Questions tagged [multivariate-regression]

Regression with more than one response (dependent) variable.

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51 views

Multivariate analysis. Hypothesis income variable increases 2 outcome variables simultaneously

I am working on an epidemic analysis on a known blood disease. My outcome variables are two, lets call them A and B. I have already two income variables lets call them c and d, that have been proved ...
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1answer
699 views

Time series Prediction as a multi-output multivariate regression for many input and output values for each lag [closed]

Recently I am working on time series prediction. My topic is related to wind turbine blades which has many sections in each blade. Now we want to predict some performance and metrics of 51 sections of ...
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1answer
108 views

Is it okay to use Multivariate Multiple Regression on correlated independent and dependent variables?

I'm confused on this one. So, I'd appreciate it if you could help me explain this a little bit. So, I have about 15 independent variables and 3 dependent variables. out of these 15 independent ...
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1answer
230 views

Is there a way to specify reduced-rank regression using $\mathbf{y} = \mathbf{X}\boldsymbol\beta + \boldsymbol\epsilon$?

In grad school, I was always taught the general linear model $$\mathbf{y} = \mathbf{X}\boldsymbol\beta + \boldsymbol\epsilon\tag{1}$$ where $\mathbf{y}$ is a vector, $\mathbf{X}$ is some matrix, $\...
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1answer
105 views

interpretation and inclusion of interaction terms in regression model

I have a 3-way interaction model as follows: Y = A + B + C + A*B + A*C + B*C + A*B*C A is a dummy and B and C are centred continuous variables. I am mainly ...
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815 views

Distribution of the residual sum of squares for *multivariate* linear regression

I want to ask about a multivariate generalization of this previous question. It is a well established fact that in univariate (i.e. the response $y$ is univariate) linear regression, that the ...
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1answer
527 views

MANOVA or Mixed Models

We are doing an interesting behavioral study on waterbirds. Let me explain the design of the study before asking the statistical advice. The lake is divided into 2 parts, In one part fishing is ...
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1answer
274 views

Multivariate analysis using multi-level models as described by Gelman

I have a data set I have been asked to provide an alternate analysis for in which 34 mothers answered a psychological questionnaire. The authors have currently conducted an exploratory analysis ...
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1answer
503 views

Interpretation of multivariate linear regression significance with interaction term

I am working through an obesity dataset for a project I'm involved in, and I wanted to run a fairly simple multivariate linear regression on the data. What I was interested in is the correlation ...
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2answers
318 views

How to model an “order-invariant” function by neural networks

I want to approximate a multi-variable function $f(x_1,x_2,x_3,x_4,x_5,y)$ from data by neural networks, and $f$ satisfies $f(x_1,\ldots,x_5,y)=f(x_{i_1},\ldots,x_{i_5},y)$, where $(i_1,\ldots,i_5)$ ...
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629 views

How does the cubic smoothing spline works in 2D case?

I was reading the Mathworks documentation about the CSAPS and TPAPS. I got confused in 2D case where I can't understand how these two penalties are different? Hows the PSS looks like in the case of 2D ...
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1answer
220 views

Specification of priors for multivariet hierarchical regression using MCMCglmm

I'm analyzing data from experiment, where people had to select a point in plane. I'm trying to asses which atributes of the task and personality are asociated with the outcome. Becouse we used ...
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1answer
1k views

How can I impute a large multivariate dataset?

I am researching a medical dataset that has a large number and complexity of variables (> 900 variabes, > 3000 with dummy variables). Not only biomarkers and the patient's demographical data is ...
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1k views

T-test for regression coefficients obtained from Ridge, LASSO etc

In ordinary least squares, for example in an experimental design case, I obtain the regression coefficents by: $ \hat B = {({X^t}{X})}^{-1}X^ty$ Then, my null hypothesis for each coefficent is: $...
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58 views

How to construct a regression model with two inter-dependent dependent variables?

Let's work through a concrete (if somewhat impractical) example: I'm a medical researcher who has reason to investigate a possible trend in a dataset of tissue samples from the human lung and human ...
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221 views

Comparability of multivariate vs multiple regression

I have 3 layers of data [in individual columns] indicating different characteristics of resistance of vegetation to stress across a city. I have another layer of median income for my study area. I ...
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1answer
57 views

problem with linear regression

I made a linear regression multiple model, I've got all the parameters insignificant with high p value, I get this result: The variables are time series. Rates except Polity which is natural number ...
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51 views

Detecting changes in multivariate time series

I have the following problem I am trying to solve. I am hoping to pick your brain on the possible solutions. I have (say) 10000 machines, each one spit out a number for me each day; I have collected ...
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126 views

Are multivariate probit models with the same set of explanatory variables for each outcome more efficient that piecewise probit regressions?

I understand that multivariate probit models are analogous to SUR models. In the SUR case, there's no efficiency gain by fitting a SUR model over several independent OLS regressions when the model ...
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45 views

Approaching a multivariate regression problem with multiple observations over days

Assume for every $Y_{n*1}$, there is a covariate matrix $X_{n*p}$. The goal is to predict $Y'_{n*1}$ when new $X'_{n*p}$ becomes available. What complicates the matter is that I have $k$, let's say ...
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1answer
142 views

Why do we need adjustment when applying Ljung-Box test over residuals?

Why do we need adjustment when applying Ljung-Box test over residuals? The following is from the Multivariate Time Series Analysis by R. Tsay. ...
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125 views

Can I try applying multiple linear regression when there is no correlation with independent variable

Can I still try multiple linear regression when there is no or very small(2 to 10%) correlation (Pearson) between the Independent variable(continuous) and Dependent variable(continuous). But very ...
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1answer
263 views

comparing coefficients from multivariate regression

I have a multivariate linear regression model where the predictors are concentrations of different drugs, of the same units, and the responses are the survival percentages of each different kind of ...
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1answer
198 views

Terminology for regression with more than 1 independent variable and more than 1 dependent variable?

I know that multiple regression corresponds to the case where we have 1 dependent variable and multiple independent variables. Multivariate regression, on the other hand, corresponds to the case where ...
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458 views

GLM in Matrix Notation

I would like to verify my thoughts here concerning matrix notation of generalized linear models (i.e. generalized general linear models). A classical generalized linear model is given by $$ Y_i = h(\...
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1answer
5k views

What's the point in neural networks for multivariate regression?

Do you have any case in which fitting a multivariate regression (so having multiple output nodes) outperforms the fitting of a single output one at a time in terms of accuracy? I ask this because ...
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0answers
357 views

What's the difference between multivariate regression and univariate regression? [duplicate]

If we have $Y$ as response variable which has more than 1 component, and we do want to do regression, then is there such a thing as multivariate regression, and if so, how those it differ from ...
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1answer
724 views

Summary of manyglm model objects running too slowly in R; can I speed them up?

I have implemented two independent multivariate abundance regressions, both of which use the manyglm function in the mvabund ...
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1answer
268 views

A reasonable multivariate regression error metric

How would you compare error metrics of a multiple output regression? Normalised mean square error for each variable? How about for the overall performance of the model, would you just take the mean ...
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2answers
6k views

Simple, multiple, univariate, bivariate, multivariate - terminology

I do realise (some of) this has already been addressed here (e.g., Why do we need multivariate regression (as opposed to a bunch of univariate regressions)?, Explain the difference between multiple ...
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4answers
18k views

Neural network for multiple output regression

I have a dataset containing 34 input columns and 8 output columns. One way to solve the problem is to take the 34 inputs and build individual regression model for each output column. I am wondering if ...
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6answers
16k views

Why do we need multivariate regression (as opposed to a bunch of univariate regressions)?

I just browsed through this wonderful book: Applied multivariate statistical analysis by Johnson and Wichern. The irony is, I am still not able to understand the motivation for using multivariate (...
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37 views

Can two multicollinear variables affect a third IV that is not correlated with the two?

I have three dependent variables, $X_1$ (my 'main' independent variable), $X_2$ $X_3$ where When I test $X_1$ against the response variable y in a bivariate regression, the results are not ...
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1answer
6k views

Multivariate linear regression with lasso in r

I'm trying to create a reduced model to predict many dependent variables (DV) (~450) that are highly correlated. My independent variables (IV) are also numerous (~2000) and highly correlated. If I ...
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1answer
471 views

Correlation of dependent variables in multiple regression

I have several regression models as below: $Y_1 = \beta_{11} X_{11} + \beta_{12} X_{12} + \epsilon_1$ $Y_2 = \beta_{21} X_{21} + \beta_{22} X_{22} + \epsilon_2$ $Y_3 = \beta_{31} X_{31} + \beta_{32}...
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1answer
217 views

What's a good way run a regression with two datasets that have common DVs but some different IVs?

I have run 20 questionnaires with 100 responses each. One of the goals of my study is to analyze how cybersecurity “literacy”, along with some other IVs, correlate with how people hear about breaking ...
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477 views

Multivariate multiple regression with multiple ordinal dependent

I have a statistical quandary I'm trying to solve, hopefully someone here can help. I have a data set with several dependent variables measured as ordinal Likert items and I want to measure the ...
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1answer
109 views

How do I do multiple regression for more than one dependent variable?

My IV variable is leader's qualities (with five categories) and my DV is school climate (with 6 categories). I would like to test whether my IV variable (with five categories) has an influenced on my ...
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0answers
150 views

Multiple multivariate regression problem - auto correlated dependent variables

I have a classic multivariate regression problem, i.e. dependent variables are stored in matrix $Y$ having dimension $n \times p$. So $p$ observations come from the same respondent $i$ and we need to ...
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1answer
461 views

How to find cross correlation of a response variable with three independent predictor variables for time series data to identify useful lags?

I have a time series data y (response variable) which I want to predict using 3 independent time series data x1, x2 and x3. My goal is to build a multivariate regression model for which I want to ...
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0answers
559 views

Multivariate multiple nonlinear regression

I am supposed to build a nonlinear regression model with multiple, correlated dependent variables and multiple independent variables, i.e. a multiple multivariate regression model. Unfortunately, I ...
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0answers
733 views

Interpreting bivariate/multivariate probit model (Rstan implementation)

I'm having trouble with inference from the posterior predictive distribution I've generated from a multivariate probit model I constructed using Rstan. My primary interest in the model is to estimate ...
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1answer
52 views

Good book on vector valued distributions? [duplicate]

I just started a new job essentially working as a Data Scientist / Software Engineer. I have a background as a math Ph.D. and as part of that training, I've taken the typical measure theoretic ...
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0answers
326 views

It is possible to do a Multiple Weibull regression?

I have a response variable that I would like to explain with several predictors. The response variable is all positive continuous data. Some of the predictors are discrete while others are continuous. ...
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0answers
116 views

Canonical Correlation as a measure of multivariate dependence

Canonical correlation is used as a measure of dependence between multivariate vectors $\mathbf{X}$ and $\mathbf{Y}$, by finding vectors $\mathbf{a}$ and $\mathbf{b}$, respectively, such that $corr(\...
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0answers
108 views

Multivariate Regression equivalent to Multinomial Regression (aggregated variables)?

Context (optional) In genetics one often uses data coming from SNP (Single Nucleotide Polymorphismes) which are genetic markers of which several (usually 2) versions (a.ka. alleles) exists in a given ...
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1answer
271 views

Choice of algorithm for fitting Multivariate Covariance Generalized Linear Models

I am using the mcglm function in R to fit a Multivariate Covariance Generalized Linear Model. Although the help for the ...
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1answer
65 views

Clarification on multivariate regression

In (what I call) standard regression, we have a problem of the form $y=f(a,b,c,d)$. Is it correct to say that multivariate regression is the problem of the form $g(x,y,z)=f(a,b,c,d)$? In case this is ...
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628 views

Multiresponse Poisson regression in R

Can I apply generalised linear regression to a multiresponse setting? I mean the regression $Y = \beta X + \epsilon$ where $\beta$ is a parameter matrix and $Y$ is a response vector, in my case ...
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0answers
33 views

Multivariate regression with relationship between outputs

Can anyone suggest some machine learning algorithms for the problem of multi-output regression when the outputs depend both on input vector and other outputs. More specifically, given input vector x ...