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st: Model fit in fractional logit

From   Maarten Buis <>
Subject   st: Model fit in fractional logit
Date   Fri, 17 Jun 2011 09:37:23 +0200

Quoting Kim Young-Choon:
> I am using the fractional logit model in stata using glm,
> family(binomial) link(logit) robust.
> I am wondering what measure of model fit I should report in the
> result tables.
> While stata provides various fit measures such as chi-square, AIC,
> BIC etc, which model fit measure would you recommend?

I would try to stick as close as possible to what is normally used in
your discipline. All these statistics have their strengths and
weaknesses, so there is no consensus on which one is "the best".
Reporting such a statistic is however intended to convey information,
and it is easier for your audience to understand that information if
it corresponds to something they are used to. There is also a
pragmatic reason: that way you get less trouble with reviewers and
other gatekeepers...

> Is there any reference on model fit in the fractional logit or
> quasi-likelihood in general?

I like chapter 4 of James W. Hardin and Joseph M. Hilbe (2007)
Generalized Linear Models and Extensions, second edition. College
Station, TX: Stata Press.

> Based on my limited search, it appears that AIC is often used.
> In my case, I have nested models, i.e. Model 1 is a baseline model
> with control variables only; Model 2 is a baseline plus one or two
> independent variables of my interest; and so on.
> If I use AIC, can I evaluate the model fit improvement, e.g. between
> Model 1 and Model 2 (as we do in chi-square)?

You can compare models, but it does not have the same interpretation
as a statistical test. If you want a statistical test you can use the
full model and use -test- to test whether a block of coefficients is
simultaneously equal to zero (which is the same as leaving their
corresponding variables out of the model).

Hope this helps,

Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen
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