There are a lot of Generalized Linear Model questions on here, but I couldn't find one that explicitly addressed this point.

The Wikipedia page starts out by saying:

[T]he generalized linear model (GLM) is a flexible generalization of ordinary linear regression that allows for response variables that have error distribution models other than a normal distribution.

However, the subsequent parts of the Wikipedia page drop the talk of non-normal errors and instead talk about non-normal responses, e.g.

The general linear model may be viewed as a special case of the generalized linear model with identity link and responses normally distributed.

I get that sometimes a non-normal response variable means that the errors must also be non-normal, but understand from this post that residuals can be normally distributed while the outcome variable is not. So why does Wikipedia bother talking about non-normal response variables?

  • 5
    $\begingroup$ See Logistic Regression - Error Term and its Distribution. Note that Wikipedia is talking about response variables that have non-normal distributions, conditional on the predictors. In ordinary linear regression, the outcome variable does have a normal distribution, conditional on the predictors: unconditionally it may be have any distribution at all. $\endgroup$ Commented Feb 29, 2016 at 13:40


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