ML parameter transformation

[Alfonso Sánchez-Peñalver]

Hi everyone,

I am interested in estimating a parameter, among others, via maximum likelihood, let’s call it tau. Now tau has to be in the interval [0,1]. Clearly estimating it directly there’s no guarantee that the estimate will fall in that interval. I was wondering if there is an apporpriate transformation that would lead to that, or any way to constrain it.

Thanks!!

[Nick Cox]

Estimating on logit scale is the usual way to do this. I guess it's taken as read that you know what to think if a program returns values very near 0 or 1.
See also https://www.stata.com/support/faqs/s...l-constraints/

[Alfonso Sánchez-Peñalver]

Hi Nick, thanks for the quick response. I've always understood that values close to 0 or 1 are to be mistrusted and make you re-think the specification of the model to estimate, in the same manner that you would have to do when an estimated correlation is close to either 1 or -1. Can you expand on how to estimate on logit scale, please? The model to be estimated is, itself, a mixed (random coefficients) logit (it has both alternative specific and non-alternative specific explanatory variables).

Thanks again,

Alfonso.

[Nick Cox]

Section 4 and section 5 of the FAQ cited apply. You'll need customized code.

[Alfonso Sánchez-Peñalver]

Thanks Nick, extremely helpful as always!