clogit: the source of model specification error?

[Chan Ge]

Dear all,
Could anyone please help me with a question? I'm estimating a conditional logit model. My question arises from the impact of the inclusion (exclusion) of a variable (VAR1) on model fit (here I refer to the statistical significance of link test _hatsq ).
The issue is: _hatsq is statistically significant if I include VAR1 in the model while _hatsq is statistically insignificant if I exclude VAR1. Moreover, when I include VAR1, the coefficient of VAR1 is statistically significant.
What do the results tell about the model specification and VAR1?
How may I proceed with specifying and estimating an appropriate model?
Thank you ahead!

[George Ford]

The first thing that comes to mind is that absent VAR1, you're model isn't very compelling. With it, it is more so. Do any of the other coefficients change size/significance when VAR1 is included?

Does VAR1 have some special relationship to Y?

[Chan Ge]

Hi George, yes, including VAR1 influences the magnitudes of some other coefficients. Could you please illustrate "the model is not compelling"? is it under-specified, over-specified, or otherwise mis-specified? The VIF suggests that the model with demeaned variables are not subject to multicollinearity concern.
Regarding both Pearson and Spearman correlations, VAR1 is significantly (p<0.01) and negatively associated with Y. Would you recommend me to assess any other statistical relationships with Y?
Thank you!

[George Ford]

Sorry. I was thinking GOF test.

The hatsq statistic should not be rejected. So including suggests it adds some type of specification error. Could try some quadratics if continuous. Specification tests are pretty sensitive to functional form.

[Chan Ge]

Sorry. I was thinking GOF test.

The hatsq statistic should not be rejected. So including suggests it adds some type of specification error. Could try some quadratics if continuous. Specification tests are pretty sensitive to functional form.

Thank you George.

[Chan Ge]

Sorry. I was thinking GOF test.

The hatsq statistic should not be rejected. So including suggests it adds some type of specification error. Could try some quadratics if continuous. Specification tests are pretty sensitive to functional form.

Hi George,

I have a new question on the same issue. The variable (an indicator for two firms headquartered in the same state) has a larger within-FE variation than pooled variation. How does including such a variable in a conditional logit model (or another fixed effect model) influence the model fit? Is it appropriate that I just exclude the variable? That variable is actually quite commonly included in the regressions in my line of research (not as granular as my FE level). Thus, I hesitate directly excluding it. If I relax the FE level to a larger group, including the variable passes the link test (hatsq is insignificant).

A follow-up summary question is: do you recommend using a larger-group FE or exclude the variable at the granular-group FE?
Thank you ahead for your insights.

[George Ford]

I do not know, honestly. I guess there is no natural FE level so you have options. Do other variables seem much affected by FE at different levels?

[Chan Ge]

I do not know, honestly. I guess there is no natural FE level so you have options. Do other variables seem much affected by FE at different levels?

Thank you a lot George.
This variation pattern occurs in the sample of one set of analyses. For this subsample, yes, if I relax the FE level, a continuous variable reports a larger within-FE variation than pooled variation.
I took a further look into the impact of this variable in other matched samples today. The variation pattern does not occur in other matched samples. But the link test results of including the variable CState still occur.
Does the above sound that there is something to do with the relation between CState and other explanatory variables and the outcome based on the data?
Thank you.

[Chan Ge]

Hi George, thank you for your help so far. I think it comes to a point that I need to exercise my judgment based on the underlying theoretical relationships and analyses practices in the research area. Your help and time on this post are highly appreciated.