a scalar smooth function $f(x)$ and a multivariate random variable $x$ with known distribution (e.g. ...
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25 views

Multiple Regression to suggest the number of stores needed per town/location

Is it possible to apply a multivariate regression to identify the number of company stores or branches required in a town or location? the dependent variable is the number of stores the independent ...
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38 views

Should the multivariate Box-Cox lambda value, of a variable against itself, be 1?

I have 10 variables, and am trying to determine which transformation between each variable provides the best linear relationship. To this end, I am using the Box-Cox method to determine a power ...
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44 views

How to interpret probability of an outcome in a multivariable logistic regression?

I am modeling a binary outcome with multivariable logistic regression, where all predictors have been found significant, but I am particularly interested in one (continuous) predictor. I would like ...
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1answer
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Multivariate Panel Regression in R [closed]

I have the data of about 30 patients on monthly visits over half a year. Each patient filled out the same tests every month (for example, the BDI for depression). Some of these tests may have a ...
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Regression - variance of predictions much lower than variance of target

I am using non-negative lasso(sklearn) on a dataset with 1.5MM data points and 120 features. It is a low R2 environment (working with noisy financial data), so $R^2$ is about 10%. What I am more ...
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compute the KL divergence between two datasets

I have two datasets $D1$ and $D2$ in two different feature spaces $\mathcal{X}_{1} \in \Re^{m}$ and $\mathcal{X}_{2} \in \Re^{n}$. Further assume that the datasets have different number of data points....
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Alternative definition of Multivariate Mutual Information

The standard mutual information (MI) is given by $$I(X;Y) = H(X) + H(Y) - H(XY)$$ which is the amount of information shared by the two random variables $X$ and $Y$. According to wikipedia article, ...
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Multivarite Linear Mixed model in R

I want to fit the following multivariate mixed effects linear model in R but am failing miserably: $y_{ijk}$ = $({\textbf{x}}_{ijk}'{\beta}_{k})$+$(\gamma_{ik})$+$(a_{0k}+a_{1k}t_{ij}+ a_{2k}{t_{ij}}^...
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IQR based outlier detection with multivariate data

One method to detect outliers in a dataset $[x_1 ... x_N], x_i \in R$ consists in finding the samples $x_i$ such that $$ x_i \lt Q_1-K*IQR | x_i \gt Q3 + K*IQR $$ where $Q_1$ and $Q_3$ are the first ...
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Conditional distribution for 3 variables [duplicate]

Everywhere it is done for bivariate or given a hints. But Not in details for trivariate.
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What assumptions about the data are require for Multiple Correspondence Analysis?

In multiple correspondence analysis, what assumptions about the data are necessary in order to find the principal coordinates for the rows and columns?
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Decomposition of interest rate risk premia

I have a question on econometric modelling techniques for decomposition. I have three variables: - V1 which is an indicator of an interest rate risk premia - V2 which is an indicator of a credit risk ...
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Is it possible to use linear model of coregionalization (LMC) for modeling Anisotropic Multivariate Random Field?

Using linear model of coregionalization (LMC) method is a well known method in creating covariance matrix functions for multivariate isotropic random fields. I was just wondering if it is possible to ...
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1answer
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Is there a non-parametric, two-way, continious data ANOVA for replicated repeated measures?

I have data of multiple factors. Let's call them: size (2 levels), geometry (2 levels) and time (242 levels but I can limit my focus to 3 levels, which are relevant). I also have a measure (dependent ...
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1answer
20 views

Different timing samples' analysis

How can I put my data in a sheet if I have a number of patients and each patient have different number of samples with different timing? How can I analyse data grouping data samples for each different ...
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42 views

Interpreting intercept in multivariate linear regression when excluding some factors

This question may have already been asked, but I cannot find anything quite like what I am asking. Background and model I am using manyglm with a negative binomial distribution (from the package ...
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Jarque-Bera Test for Normal Distrbances in a VAR

I did the test of he null hypothesis of Normal disturbances and found that it is rejected for Dlop and Dunp. Does this mean that I have a problem with my model specification? Or how can I rectify this ...
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Correlation between two multivariate measures

I'm reading a paper, but I'm with a problem. The authors say: Let $\boldsymbol{X} = (X_1, \ldots, X_p)^T$ be a vector $m \times 1$ whose the estimative of variance is proportional to $\boldsymbol{\hat{...
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What is the point of univariate regression before multivariate regression?

I am currently working on a problem in which we have a small dataset and are interested in the causality effect of a treatment on the outcome. My advisor has instructed me to perform a univariate ...
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Does joint IID imply marginal IID?

Suppose you have a 2 dimension random vector denoted $(X,Y)$ that is Independent and Identically Distributed (IID) for a sequence of draws $((X_1,Y_1),(X_2,Y_2),...,(X_n,Y_n))$. Does this imply that ...
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How to identify Post Treatment Bias?

I have a question about post-treatment bias. I'll use the following example: Let's say I created a multivariate regression model for how many points a basketball player will score at a given night. ...
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What is the added value of a multivariate Bernoulli distribution over a multinomial distribution?

I came across the multivariate Bernoulli distribution of Dai, Ding & Wahba (2013) that has the following form (in the bivariate case): $P(X_1,X_2)=p_{11}^{x_1 x_2} p_{10}^{x_1 (1-x_2)} p_{01}^{(1-...
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Multivariate Adaptive Regression Splines interpreting hinge coefficients

I am learning MARS using the earth package in R. I read about MARS on page 321 of The Elements of Statistical Learning https://web.stanford.edu/~hastie/Papers/ESLII.pdf and the tutorial here http://...
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Combining independent variables in linear regression - does it make sense?

I try to model energy consumption for a set of about 50 relatively similar production facilities. I have annual data of energy consumption and 3 independent variables that - from a technical point of ...
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Covariance of Random Proportions in Multinomial Counts

In Agresti's Categorical Data Analysis Second Edition, at Section 14.1.4, there is a proof of the Asymptotic Normality of Functions of Multinomial Counts. It is stated that for a vector of responses $...
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1answer
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Optimal multivariate binning where the cut-points must be the same for all observations

I have a large data set with many discrete and continuous variables. All the variables are present in every observation. I want to explain (the log of) one continuous variable using all the other ...
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Statistical Model for multivariate timeseries

I'm new to timeseries prediction and I would like to try several classical methods before getting into more complicated model. Concretely, I have a multivariate timeseries of ...
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Expectation of Multivariate Function

Let's say $p$ is a function of two, possibly correlated, other random variables $a$ and $w$ per the function $f()$: $p = f(w , a)$ What assumptions are necessary to express $E[w|p]$ as a function of ...
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1answer
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Name of classification algorithm based on gaussian distributions estimated from data?

Can you help me find the name of this classification method: Assume we have the following data: $n$ dimensional feature vectors we want to classify in two classes. We model the classes as two $n$ ...
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Setting up contrasts in lmer?

0 I have 139 subjects (ID), with measurements taken at two time points (Time1, Time2), at 148 brain regions, a dependent measure called volume, and a covariate called thickness. Each subject has 148 ...
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1answer
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How to interpret MANOVA results after adding gender, splitting the file?

I am analyzing my 2x3 between subject design with MANOVA in SPSS at the moment. In the main model, there is 2 IV's and 2 DV's. Result of the test is 1 main effect and no interaction effect. In an ...
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1answer
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why p value = 0 in CV-ANOVA?

i am using SIMCA 13.0 to build a opls-da model. To validate the model,SIMCA perform ANalysis Of VAriance testing of Cross-Validated predictive residuals(CV-ANOVA).Then output a table(attached). In ...
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Evaluating ecological community over time with NMDS?

I have sampling data of insect communities per month for 7 months. The sampling occurred in the same location with the same methods once a month. I want to be able to see community changes over time ...
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Are all symmetric matrices with diagonal elements 1 and other values between -1 and 1 correlation matrices?

A question for the statisticians and other math lovers: Are all symmetric matrices with diagonal elements 1 and other values between $-1$ and 1 correlation matrices?
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Confused with Multivariate time series analysis Book equation

I am reading the Wiley's Multivariate Time Series Analysis Book and there is an step that I don't understand. At pag. 18 it gets the following equation: $\mu = c + \sum_{i=1}^{\infty} \pi_i \mu$ ...
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1answer
59 views

Lmer set up for repeated measurements?

I have 139 subjects (ID), with measurements taken at two time points (Time1, Time2), at 148 brain regions, a dependent measure called volume, and a covariate called thickness. Each subject has 148 ...
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23 views

Principal component analysis for variable reduction

In the textbook “Principal Component Analysis” Jolliffe (§9.2) suggests the following method for variable reduction: “When the variables fall into well-defined clusters, there will be one high-...
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classification-multivariate analysis+creation of class variable

I am working on a university R project of multivariate analysis and I need some help: DATA: MIXED, with 17 variables : 4 qualitative and the 13 are continuous. PROBLEM: I don't have a class variable, ...
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Determine if attributes of sample users are similar to attributes of the full population

I'm a product owner responsible for running a lot of A/B tests comparing an experiment vs a control group. Usually, both groups are a subset of a larger overall population (million plus users). I'm ...
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Modeling relationships between 100+ variables

I have been interested in DS/ML for a few years now and I have been able to build some relatively simple models actually performing pretty well. Now I have this idea in mind but I am not sure how to ...
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Deriving the sampling distribution of MLE for Normal distribution

Let $X_1,\ldots,X_n$ be an observed random sample from $N_p(\mu, \Sigma)$. I know that the MLE of $\Sigma$ is $\frac{1}{n} \sum_i^n(X_i -\bar X)(X_i -\bar X)^T$, which is biased. We define $S = \...