Ordered logit or ordered probit?

[Fred Dzanku]

Is there a theoretical justification for choosing an ordered logit model over the ordered probit, and verse versa? I can't find any? Is it a similar case of logit versus probit in the binary case, unlike multinomial logit and probit where one could use IIA, for example, to decide which may be more appropriate for a given data?

[Clyde Schechter]

As far as I know, the choice betwen logit and probit, or ologit and oprobit, is a matter of personal taste or disciplinary tradition only. The logistic and normal distributions are nearly indistinguishable, except in the far tails that are rarely reached in typical research data samples anyway. The results are different in the coefficient metric do to the standard normal distribution having a variance of 1 and the logistic having a variance of pi²/3. But the coefficients pretty much scale in a pi/sqrt(3) ratio, and inferences are seldom different except in very borderline cases.

Besides multivariate, the only other area I know of where logit vs probit makes a difference if you want a fixed-effects panel model: the fixed effects can be factored out of the likelihood for the logistic model, so it is possible to do inference conditional on the fixed effects, whereas the likelihood for the fixed effects probit model does not simplify in that way and is intractable to work with.