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Questions tagged [multivariate-regression]

Regression with more than one response (dependent) variable.

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Write Lack-of-fit Sum of Squares in Quadratic Form

Let \begin{equation} SSLF = \sum_{i=1}^{m}n_{i}(\bar{y_{i}} - \hat{y_{i}})^{2} \end{equation} then \begin{equation} \sum_{i=1}^{m}n_{i}(\bar{y_{i}} - \hat{y_{i}})^{2} = n(\bar{\overrightarrow{y}} -...
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28 views

Integrated mixed model testing correlation and difference in correlation across factors

I'm currently performing the following analysis : Computing $r_j(Y_{ij}, X_{ij})$ for each design cell (factor with level 1 or 0 for each unit) Estimating effect of factor on $r(Y,X)$ with a linear ...
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1answer
16 views

Null hypothesis for individual coefficient's p-value in multivariate logistic regression

When calculating $p$-values for individual coefficient $a_i$ (for variable $X_i$) in a multivariate logistic regression, is the null hypothesis that all $a$'s are zero? that $a_i$ is zero and others ...
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Testing for Heteroscedasticity of Multivariate Multiple Regression [closed]

I want to test for heteroscedasticity on a regression model with multiple dependent variables using R. I want to see if the indenpendent variable has an effect on the variance of all of the dependent ...
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1answer
32 views

Linear regresson with four values as input and two values as output

I have the following problem for a personal project of mine: I am solving a system of two differential equations that has 4 changing parameters. The output are two vectors of numbers. Let's say I am ...
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17 views

Multivariate regression vs. multiple univariate regression models

This is a naive question, but I am a little confused over the term "multivariate" regression. And note this question does not (to my knowledge) pertain to "multiple" regression. When people use the ...
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20 views

thin-plate spline projection pursuit regression?

Is projection pursuit regression limited to univariate smoothing splines only? I am essentially looking for a multivariate ppr method. Is there such a method that searches for the most curved surfaces ...
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Default inferential methods for multivariate exploration or model checking

What are your default methods to explore or understand a multivariate relationship between let us say a fixed outcome $Y$ and a limited set of explanatory variables $X_i$ ($i=1,…,n$) (with $k$ not too ...
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31 views

multivariate linear regression without b_0 [duplicate]

I created a multivariate regression following the scheme $$y = \beta_0 + \sum^n_{i=1}\beta_i*x_i$$ and got an average deviation ofaround 5%. When I tried the regression without the $\beta_0$ I got a ...
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33 views

multi-response outcome: multivariate or univariate regression?

I have a dependent variable which represents participants' responses on 20 words, coded as 1 = correct , 0 = incorrect Question: I am keeping the regression as univariate for now (as far as dependent ...
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98 views

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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38 views

Suppression Effect or Something Else?

I am working on a project using multivariate regression where I have an independent binary variable exerting a non-significant effect on my dependent variable. However, upon inclusion of another ...
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22 views

Multivariate Out-of-Sample Evaluation

I have a question about multivariate hypothesis testing in out-of-sample evaluations. Generally, let`s asssume we want to predict three different stock returns in a 1-month ahead forecasting setting. ...
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16 views

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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2answers
54 views

$R^2$ and p-value for multivariate linear regression with confounders

I am working on a project where I am interested in the following variables: Dependent variables: $y_1,\, y_2,\, y_3,\, y_4,\, y_5$ (continuous) Independent variables: $x_1,\, x_2, \ldots,\, x_{18}$ ...
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1answer
81 views

Conjugate priors for dynamic model $x_{t+1}=Ax_{t}+\eta_t$

What conjugate priors do we have for the model(multivariate) $x_{t+1}=Ax_{t}+\eta_t$, where $\eta_t\overset{iid}\sim N(0,\Sigma)$? I was thinking of using $\tilde{x}=Diag[x_1,...,x_{n-1}]$, $\tilde{y}...
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54 views

Different method for parameter estimation auto.arima

I am trying to fit a multivariate time series with the auto.arima() function in R. Since my time series has seasonality I included Fourier approximation and used ...
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14 views

Distribution of maximum variance explained by 1 variable

Say I do principal component analysis on $n$ variables, and I sort the fractions of variance explained to find the largest. What is the probability distribution for this figure? For context I just ...
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1answer
47 views

What is the best way to test and validate a multivariate regression using OLS?

I am implementing a multivariate regression from scratch using Ordinary Least Squares to get the weights. I noticed that this method does not have any hyperparameters to tweak, so I am not sure what I ...
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31 views

What plots and summary statistics are usually used for exploratory data analysis of multivariate time series?

For multivariate cross-sectional data, tools such as scatterplot matrices, the five numbers summary, faceted boxplots and so on, allow an efficient exploration of a new data set, and can suggest how ...
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Using the Volume of Sales obtained today to predict volume of Sales at the Event

I wonder if anyone can help. I have a set of data on event ticket sales. I have information on eventdate, location, capacity, cumulative sales, sales date, total sales. I want to be able to build a ...
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36 views

Multivariate categorical linear models

I've got a real-valued normalised input with around 300 dimensions (features). The output is a two-dimensional categorical variable. And I want to perform feature-selection on the input space. So far ...
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20 views

What are the novel techniques for multivariate response prediction?

What are the novel techniques of multivariate response prediction? Are there any GAM model versions for multivariate predictions?
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1answer
171 views

forward model selection on multivariate polynomial regression with high dimension data

I am trying to fit the best multivariate polynomial on a dataset using stepAIC(). My problem is that I have more variables (p=3003) than observations (n=500), so ...
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1answer
108 views

Variance of linear combinations of Normal RVs in linear regression

I am working with a standard multivariate linear regression model ($Y = X \lambda + \epsilon$, $Y$ and $\epsilon$ of length $n$, $X$ is $n$ x $m$, $\lambda$ of length $m$). $X$ is said to be "column-...
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1answer
73 views

Multivariate Power Function Regression Analysis of Data Set with Two Dependent Variables

I have been struggling to create a general equation for a data set with two dependent variables. I have been trying to use excel to model the equation but I am unable to match my data set. Using ...
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1answer
173 views

Predicting a single response variable with a multivariate regression model

For my research I am interested in performing inferential and predictive analysis on a single response variable. I have already made one univariate and one multivariate regression model. In the ...
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2answers
75 views

Bivariate/multivariate models for multinomial response variables

I need to fit two categorical (potentially correlated) response variables (each has three classes) on a set of explanatory variables, while considering for the response variables' correlation. What ...
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25 views

Is there a way to compare the same multivariate regression model for two groups?

I am conducting a multivariate regression with three outcome variables and several predictors. Is there a way to see if the overall model and each predictor are equivalent in two different groups?
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33 views

How to perform Feature selection and Shrinkage on multivariate data using Lasso?

Data description: The data is the electricity consumption of three months for each hour. The outcome is the value observed at the source and there are eight sources The indepdent variables are the ...
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1answer
41 views

How to determine the type of regression to be used? [closed]

I am relatively new into the machine learning field and I came up with the following problem that is giving me some headaches, so any help on it would be greatly appreciated for my inner peace. ...
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38 views

Multivariate Generalized Linear Mixed Models within Bayesian framework

Can anyone recommend an accessible online text where I can learn about Multivariate Generalized Linear Mixed Models within a Bayesian framework? I have been able to find three pdfs on the subject (...
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Is there a GRS (or GMV) statistic in R to test the portfolio efficiency of adding test assets to a benchmark portfolio?

There are many ways to test the efficiency of a portfolio where the particular test statistic tests whether adding a couple of test assets to the portfolio that consists of 1 or more benchmark assets ...
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multivariate cox regression - combining genotypes for each SNP

For 53 SNP I have coded genotypes as 0 for aa, 1 for ab, and 2 for bb for 29 samples and I have outcome and time to outcome. Here outcome is called "BCR" below. I am using the survival package in R ...
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Geometric intuition of residuals sample variance as a ratio of two determinants

We are estimating a regression $$ y_i = \hat\beta_1 + \hat\beta_2 x_i + ... + \hat\beta_k z_i + \hat u_i $$ I am searching for the geometrical intuition behind the formula $$ sVar(\hat u) = \frac{\...
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69 views

Multivariate Regression with Uniform Errors

I'd like to know if there is a multivariate regression model with uniform errors. More specifically, I'd like to find the Maximum Likelihood Estimators for $\beta^a$ and $\beta^b$. The model is given ...
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93 views

Multivariate model LMER

I have 3 outcome variables that I'm working with and I'm trying to model them as a function of two factors lmer. I have some intuitions on how I should fit the model, but I'm wondering if I could get ...
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16 views

How to forecast potential growth with increased rate?

I want to create a formula, which will solve my problem! I have the client A from 2013 till now. I help him to sell via 8 Publishers. Those are the following: ...
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2answers
305 views

Logistic regression with multiple outcome variables (all categorical)

I am completely in over my head with logistic regression at the moment, so what follows is probably very basic and silly questions. But I would appreciate it hugely if anyone took the time to respond ...
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3answers
154 views

Estimating the contribution of covariates in a boral latent variable model

I'm attempting to use latent variable modelling, as described by Hui (2016) and using the boral package in R, to explore relationships between plant species composition and environmental variables ...
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What is the added benefit of conducting a “multivariate multiple regression” over several “multiple regressions”? [duplicate]

SPSS, Stata and SAS can all conduct multivariate multiple regressions (i.e. more than 2 continuous predictors and more than 2 outcomes) as GLM. Consequently, the multivariate tests answers the ...
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54 views

Interpreting the correlations between linear and quadratic random effects in multivariate multilevel modeling

I'm interested in a simple (unconditional) multivariate multilevel growth curve model encompassing two dependent variables recp and recm. I ran this model using Paul Bürkner's brms package in R (...
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2answers
53 views

R-Square Change in a Multivariate Regression

I am investigating whether the predictive validity of the Big Five personality traits can be improved by controlling for sources of self-report error (e.g. memory, interpretation biases, ect.). I am ...
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1answer
369 views

Multiple dependant variable in multiple linear regression [duplicate]

I have 8 independant variables and 2 dependant variables.Iam using multiple linear regression.I just finished the regression topic so iam a starter in this.Can anyone say how to approach this one??
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1answer
86 views

How to interpret mean squared error matrix in the context of multiple time series?

Consider the time series of 2 variables $x_1$ and $x_2$, put together $y=(x_1,x_2)$: $$ y_t = \begin{bmatrix} v_1\\ v_2 \end{bmatrix} +\begin{bmatrix} c & d\\ e & f \end{bmatrix}y_{t-1} + u_t....
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1answer
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What do you call variable that switches on/off the effect of another?

Suppose we have a model $Y = \beta_1 X_1 + \beta_2 X_1X_2 + \epsilon$ Hence $X_1$ has an effect on $Y$ regardless of the value of $X_2$, but $X_2$'s effect on $Y$ is mediated or enabled by $X_1$. ...
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1answer
70 views

Regression predicting 2 dependent variables

Imagine I have a big dataset $\textbf{X}$ that constitutes my independent variables and I want to predict a vector of 2 components, $\mathbf{Y} = (y_1, y_2)$. A regression will be something like $\...
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25 views

Multiple imputation when have more than 1 outcome variable

Is there a good paper or reference for doing multiple imputation when there is more than one outcome variable? Anything that specifically addresses building the imputation model or software to use for ...
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1answer
93 views

time series mainly characterized by structural breaks - how to model?

I am given a financial time series that is characterized by a bunch of structural breaks, i.e. the series isn't moving (literally at all), but at some points in time the series jumps up or down. Then ...
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2answers
1k views

gaussian process regression for large datasets

I've been learning about Gaussian process regression from online videos and lecture notes, my understanding of it is that if we have a dataset with $n$ points then we assume the data is sampled from ...