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Re: st: Choosing a family using glm


From   Laurie Molina <molinalaurie@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Choosing a family using glm
Date   Tue, 24 Aug 2010 19:36:10 -0500

Thank you again Phil, in fact i come from an econometrics background
but anyway i think i was confused so your help has been very useful.
The thing that i dont get is how you say that with the asumption of
error term with a normal (0,sigma2) distribution conditional on x, it
is implied that the conditional (on x) distribution of y is also
normal. I don´t know if i am asking a very simple question but i hope
you could help me on this. Is it true only if the x are non random? is
it a general result?
Again, thank you very much in advance.


On Tue, Aug 24, 2010 at 5:38 PM, Phil Schumm <pschumm@uchicago.edu> wrote:
> 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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