DEAR KELVYN, COULD YOU PLEASE ELABORATE MORE ON THE CONCEPT OF INCIDENTAL PARAMETER PROBLEM? WHAT DO YOU EXACTLY MEADN WITH THIS TERM? COULD YOU PLEASE PROVIDE AN EXAMPLE OR ANY REFERENCES?

REGARDS

EDOARDO

Dear Eduardo

Apologies, I have deliberately asked the question this way as I do not want to colour the answers.

Thanks

Kelvyn

thnaks for the motivation. regards

edoardo

Dear Kelvyn,

I think the most natural setting to consider the incidental parameters problem is when you want to add fixed effects in a probit model. The classic by Heckman provides some monte carlo evidence as well: http://eml.berkeley.edu/~mcfadden/discrete/ch4.pdf

I came also across this exposition but have not read it in detail: http://www.r-bloggers.com/incidental-parameters-problem-with-binary-response-data-and-unobserved-individual-effects/

I know you work with Bayesian methods quite often. The handbook by Simon Jackman provides some references to work by Diaconis and Freedman on the incidental parameters problem in a Bayesian setting. I checked, the references are on p.437, 438. Simon explaims that Bayesian techniques are not immune and the mean of the posterior is inconsistent (tends to the wrong limit). However Jackman does suggest that large sample properties might be better.

Not an expert on this but  maybe the references are of some help. 

[edited for typo's]

Louis

Thanks

Kelvyn

Dear Kelvyn,

I hope that my answers can be helpful.

The incidental parameter problem (IPP) tends to occur whenever:

(1) your fixed effects nonlinear model deals with panel data covering a time period that is fixed (T) and a high number of individuals (N) or

(2) your time effects nonlinear model deals with a fixed N and a large T.

The main consequence is that your coefficients will be inconsistent.

What shall a researcher do in this case? In 2017, Cruz et al. proposed two commands in STATA (probitfe and logitfe) that can treat IPP. You can take a look to their study that was very helpful at least for my research.

Cruz-Gonzalez, M., Fernández-Val, I., & Weidner, M. (2017). Bias corrections for probit and logit models with two-way fixed effects. The Stata Journal, 17(3), 517-545.

Nicolae Stef Thank you that is helpful.

It was proposed by Chamberlain (1980) an adequate statistic for this. Accordingly, he suggests maximizing the conditional likelihood function. I proved in my PhD thesis that the incidental parameter problem was overcome. But thesis is still in the writing phase.

Thank you, it will be good to see it when completed

Thank you very much:)