----- Original Message -----
From: "Clive Nicholas" <[email protected]>
To: <[email protected]>
Sent: Wednesday, October 29, 2003 12:09 AM
Subject: st: ADDENDA
> Scott,
>
> Also, what's wrong with fitting a random-effects logit model? My models
> are identified at the respondent-level (as I think practically said just
> now!).
>
> C.
>
Nothing (as far as I know).
Perhaps, the expert you were referring to had Maddala on her mind. The
following quote is from Greene:
"Consider, as well, Maddala (1987) who states
'By contrast, the fixed effects probit model is difficult to implement
computationally. The conditional ML method does not produce computational
simplifications as in the logit model because the fixed effects do not cancel
out. This implies that all N fixed effects must be estimated as part of the
estimation procedure. Further, this also implies that, since the estimates of
the fixed effects are inconsistent for small T, the fixed effects probit model
gives inconsistent estimates for B as well. Thus, in applying the fixed effects
models to qualitative dependent variables based on panel data, the logit model
and the log-linear models seem to be the only choices. However, in the case of
random effects models, it is the probit model that is computationally tractable
rather than the logit model.' (Page 285)
While the observation about the inconsistency of the probit fixed effects
estimator remains correct, as discussed earlier, none of the other assertions in
this widely referenced source are correct. The probit estimator is actually
extremely easy to compute. Moreover, the random effects logit model is no more
complicated than the random effects probit model. (One might surmise that
Maddala had in mind the lack of a natural mixing distribution for the
heterogeneity in the logit case, as the normal distribution is in the probit
case. The mixture of a normally distributed heterogeneity in a logit model might
seem unnatural at first blush. However, given the nature of 'heterogeneity' in
the first place, the normal distribution as the product of the aggregation of
numerous small effects seems less ad hoc.)"
William Greene, 2001 Fixed and Random Effects in Nonlinear Models, page 14,
available at: http://pages.stern.nyu.edu/~wgreene/panel.pdf
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