general linear models vs. generalized linear models

General linear models vs. generalized linear models

• Wikipedia: Comparison of general and generalized linear models (modified)

	General linear model	Generalized linear model
Typical estimation method	Least squares, best linear unbiased prediction	Maximum likelihood or Bayesian
Special cases	ANOVA, ANCOVA, MANOVA, MANCOVA, ordinary linear regression, mixed model, t-test, F-test	linear regression, logistic regression, Poisson regression, gamma regression
Function in R	lm()	glm()
Function in Matlab	mvregress()	glmfit()
Procedure in SAS	PROC GLM, PROC MIXED	PROC GENMOD (PROC LOGISTIC for logistic regression only), PROC GLIMMIX Comparing the MIXED and GLIMMIX
Command in Stata	regress	Stata Generalized linear models
Function in Mathematica	LinearModelFit	GeneralizedLinearModelFit
Command in EViews	ls

• Generalized linear models have the flexiblility for response variables that have other than a normal distribution. If a generalized linear model uses an identity link function and a normal family distribution, then this model is equivalent to a general linear model.
• Generalized linear mixed models have the flexibility to model random effects and correlated errors for nonmormal data.