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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 > > * > * For searches and help try: > * http://www.stata.com/help.cgi?search > * http://www.stata.com/support/statalist/faq > * http://www.ats.ucla.edu/stat/stata/ > * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: Choosing a family using glm***From:*Laurie Molina <molinalaurie@gmail.com>

**Re: st: Choosing a family using glm***From:*Phil Schumm <pschumm@uchicago.edu>

**Re: st: Choosing a family using glm***From:*Phil Schumm <pschumm@uchicago.edu>

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