# Questions tagged [multivariate-regression]

Regression with more than one response (dependent) variable.

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12 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 ...
26 views

### 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 ...
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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### 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) ...
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 ...
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 ...
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 ...
1 vote
29 views

### 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: ...
175 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 ...
1 vote
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### How do I model relative time spend 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 ...
1 vote
201 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 ...
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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
53 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 ...
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 $\boldsymbol{X}.$ ...
246 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 ...
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 ...
165 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 ...
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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 ...
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=(...
4k 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 ...
169 views

### 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 ...
195 views

### What does an interaction with a confounder mean within a multivariate regression analysis?

In a multivariate regression analysis, I examine the effect that a treatment method has on subjects' hemoglobin levels. Since this is a retrospective study, I could not control for gender (or age) by ...
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### Auto. Arima and ARIMAX for multi variate time series forecasting

I'm trying to do multivariate time series forecasting using the forecast package in R. The data set contains one dependent and independent variable. From the cross-correlation the 0 day lag of the ...
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### ARIMAX and auto.arima for multivariate time series forecasting in R

I'm trying to do multivariate time series forecasting using the forecast package in R. The data set contains one dependent and independent variable. From the cross-...
1k views

### Linear regression with vector outputs

Suppose I wanted to make a linear fit to a dataset with vector input and output, by minimizing the least square error. Then the square error equation would be E = \frac{1}{2}\sum_i(W\vec{x}^{(i)} - \...
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### Determine if two groups differ for a series of binary variables - logistic regression

I am trying to determine how to analyze my dataset. I have two stimulus categories (Type 1 and Type 2) and then a series of variable observations that are binary (did respond/didn't respond, did ...
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### How is this equation deduced?

These two equations are from the book Gaussian Process for Machine Learning. First we already have equation (2.8). $p(\mathbf{w}|X, \mathbf{y}) ∼ N (\frac1{\sigma_n^2}A^{−1}X\mathbf{y}, A^{−1})$ (2.8) ...
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### How to choose the right variables for the logistic regression in an observational study?

I have read answers to the similar questions here and read other resources but I could not find a solid answer to this point. Sorry for my simple terminology. While analyzing the data from an ...
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### Binary logistic regression model shows unrealistic OR and 95% CI

I've just done a multivariate regression analysis, using a p-value from bivariate regression analyses of <0.20 as a cut-off to determine which variables will be included in the multivariate model. ...
Suppose I have a set of $k$ dependent variables which are all correlated with each other and known a priori that they are dependent. I also have a set of $p$ independent variables (predictors) which ...