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Re: st: Choosing a family using glm


From   Phil Schumm <pschumm@uchicago.edu>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Choosing a family using glm
Date   Tue, 24 Aug 2010 17:38:22 -0500

On Aug 24, 2010, at 4:14 PM, Phil Schumm wrote:
To my understend in a clasical linear regression the asumption of normality is in the distribution of the error term, but in glm the asumption defined by the family selection is on the distribution of the dependent variable. Isnt that a huge cost for using glm instead of a clasical linear regression model?


You are laboring under a misunderstanding. To say that the distribution of Y conditional on X is Normal with mean XB and variance sigma^2 is the same as saying that the distribution of the errors (i.e., Y - XB) is Normal with mean 0 and variance sigma^2. And to emphasize the GLM approach, what is most important (if you're fitting a linear regression) is that the mean is XB and the variance is constant (i.e., that your assumptions about the first and second moments are correct).


It just occurred to me (and I should have thought of this initially, given that your data are on housing rents) that you may be coming from an econometrics background rather than statistics. If so, you may have seen linear regression developed without taking X to be fixed but rather in terms of assumptions regarding the error term (e.g., conditional on X, the errors have mean zero and constant variance). This is a different approach from that normally taken in basic statistics texts, where the covariates are treated as fixed and the assumption that the errors are uncorrelated with the covariates is treated as definitional rather than scrutinized (note, however, that these two approaches lead to many of the same basic results). Generalized linear models are normally presented from the perspective of the latter approach (e.g., as in the book Generalized Linear Models by McCullagh and Nelder, or in [R] glm).

I only mention this in case it may have been partly responsible for your confusion.


-- Phil

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