# 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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1 vote
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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 ...
27 views

### 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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### 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 (...
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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, ...
31 views

### 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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1 vote
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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 ...
13 views

### 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 ...
1 vote
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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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1 vote
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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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1 vote
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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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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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1 vote
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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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1 vote
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1 vote
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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 ...
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1 vote
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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: ...
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281 views

### 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 ...
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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 ...
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### 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 ...
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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 ...
1 vote
86 views

### 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 ...
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1 vote
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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 $\boldsymbol{X}.$ ...
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### 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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1 vote
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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 ...
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 ...
41 views

### 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 ...
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1 vote
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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=(...
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 ...
1 vote
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### 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 ...
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