Generalized linear models (GLMs) allow the response variable to have arbitrary distributions using a link function

Generalized least squares account for errors that are heteroscedastic and correlated.

But is generalized least squares a special case of GLMs? or are they two different methods altogether?


2 Answers 2


As said, those are generally two different things.

GLM framework = link function + other distribution than normal

GLS framework = generalizes the iid normal in LM to a multivariate normal, which allows specifying correlations between the residuals + change of dispersion (in R, this is easiest done with nlme, which provides several corClasses to specify correlation structures, and the varFun function to specify a formula for the dispersion)

However, it is possible to mix both ideas, i.e. specify a GLM(M) with a GLS-type correlation term (as a random effect) on the linear predictor, e.g. to account for spatial autocorrelation in GLMs, as, e.g., done in glmmPQL.


No, these are two different things. GLMs are models whose most distinctive characteristic is that it is not the mean of the response but a function of the mean that is made linearly dependent of the predictors.

GLS is a method of estimation which accounts for structure in the error term. An ordinary linear model could be estimated by GLS if you think that errors are not independent and homoscedastic.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.