Questions tagged [multivariate-regression]
Regression with more than one response (dependent) variable.
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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},$$
where $\mathbf{Y}, \mathbf{X}$ and $\mathbf{E}...
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HAC Robust Errors - Simple Static Time Series Regression
We're working with Wooldridge Econometrics without matrix algebra.
My professor introduces a simple static time series model:
$$y_t = \beta_0 +\beta_1x_t+u_t$$
In the presence of serial correlation, ...
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Is multivariate probit the right approach?
I am interested in what determinants may drive a car manufacturing firm to sell its products only in specific countries. The same car can be available for sale in countries A and B but not in country ...
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How can I generate bootstrap confidence intervals for a multivariate regression network?
I am reading "Confidence Intervals and Prediction Intervals for Feed-Forward Neural Networks" by Richard Dybowski. In this paper, an ensemble of neural networks are trained on bootstrapped ...
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Test for multivariate regression coefficients
Given a multivariate regression, how can I test if each element in the coefficient matrix is statistically significant? Would doing a t-test be right?
$$\mathbf{Y}=\mathbf{X}\mathbf{B}+\mathbf{E},$$
...
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Multivariate regression with constrained target
Consider the multivariate regression $Y = (\hat{y}_1, \hat{y}_2) = f(x_1,\ldots,x_n, y_1/y_2) = f(X)$; as we see, the ratio of outputs $\frac{y_1}{y_2}$ is among the inputs $X$, thus a trained model ...
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Performing 3 multivariate linear regressions at once
I have 3 variables X, Y and Z. I want to perform 3 OLS regressions: X dependent on Y and Z, Y dependent on X and Z, and Z dependent on X and Y.
Instead of doing the 3 of them sepparately, I want to ...
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How to handle multiple multivariate timeseries?
I am trying to develop a model using machine learning that reproduces a biological behavior. My goal is to do a regression of timeseries e.g from multiple input each time_step predict multiple output ...
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Heteroscedasticity robust variance-covariance matrix for weighted multivariate regression
I need heteroscedasticity robust standard errors for a multivariate linear model (MLM) with weights. In R we usually use sandwich::vcovHC with type ...
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Logistic Regression models with two or more response variables in R/SAS
There are a lot of inconsistencies in the literature over what should be the appropriate term(s) for the regression models involving two or more responses, and if they are binary/continuous, for more ...
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MSE for multivariate case
This is very basic, but I want to clarify the MSE in a vector-valued setting.
Given observations
$$ \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 ...
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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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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 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 ...
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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 ...
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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 ...
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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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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 ...
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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 ...
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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=(...
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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 ...
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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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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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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-...
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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.
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When should multivariate GLM(M)s be used?
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 ...
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Signs of MarginalEffects and CoefficientEstimates in Multivariate Probit
Could someone explain that the sign of coefficient estimates and their corresponding marginal effects in the Multivariate Probit Model is the same or they could be different? IF they are different, ...
