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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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Fitting a multivariate AR(1) with covariates?

I have time series data where my main question of interest is making inference on predictive covariates, and accounting for the correlation (one observation each day) is just a nuisance issue. The ...
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multivariate normal distribution with mean vector 0 and covariance matrix Σ

I am newby in statistics and I have huge data with "p" variables and "n" samples. My data is a two dimensional matrix with "n" columns (each column is a sample) and "p" rows (each row is a variable). ...
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Is there a way to run a multivariate mixed effects model (e.g. RDA) with an unbalanced number of observations per level of the random factor?

I have a community matrix (fish gut microbiome) from a laboratory experiment consisting of 2 treatments, each with 3 independent aquaria, which were sampled 3 times. At each sampling event 6 fish were ...
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Where can I find high-dimensional (p>n) datasets? [closed]

I am looking for "high-dimensional" data for a course project. The requirements of an ideal dataset for me are: 1.$p>n$ (or at least $p> \sqrt{n}$), where $p$ is the number of variables and $...
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Modelling with a delay

Im just at the stage of looking at my data and seeing how I can model it. My data is on the cooling effect of tree shade given various measured tree variables but to make the model useful I also need ...
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Analysis of model and data relationship in PLSR

Validated! This is a quite broad subject topic but I will try to boil it down into a few specific questions. I've been working with a clients data on a PLS (partial least squares/project to latent ...
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No convergent solution using metaMDS in vegan in R

I have a data set of proportions (i.e. each sample sums to 1) of several hundreds samples and 30 variables that I'm trying to analyze with metaMDS in the ...
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Should I use independent variables whose correlations with dependent variable are not significant in a linear regression model

I have performed correlation tests between my dependent and all independent variables to examine linear relationship. However, the correlation coefficients from all the tests are non-significant. What ...
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Concept of square in multivariate statistics

This might be more of a linear algebra question, but here we go. I have always been confused about how the concept of squares in $\mathbb{R}^1$ sometimes corresponds to a matrix product $A^{T}A$ and ...
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conditional three-level model and repeated measures using glmer in R

I have been trying to find out the most adequate formula for my data but I found no example that reflects the structure of my data, as pictured in figure above. My data is dichotomous [correct/...
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A question about sample partial correlation coefficient and multiple correlation coefficient

Question: My problem: All possible formulae of Multiple and Partial Correlation Coefficient I know :- But I am not sure, which one to use to know about the situation or condition mentioned in the ...
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A problem about Partial Correlation Coefficient

Question: Prove that for a set of p variables, if all the simple correlation coefficients are negative, then all the partial correlation coefficients of all orders are also negative. My problem: I ...
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A question about Trivariate Normal Distribution

Question: Let $(X_1,X_2,X_3)\sim N_3\left[\mathbf0, \begin{pmatrix}1&\rho_{12}&\rho_{13}\\\rho_{12}&1&\rho_{23}\\\rho_{13}&\rho_{23}&1\end{pmatrix} \right]$ Show that ...
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Constrained multivariate random variable

Question 1. Is is possible to generate a random variable $\mathbf{X} = \{X_1, \dots, X_N \}$ such that: for each instance $\mathbf{x} = \{x_1, \dots, x_N \}$ of $\mathbf{X}$ we have $\sum x_i = 1$ ...
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For three variables $X,$ $Y,$ and $Z,$ prove that the sum of all the pairwise correlations is atleast $-3/2$

As I can understand about the question, it is required to prove, $$\operatorname{Corr}( X, Y ) + \operatorname{Corr}( X, Z ) + \operatorname{Corr}( Y, Z ) \geq -3/2 \tag i$$ But for any two ...
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Can I combine two data set with different unit for multivariate analysis?

I have several fungi and measured some parameters (C1 ~C6) with two technologies. For multivariate analysis like PCA, PLSDA, I have to combine the data from two technologies, but as seen in the ...
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A question about the change in value of multiple correlation coefficient on multiplying each value with a variable quantity

Question: I know the formula of multiple correlation coefficient is; ( |R| is the correlation matrix and R11 is the cofactor of the (1,1)th element of R. But I really cannot figure out, how to deal ...
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Methods for training on continuous data

I have a large set ($M$) of profiles (e.g. concentration vs position and time) for which each profile consists of a sequence of data points, $(x_i, y_i)$, without any known functional form. Every ...
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Is it possible to use Multivariate regression analysis in the below mentioned research?

In a study we want to evaluate relationship between many varibles with a disease; for example gender(male/female), age(quantitative), weight(quantitative), dibetes(yes/no) etc... Most of our ...
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To find the covariance given the joint probability density function.

Question: I was solving some question papers and got stuck in this problem. My problem: I know how to find "marginal probabilities" from a joint probability density function and also know how to ...
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Porbability of an observation to belong to a specific group

I have a group with about 200 observations,and each observation has 2 variables (which are the first two components of PLS, if it matters). It looks like this: ...
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Find significantly differences between multi-variant groups

I have 11 groups, each consist of about 200 observations, and each observation has 2 variables (which are actually the first two PLS components if it makes any difference). Each group is a substance ...
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Differntiate between “Sample Multiple Correlation Coefficient” and “Population Multiple Correlation Coefficient”

I know what is a "Multiple correlation Coefficient". If Multiple regression of x1 on x2, x3, ..., xp is linear and the regression equation is given by, x1= x_1.234...p + e Then the product moment ...
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Removing an outlier in a single measure in multivariate data

We have recorded some kinematic data, and are looking at three measures derived from the movement data for each subject. In order to identify outliers, we are using the Mahanalobis distance. I got ...
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How to deal if different univariate time series which has different AR and MA orders. Can multivariate model like DCC model be a fit in such scenario?

I am planning to run DCC model on some time series. The problem is that all time series have different AR and MA orders. Many articles have taken AR and MA (1,1) order without discussing the rationale ...
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Effect of a continuous variable on several DVs?

I am trying to find the best way to analyse my data, but not very sure what to do, so hopefully someone will be able to shed some light on. Let me go through my study. Participants need to do a ...
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How can I explore how the correlation of two variables vary with another variable?

Say if I have two tests A and B, and I conducted the test for 100 participants, and I suspect that the correlation of test scores of A and B varies with their income, and the relationship may be non-...
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Relation between Vector Auto-regressive models and correlation matrix

I am generating a multivariate time series using Vector Autoregressive Models- $$X(t) = AX(t-1) + \epsilon$$ where $X \in R^{n \times 1}$, $A \in R^{n \times n}$ and $\epsilon \in R^{n \times 1}$ is a ...
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Pro and cons on multivariate time series approaches

So I am working on a project where I want to forecast how a team will perform in their next match in a number of specific categories (goals scored, time spent in certain parts of the field, passes, ...
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Wich non-parametric test for multivariate analysis?

I'm lost to analyse my data... Context: I've 2 groups with 2 treatments, 7 dependent variables and 3 assessment times (T1, T2, T3). Group 1 n=7 Group 2 n=8 An example of dataset to analyse : <...
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Why robust PCA results change with each run?

According to Filzmoser et al. 2009, the best way to conduct a principal component analysis for compositional data with outliers is: using a robust PCA method and using the isometric log ratio ...
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multi-response forecasting

General Dear community, I really struggle with some imporant issues for my next project. In general, the investigation is about multi-response forecasting with financial data. The predicability of ...
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Benchmark data sets for anomaly detection algorithms in multivariate time series

as per title, which datasets are commonly used to benchmark novel methods to detect anomalies in multivariate time series? I'm particularly interested in moderately high-dimensional (10-40 components),...
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Multivariate techniques that discriminate community composition based on environmental variables between two a priori defined groups?

I have a methodological question that I have not been able to get an answer of. Basically, I am investigating the impacts of invasive species on soil microbial communities. I have a study design where ...
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Is there a way to estimate the R2 proportion of a non-linear/spline term in a multivariate model?

I am running a multivariable model with a spline term as well as 5 other variables (linear terms). Is there to a way to estimate the significance of each the spline term (something similar to ...
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Quantifying separation of groups of bivariate data

Simple question really; is there a statistical test for significance between groups using bivariate data? If I have two groups on a scatterplot that clearly separate, how can I quantify that. For ...
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Repeated Measures Permanova with adonis

I have a between subject variable "treatment" and have a pre and a post measurement for each subject (50 per treatment = 100). The multivariate outcome are bacterial abundances. I control for 2 ...
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How to quantify the effect of one variable in a multivariate problem

I'm sitting here watching election returns and idly wondering whether it's possible, with 470 elections, to quantify the effect of a single variable--gender--when we know elections are influenced by ...
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How to compare two multivariate datasets

I have two datasets consisting of 20 features, one set contains 50k records and the other 70k. I want to check if they are from the same population. Datasets contain discrete features and the ...
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Logistic regression probabilities in scikit-learn

When using logistic regression in Python's scikit-learn, one may handle multiclass problems even with binary logistic regression. If there are $K$ classes, then coefficients (i.e. weights and biases) ...
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Usage of both FE and RE model in panel data

depending upon the value of Hausman test, RE model has been chosen to run the panel data model of 275 data points. Random effects model does not consider the group effects such as the change due to ...
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matrix inequality related to finance

I'm trying to show that, for certain investment strategies, it pays to have more precise estimates of the covariance matrix of your returns. I have always took this for granted, but I've been having ...
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Multi-dimensional Gaussian process regression

Are there extensions for Gaussian process regression (GPR) from the one-dimensional case to examples where GPR can handle multi-dimensional inputs and/or outputs? If so, could you refer me to basic ...
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A function that changes the dimension of a random vector make the random vector discrete?

One of my problems ask the question Let $\vec{x} \in \mathbb{R}^n$ be a random vector, and $g: \mathbb{R}^n \to \mathbb{R}^k$ be measurable. Then show that $g(\vec{x})$ is a discrete random vector. ...
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Analysis of multiple dependent variables all influenced by one indepdenent variable

I am analyzing a psychophysiological experiment. I ran a model on my response times and accuracy data, which gave 7 parameters [dependent variable] per participant ( n = 12) all depending on one ...
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Variable importance (?) for multivariate time series anomaly detection methods

I'm working on anomaly detection methods for multivariate time series $[\mathbf{x}^{new}_1,\dots,\mathbf{x}^{new}_T]$ where $\mathbf{x}^{new}_{i}$ is $p-$dimensional. I won't go into the details of ...
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Obtaining point forecasts from a DCC-GARCH model in rmgarch in R [closed]

I am becoming more acquainted with GARCH models in R, but I am not sure my code is right for what I am trying to do, so I would appreciate any help. Based on an xts I create using data from a csv ...
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Confidence regions on bivariate normal distributions using $\hat{\Sigma}_{MLE}$ or $\mathbf{S}$

Given a $5 \times 2$ dataset $\mathbf{X} =\left( \begin{array}{rr}-0.9&0.2\\2.4&0.7\\-1.4&1.0\\2.9&-0.5\\2.0&-1.0 \end{array} \right)$. Assume that $X\sim N_2(\mu, \Sigma)$. ...
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VAR(p) models and its application in describing GDP growth

Im currently reading up on Vector Auto Regression models however I cant wrap my head around how you set a model to describe a variable. My goal is it use interest rate, imports and exchange rate to ...
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Visit level variables along with merchant level variables

I am using mixed model and my dependent variable is conversion. Records are at visit level. I have merchants selling different products in the data set, and each merchant has attributes: merchant name,...