Regression with more than one response (dependent) variable.

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Getting a confidence interval for a predicted value in regression

So I have this table of statistics which I'll try to reproduce below. It is meant to be a summary of a multivariate regression of "PolityIVScore" against log foreign aid and a dummy variable for ...
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33 views

Is there such thing as regression involving a pairwise response variable? (X,Y)~Z0+Z1*B1

I'm trying to model a pairwise outcome of basketball game scores. Ie. (94,87),(102,98),(76,54),... My input variable is a single performance metric for each team. Ie. (12,9),(14,17),... Is there a ...
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94 views

How to do MANCOVA in R?

I have two groups of persons, GRP0 and GRP1, on which I measured three continuous variables: VAR1, VAR2 and VAR3. I would like to use Mancova in R with: - VAR1, VAR2 and VAR3 as outcome variables - ...
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13 views

Pairwise comparison of slopes from multivariate regression model in R

I am investigating size changes over time. I have five size variables in a multivariate linear model against year. I used the Anova() function in the car package to test whether the slopes are equal ...
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18 views

Sparse PLS: algorithm for variable selection and model fitting

In the spls package in R (based on the manuscript by Chun and Keleş [1]), there is a separate specification for the variable selection and fitting in the main function, ...
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24 views

RANSAC Multivariate Regression

I am using RANSAC as my robust regression method. I saw many examples for a line and a plane but what if there are many independent variables as in multivariate regression. Is there anyway handle ...
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11 views

Multiple binary dependent variables

I want to model multiple binary outcomes with some predictors. Does MANOVA can handle this or is there any other techniques I can use? Thanks !!!
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27 views

Multivariate regression with 3 dependent variables and only 1 independent variable?

I need to compare the marginal effect of one independent variable (X) in 3 different dependent variables (Y). I did a multivariate regression using Stata commands manova and mvreg, but I am doubting ...
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32 views

Bivariate Zero-inflated negative binomial distribution regression?

I have two correlated random variables, for one experiment, the readout look like: For random variable A: ...
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43 views

Curse of dimensionality mimics multicollinearity?

Why does the curse of dimensionality mimic multicollinearity, in the following sense.. Consider the random vector $Y = [y_{1}, \dots, y_{4}]$ where each element is ~ Uniform (0,1). Take 10 samples ...
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39 views

Compare $R^2$ statistical significance in multivariate multiple regression

I have a multivariate multiple regression model with 3 dependent variables and the same 5 covariates. I used manova and mvreg in ...
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118 views

Many dependent variables, few samples: is this an example of “large $p$, small $n$” problem?

"Large $p$, small $n$" typically refers to "many independent variables, few samples". In my case, I have $1$ independent variable, $300$ dependent variables, and $n < 20$ samples. Thus, my case ...
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Covariance for a multivariate Bayesian Additive Regression Tree

Chipman, George, and McCullogh (2010) state that: One can also extend the sum-of-trees model to a multivariate framework such as: $$ (29) \qquad\qquad Y_i = h_i\left( x_i \right) + ...
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What are some suggestions for analysis of and model development for a small sample of data?

I originally planned on path analysis utilizing multivariate multiple regression to test my hypothetical model - but I am not getting my sample size. I have looked at non-parametric regression ...
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1answer
107 views

Multivariate Linear Regression in Python

How to compute the overall standard error of a linear regression model using Python? Which library should I use? I am looking for something like this, however, I can't see how to get the overall ...
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1answer
92 views

Which regression analysis should I use for ranked dependent variables and proportional independent variables?

I am analysing the effect of deprivation on breastfeeding and am wondering which type of regression analysis I should use. It is area level data. Deprivation data is available as a score from 0 - ...
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References suggested for multivariate analysis of several similar time series

I have a time series dataset that reports the hourly page views and social media shares of online news stories. What I hope to obtain is the relationship between the two variables. I would imagine ...
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37 views

Using a PCA to reduce response variables or multivariate multiple regression?

Does it make sense to use a PCA (principal component analysis) on a set of response Y variables and then conduct a multiple regression, or carry out a multivariate multiple regression all response ...
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113 views

How to do multivariate regression in R?

I need to preform a multivariate normal regression in R. The question is: Let $Y_1$, $Y_2$, and $Y_3$ follows multivariate normal distribution. What is the conditional of $Y_3$ given ...
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1k views

Lag order for Granger Causality Test

Suppose I'm considering several independent variables for possible inclusion in an ARIMAX model I'm developing. Before fitting different variables, I'd like to screen out variables that exhibit ...
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26 views

What are some multivariate models with feature interactions

I have dependent variable matrix $Y_{i,j}$ and feature matrix $X_{i,k}$. My objective is to predict each element of the vector $[y_{i,0},...,y_{i,J}]$ by using new observations of the features, ...
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20 views

Covariance matrix specification in multivariate probit

Im having trouble with a multivariate probit model with partial observability/sample selection (written in GAUSS). In this model there is a probit at each of multiple stages, and only one of the two ...
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15 views

Marginally Uncorrelated Responses in Multivariate Regression

Consider the multivariate regression with random predictors as described in Izenman's Modern Multivariate Statistical Techniques, that is, $X : r \times 1$ and $Y: s \times 1$ are jointly normally ...
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48 views

Regression by multiple dependent variables with constraints & feature selection

I have a data set of 1000 records. Each record has three dependent variables $y_1, y_2, y_3$ and 100 independent variables $x_1,...,x_{100}$, where the dependent variable $y_i$ satisfies: $0\le y_i ...
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84 views

Alternative to MANOVA when group covariance matrices are heterogeneous?

I'm running into problems meeting some of the assumptions of MANOVA, namely homogeneous group covariance matrices and normality. I'm looking for an alternative approach where assumptions are not ...
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46 views

Parameter covariance matrix for a multivariate (matrix-Y) logit model

I've got a partially-observed unidirectional network. Nodes can be linked (0/1) in one of many ways. For now, lets call them $y_1$ and $y_2$. The unit of analysis is the potential network link ...
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980 views

Multivariate regression with weighted least squares in python?

I have a multivariate regression problem that I need to solve using the weighted least squares method. In particular, I have a dataset X which is a 2D array. It ...
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388 views

What is the difference between multiple regression & mutivariate regression?

I have data on GDP growth as a dependent variable and growth in main production sectors of Pakistan such as mining, electricity, communication, manufacturing and electricity. I am supposed to run a ...
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18 views

Multi variate regression in SPSS… How?

I want to conduct multivariate regression (Regression on more than 1 dependent variables) in SPSS. But I couldn't find any option. I am using SPSS 22. All I could find is linear regression option but ...
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45 views

$R^2$ in multivariate regression

I'm trying to determine how the population $R^2$ value is defined in the multivariate regression model where we have $Y_i = \mu_y + B^\prime(X_i - \mu_x) + err$ Where $Y_i \in \mathbb{R}^q$ and ...
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57 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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1answer
125 views

What type of multivariate linear regression is this?

I'm trying to reproduce a result from a book (see bottom) and it doesn't work. I would like to do some further readings about this method but he doesn't specifically give the method other than a ...
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50 views

Self study problem: Predicting performance using multivariate linear regression

I'm trying to improve my statistics knowledge using football(soccer) results. So, this is a self study problem. You don't have to provide a complete solution. Pointing me in the right direction is ...
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28 views

Controlling for respondents' propensity to rate high/low or moderate/extreme

I am doing a simple linear regression to test the relationship between voters' self-reported policy stands and their approval ratings for two hypothetical presidential candidates in a simulated ...
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60 views

causal inference with correlated multivariate outcomes

I've been struggling with how to think about the causal estimate of a program on two outcomes, when one of the two outcomes affects the other outcome. It seems sort of like simultaneous equations, ...
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139 views

Comparing 2D heat maps of observed data to 2D model predictions

From "How to ask a statistics question": PROBLEM you are trying to solve: Given two-dimensional heat maps of responses (DV), choose the 2D model (also a heat map, but can have different ranges of ...
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203 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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302 views

Finding the best linear model for each response variable in multivariate multiple regression using R

I don't know if a similar problem has been asked before so if it has been, please provide me a link to the related/duplicate questions. I am sorry if I seem to be asking too much. But I really like to ...
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122 views

Prediction Intervals for General Linear Model

How do I derive prediction intervals for a general linear model? My general linear model written in matrix form is, $$ \mathbf{Y} = \mathbf{X} \mathbf{B} + \mathbf{R}$$ with each of the rows of ...
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40 views

Modeling consumer demand for a multi-tiered product that is subject to cannibalization?

I'm looking for research/white papers on demand estimation for goods/services that are offered on a tiered-basis with varying prices (i.e. more complex the good/service, higher the price.) I'm not ...
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448 views

Casting a multivariate linear model as a multiple regression

Is recasting a multivariate linear regression model as a multiple linear regression entirely equivalent? I'm not referring to simply running $t$ separate regressions. I have read this in a few ...
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Coupling time series information from sources with multiple spatial resolutions/scales

I have many satellite raster images available from different sensors. From these, the coarser ones have a very abundant temporal resolution. The medium resolution rasters tend to have less acquisition ...
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45 views

how to explain the anova object for a multivariate linear regression?

I performed a multivariate linear regression such that: fit<-lm(as.matrix(y)~mwtkg+mbmi+mage,data=x) where $y$ is a $500 \times 26$ multivariate outcomes. ...
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161 views

Why signs of coefficients change when doing multivariate vs. univariate logit regression?

Excuse my dumb question, but I did an univariate logistic regression where the sign of the coefficient of my variable was negative (and it was significant). Once I have input it into a multivariate ...
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107 views

Is it ever appropriate to put dependent variables in a model when they calculate the independent variable directly?

Is it ever appropriate to fit a multivariable regression model with dependent variables that directly calculate the independent variable? For example, I know that fitting a model to predict BMI by ...
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151 views

General linear hypothesis testing in repeated-measures multivariate linear model

In a multivariate linear model $Y = XB + U$, where within-subject (or repeated-measures) factors are coded as simultaneous response variables in $Y$, a general linear hypothesis can be formulated as ...
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71 views

Parameter space exploration

I do realise this question is quite specific and practical, but I seek for some general help which helps me progress further in my analysis. Let $y(\boldsymbol{x})\in\mathbb{R}$ be the function I'd ...
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1answer
113 views

Definition of multivariate regression coefficient

I know that the regression coefficient of $Y$ and $X$ is defined as $$\beta(Y,X) = \frac{\mathrm{Cov}(X,Y)}{\mathrm{Var}(X)}$$ Does this expression also hold in a multivariate regression with $Y$, ...
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152 views

Seemingly unrelated regression and multivariate Regression

I have a problem with an linear regression model in which I have 2 dependent variables. Both are highly correlated with each other and should both be explained by the linear model ...
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196 views

Multivariate response regressions vs many linear models

Would anyone be willing to venture an intuitive description of the situations under which a multivariate response model is more appropriate than many linear regressions? As an example, take a ...