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Questions tagged [multivariate-regression]

Regression with more than one response (dependent) variable.

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Bayesian multivariate regression with repeated measures

I am trying to estimate variance components (specifically, genetic correlations) using mixed-effects models. My random effect is subject id and my dependent variables y1 and y2 are categorical scores ...
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Predicting continuous variable based on curve

I have a dataset of a set of curves measured at different frequencies, so it is composed of curves as the figure below for example. My dataset has many more curves of course. A curve is associated ...
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Deriving orthogonality of residuals without normal equation?

In my reading I stumbled across this page which seems to prove the expression for the OLS estimator using the fact that $X^T\hat{\varepsilon} = 0$. However I cannot seem to find a proof of this former ...
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Target encoding in linear regression

I have a dataset with the loss rates of each contract as dependent variable. As independent variables I have country (four values), profession (5 values) and income (continous variable). I apply ...
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Understanding the significance of a few results derived in the course of linear regression

I am reading up on linear regression from 18.650 MIT. In the way of explaining it, the professor derives a few results and I have attached them in the image The first result gets used along with the ...
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A question about linear regression results

This is from the lecture slides of mit 18.650 Here $\sigma^2$ is the variance of the error term ($\epsilon$) in the true model $Y = \beta X + \epsilon$ and $\hat{\beta}$ is the model's estimate of $\...
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Multivariate statistical criterion to select key variables

I have a complex dataset with several predictor variables $X_i$ ($i=1,...,m$) and several outcome variables $Y_j$ $(j=1,...,n$). The problem is that many of the predictor variables are correlated ...
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Terminology: multivariable when multiple levels of categorical variable?

Oftentimes, one sees people use terms such as univariate and multivariate logistic regression, where they clearly refer to number of predictors rather than number of response variables. I know it ...
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Univariate approach to a Bivariate logistic regression

Consider a situation where two independent agents (out of a set of many agents) look at the same problem and attempt to solve it with a yes/no response, obtaining $(Y_{i1},Y_{i2})$ for $i \in \{1,\...
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Multivariate Regression - Categorical and Continuous Outputs?

I am performing process characterization of a welder and want to put together a model of the inputs vs outputs of the system. Currently I am performing individual multiple regressions with 4 inputs (...
noah's user avatar
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Logistic regression - When to include or exclude a confounding variable from the model?

I am working on determining if there is an association between a medication (yes/no) and a health outcome (yes/no). However, the lines between what is a confounding variable to include in the model, ...
learning_890's user avatar
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How can I quantify uncertainty for a least squares estimator in a multivariate linear regression with covariance structure?

Suppose that we have $$\mathbf{y}\sim\text{N}(\mathbf{X}\boldsymbol{\beta},\sigma^2\mathbf{M}\mathbf{M}'),$$ and let $\boldsymbol{\hat{\beta}}$ be the least squares estimator for $\boldsymbol{\beta}$. ...
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How do I find all the independent variables for a time series regression model?

Suppose I have a single time-dependent variable $y_{t}$ (e.g. stock price) and a few hundred independent variables $X_{it}$ with data available for the same time frame as $y_{t}$ (e.g. company revenue,...
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meta-analysis of prognostic factor for models with different parameters

I am trying to meta-analysis the OR of a variable (troponin) for a dichotomous outcome (mortality). There are several multivariate logistic regressions out there, but none of them share the exact same ...
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How to multivariate regressors work?

while I seem to understand that there is a general matrix-based formula that allows us to solve for multivariate regressors, when looking at the non-matrix solution for a bi-variate $\beta$ I realised ...
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Linear Trend across Sessions and Timepoints: Which Matlab function?

I would like to test for linear a increase in performance in my training study using MATLAB. In this study each participant went through 6 training sessions, each session containing 4 time points of a ...
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How to model the additive components of a random variable whose value is known

I would like to model the variables $Y_1, Y_2, …, Y_n$, which satisfy the constraint $Y_1 + Y_2 + … + Y_n = Y$; where $Y$ (or at least an accurate estimate $\hat{Y}$ thereof) is readily available. ...
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Analysis of multivariate ranking data

I have data on companies, each company ranks how important are the following 4 elements (price leadership, quality, innovation, and customization) for its competitive strategy. There are 4 dependent ...
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"Smooth" multivariate regression

I'd like to model $$y_t = X \beta_t + \epsilon$$ where the predictors are powers of a single variable $x$ (this should be polynomial regression), and I have data for multiple time points $t$. I know ...
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What does small optimism in predictor effect mean?

I'm reading the following paper by Burke et al. Minimum sample size for developing a multivariable prediction model: Part I – Continuous outcomes The paper discusses the minimum number of samples ...
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Hyperparameter tuning and initialisation doubts in multivariate gaussian process model

I'm trying to train a multivariate Gaussian Process model using the code here https://github.com/Magica-Chen/gptp_multi_output. However I noticed how problematic is to initialise the length scales of ...
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Confused about multivariate analyses

I have a dataset with three categorical predictors and four continuous response variables. The response variables are various measurements of the subjects' behaviour and they are fairly highly ...
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Use centered variables or include an intercept in time series analysis?

I have read that analogous to univariate AR(p) models, there are two possibilities to allow for a non-zero mean with VAR(p) models: a) either use centered variables in the model: Φ(B)(Xt − μ) = Zt b) ...
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estimate household expenditure pattern using a multivariate regression model, or other approach?

I am working on my school project, is about the study of household expenditure pattern using regression approach. Say that I having following linear ols regression model, where y is household ...
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How can I combine model parameter uncertainty and input uncertainty?

Suppose I have a finite data sample $\mathbf{S} = \{ (\mathbf{x}^{(1)}, \mathbf{y}^{(1)}), \dots, (\mathbf{x}^{(N)}, \mathbf{y}^{(N)}) \}$ from an unknown data-generating function of the form $$ \...
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Minimum number of observation in multivariate regression

Given a multivariate regression, in a form bellow, what would be the minimum number of observations ($n$)? $$\mathbf{Y}=\mathbf{X}\mathbf{B}+\mathbf{E},$$ where $\mathbf{Y}, \mathbf{X}$ and $\mathbf{E}...
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How can I generate bootstrap confidence intervals for a multivariate regression network?

I am reading "Confidence Intervals and Prediction Intervals for Feed-Forward Neural Networks" by Richard Dybowski. In this paper, an ensemble of neural networks are trained on bootstrapped ...
Jacob's user avatar
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2 votes
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Test for multivariate regression coefficients

Given a multivariate regression, how can I test if each element in the coefficient matrix is statistically significant? Would doing a t-test be right? $$\mathbf{Y}=\mathbf{X}\mathbf{B}+\mathbf{E},$$ ...
statwoman's user avatar
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Performing 3 multivariate linear regressions at once

I have 3 variables X, Y and Z. I want to perform 3 OLS regressions: X dependent on Y and Z, Y dependent on X and Z, and Z dependent on X and Y. Instead of doing the 3 of them sepparately, I want to ...
Hiperfly's user avatar
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Heteroscedasticity robust variance-covariance matrix for weighted multivariate regression

I need heteroscedasticity robust standard errors for a multivariate linear model (MLM) with weights. In R we usually use sandwich::vcovHC with type ...
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Logistic Regression models with two or more response variables in R/SAS

There are a lot of inconsistencies in the literature over what should be the appropriate term(s) for the regression models involving two or more responses, and if they are binary/continuous, for more ...
AAA's user avatar
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MSE for multivariate case

This is very basic, but I want to clarify the MSE in a vector-valued setting. Given observations $$ \begin{bmatrix} [x_1, y_1,z_1] \\ \vdots \\ [x_n, y_n,z_n] \end{bmatrix} $$ And estimations $$ \...
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Python / R package for multivariate gaussian process regression for circular data?

I have two circular predictor features (two angles between 0 and 360 degrees) and a circular outcome (another angle, between 0 and 360 degrees). I'd like to be able to fit a model and get predictions ...
ach's user avatar
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Which Cox PH model for different treatments and sites

I am building a Cox PH model in r to analyze my data and I am unsure what the best way to do it is. It is observational data and the idea is that we want to know the effect of a treatment A used at ...
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Can I use the multivariate response predictions of some variables as covariates to predict another correlated response?

I have covariates to predict 3 multivariate response variables, and would like to use those 3 predictions to predict another forth variable that is also correlated with the other variables: ...
vie2bgd's user avatar
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1 answer
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Can I combine dichotomous and continuous outcomes into a single regression model?

I am doing analysis on an educational product that aims to predict what impacts whether or not a student gets a question correct or incorrect. The DV includes item scores from four different question ...
Mezy's user avatar
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How do I model relative time spent doing different behaviours?

I have a dataset comprising observations of ducks performing different behaviours. Specifically, ducks were observed for 1 minute each, and during each 1 minute observation the amount of time that ...
willpkay's user avatar
1 vote
1 answer
303 views

Multivariable Cox Regression Analysis

I would like to know if in multivariable Cox regression analysis there is a way to yield only models that include a variable of interest (and if no model is statistically significant to just answer ...
Elodie's user avatar
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1 answer
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Multivariate regression and process control

I have a question regarding process control with the use of multivariate regression. The setup is as follows: say we have some data, representing the results of a plant process. Specifically, several ...
krzysiekb's user avatar
1 vote
1 answer
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interaction term in Cox PH model

I have a question with regard to interaction term in Cox PH model. I'd like to analyze the impact of variable A on cardiovascular (CV) event. Variable A levels are different according to sex, although ...
doyle's user avatar
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2 answers
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How to calculate a cross-product like R^2?

$\lbrace Y_1, Y_2, \boldsymbol{X} \rbrace$ are jointly normally distributed (it is not essential to assume normality, I think). Let $\Sigma_{X}$ be the variance-covariance matrix of $\boldsymbol{X}.$ ...
user67724's user avatar
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5 votes
1 answer
299 views

How to construct a confidence interval for the coefficients of a multivariate regression with dependence between dependent variables?

Suppose we have two linear regression models $y_1=a+bx+\epsilon_1$ where $\mathbb[\epsilon_1]=\sigma_1$ and $y_2=c+dx+\epsilon_2$ where $\mathbb[\epsilon_2]=\sigma_2$. In other words, I am using the ...
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Extracting factors of a large (dimension m,n) matrix M which correlate with a vector P (length m)

So I'm dealing with a large gene expression dataset (m sample by n genes, where m ~ 1000 and n ~ 20,000). For each of these samples, a phenotype of interest P exists. I'd like to be able to say ...
Dermot Harnett's user avatar
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250 views

Adjusted $R^2$ (R-squared) for multivariate regression

For univariate or single independent variable regressions, this formula can be used (details here): $$R^2_{adjusted} = 1- \dfrac{SSRes}{SSTotal}\dfrac{n-1}{n-p}$$ However, I cannot find a similar ...
Bernardo Costa's user avatar
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Working with a Dataset containing multivatiate numerical Timeseries which is highly sparse

I am working currently on a private dataset that has a similar structure to MIMIC-III. The dataset has following structure: p Patients, e Examinations, t Timepoints For every patient there are ...
Alex's user avatar
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1 answer
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I have set of features to relate to two different values. When I made a regressor for only one it worked well but if i use two it does not?

I have a set of 33x1 features (x) and they can be related to different two values in (y) and I have 1203985 observations. Using np.shape() you can see the dimensions of x and y. x= (1203985, 33) y=(...
Hamzalihi's user avatar
3 votes
3 answers
6k views

Visualizing multivariate multiple regression of continuous data in R

I have created a multivariate multiple regression model with 3 dependent and 3 independent variables in R, and would like to generate meaningful visualizations. All variables are continuous. When ...
sethparker's user avatar
1 vote
1 answer
44 views

Multivariate Regression with Two Different Types of Response

Problem Setting: I have an interesting question related with longitudinal study and multivariate regression. I found that in lots of biomedical studies, multiple discrete and continuous endpoints are ...
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How analyze annual data with one IV and multiple DVs

I'm currently working with a data set that includes multiple variables associated with each of 10 years of data. The basic structure, with (example hypothetical) variables in caps, is from YEAR to ...
DaGu's user avatar
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2 votes
1 answer
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Multivariate regression - test difference between coefficients

I am trying to figure out how to test the difference in slopes for the same explanatory variable in a multivariate linear regression. What type of test should be used and how can I perform this using ...
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