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I heard a remarkable claim at work last week

Fixed effects in logistic regression of panel data introduces bias, so we would want to do a linear probability model.

I find this remarkable for two reasons.

  1. The usual maximum likelihood estimator for a logistic regssion is biased, so if you are intolerant of biased estimators, the usual logistic regression was never for you.

  2. The whole point of GLMs is that they do so much similar to linear models, just with a nonlinear link function, and the proposed alternative of a linear probability model is exactly such a model.

What's the deal with including fixed effects in a logistic regression on panel data? (Why) Does such inclusion cause problems in a logistic regression but not in a linear regression?

Dave
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  • ad 1, if it only were bias, I would agree, but as it turns out, when the number of waves is small and asymptotics are done, as is common, with respect to the number of units in the panel, FE logit is even inconsistent. One would need to resort to conditional (on a sufficient statistic) ML instead. See e.g. https://www.sciencedirect.com/science/article/abs/pii/S016517659700044X

    ad 2, I would agree, running away from one problem only to run into a potential other (i.e. a linear model for a probability) need not be an improvement...

     – Christoph Hanck Jan 30 '23 at 15:21
  • In a nutshell (at least how I think of it, fwiw), the MLEs for the individual-specific effects and the slope coefficient of interest are not independent, which, unlike in a conventional linear panel model, also leads to the slope coefficient being "polluted" by the estimates for the individual-specific effects which can only be found from a finite number of waves of a panel and hence will not be estimated consistently. – Christoph Hanck Jan 30 '23 at 15:28
  • @ChristophHanck I'm trying hard to reconcile this with the idea that MLEs are consistent. Is there an $iid$ violation? – Dave Jan 30 '23 at 22:30
  • I'd say they aren't always - e.g., when there's an omitted variable bias the MLE (=OLS) isn't consistent either. What I should have probably added is that this is also an instance of the Neyman-Pearson incidental parameter problem, where the MLE is also known to be inconsistent. See e.g. https://stats.stackexchange.com/questions/196578/difference-of-dynamic-panel-nickell-bias-and-the-incidental-parameter-probl/196674#196674 – Christoph Hanck Jan 31 '23 at 04:49
  • Neyman Scott, that is – Christoph Hanck Jan 31 '23 at 06:43

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