Multivariate Linear Regression
When you need to include more than one response variable in a regression
model, use a multivariate linear regression model. A multivariate linear
regression model expresses a d-dimensional continuous
response vector as a linear combination of predictor terms plus a vector of
error terms with a multivariate normal distribution. You can use mvregress to create a
multivariate linear regression model.
Partial least-squares (PLS) regression is a dimension reduction method
that constructs new predictor variables that are linear combinations of the
original predictor variables. To fit a PLS regression model that has
multiple response variables, use plsregress.
Note
A multivariate linear regression model is different from a
multiple linear regression model, which models a univariate
continuous response as a linear combination of exogenous terms plus
an independent and identically distributed error term. To fit a
multiple linear regression model, use fitlm or fitrlinear.
Functions
mvregress | Multivariate linear regression |
mvregresslike | Negative log-likelihood for multivariate regression |
plsregress | Partial least-squares (PLS) regression |
Topics
- Set Up Multivariate Regression Problems
To fit a multivariate linear regression model using
mvregress, you must set up your response matrix and design matrices in a particular way. - Multivariate General Linear Model
This example shows how to set up a multivariate general linear model for estimation using
mvregress. - Fixed Effects Panel Model with Concurrent Correlation
This example shows how to perform panel data analysis using
mvregress. - Longitudinal Analysis
This example shows how to perform longitudinal analysis using
mvregress. - Partial Least Squares Regression and Principal Components Regression
Apply partial least squares regression (PLSR) and principal components regression (PCR), and explore the effectiveness of the two methods.
- Multivariate Linear Regression
Large, high-dimensional data sets are common in the modern era of computer-based instrumentation and electronic data storage.
- Estimation of Multivariate Regression Models
When you fit multivariate linear regression models using
mvregress, you can use the optional name-value pair'algorithm','cwls'to choose least squares estimation. - Partial Least Squares
Partial least squares (PLS) constructs new predictor variables as linear combinations of the original predictor variables, while considering the observed response values, leading to a parsimonious model with reliable predictive power.
