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多元回归

具有多元响应变量的线性回归

函数

mvregressMultivariate linear regression
mvregresslikeNegative log-likelihood for multivariate regression
polytoolInteractive polynomial fitting
polyconfPolynomial confidence intervals
plsregressPartial least-squares regression

示例和操作指南

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.

偏最小二乘回归和主成分回归

此示例说明如何应用偏最小二乘回归 (PLSR) 和主成分回归 (PCR),并讨论这两种方法的有效性。当存在大量预测变量并且它们高度相关甚至共线时,PLSR 和 PCR 都可以作为建模响应变量的方法。这两种方法都将新的预测变量(称为成分)构建为原始预测变量的线性组合,但它们构建这些成分的方式不同。PCR 创建成分来解释在预测变量中观察到的变异性,而根本不考虑响应变量。而 PLSR 会考虑响应变量,因此常使模型能够拟合具有更少成分的响应变量。从实际应用上来说,这能否最终转化为更简约的模型要视情况而定。

概念

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.