Fixed Effect Coniditional Logit - Measure of fit

[Stephanie Atala]

Hi,

I am using the xtlogit, fe nolog to create a fixed effects logit model. I have around 16 predictors in my model. After running the code and using the "fitstat" command, I get an adjust McFadden Rsquare of about 0.064. Also, not all of my regressors are significant.

Can anyone suggest how to assess the fit of a fixed effects logit model? I was not able to find anything in the literature and I am not sure if 0.064 adjusted McFadden R square is too low. Any insight or source that I can check?

Thank you.

[Joao Santos Silva]

Dear Stephanie,

All the R2 measures are more or less meaningless so I would not worry about them. If you are worried about the suitability of your model I suggest you perform a reset-type test. That is, get the predicted index xb, square it and cube it, and run the model including the new variables. If they are jointly significant that provides evidence against your model.

Best wishes,

Joao

[Phil Bromiley]

I'm not sure if this is programmed, but it is also quite common to have a 2x2 table of actual (0,1) and predicted (0,1) to give an idea of how good the predictions are.

[Joao Santos Silva]

Phil Bromiley, with the FE logit we cannot get predicted probabilities, so that cannot be done.

Best wishes,

Joao

[Phil Bromiley]

@Joao - thanks for pointing that out.

Could you help me understand the manual? xtlogit postestimation with fixed effects refers to providing either "predicted probability of a positive outcome conditional on one positive outcome within group; the default" or "probability of a positive outcome assuming that the fixed effect is zero". If one did have one positive outcome per group, then why is the first one not a reasonable predicted probability?

The interpretation of a predicted probability based on a model with fixed effects assuming fixed effects are zero does seem problematic.

What am I missing?

Phil

[Joao Santos Silva]

Dear Phil Bromiley,

The problem is exactly the restriction of a single positive per group. Indeed, if we had just a single positive for each group we would have a very homogeneous population and the fixed effects would probably be unnecessary. In realistic settings, the number of positives per group will vary substantially and the probability of a positive conditional on a single positive in the group is meaningless.

Consider the unionization example for xtlogit in the manual which uses a panel with T up to 12. Computing the probability that someone is unionized in a particular year given that over the period of observation was unionized in a single year is not a particularly interesting thing. This is particularly true in this case because T varies from 2 to 12 and being unionized once in 12 years is very different from being unionized in one of two years. So, the interpretation of what is computed varies from individual to individual.

Best wishes,

Joao

[Phil Bromiley]

Excellent!

Thank you.

Phil

[Ben Barber]

Dear Joao Santos Silva,

First, I would like to thank you for providing some guidance to this issue. I've scoured the internet and could find very little until stumbling across your post.

However, I wanted to try and get more clarity to your response because I don't know if I fully understand the answer to the question. Is it still impossible to get predicted probabilities from the conditional logit if you do only have one observation per group?

To give you the scenario that lead me to search for this: there is literature on firm location where people investigate what factors determine whether a firm will locate a new establishment across space. Within this literature it is common to use fixed effects at the investment level leaving only one positive outcome per investment.

In a scenario like this, could you interpret the predicted probabilities as normal? And, if so, is there a citation for this?

Thanks,
Ben