Re: [Gretl-users] Interval regression model

On Mon, 16 Jun 2014, Mārtiņš Liberts wrote: In brief: we introduced the concept of a "pseudo-point" observation, to deal with cases when the interval between the high and low bounds is so narrow, and so away from 0, that the relevant loglikelihood cannot be computed reliably. In that case, the observation is treated as if it was a point observation, with value equal to the midpoint. According to your output files, this happens for 1 observation out of 6170, but is enough to alter substantially the shape of the log-likelihood, so the algorithm converges to a slightly different maximum. It's difficult to be more specific without looking at the data, but I can't help noticing that the normality test strongly rejects the null in both output files; therefore, I'm inclined to think that the normal-based interval model is not particularly appropriate for your data, and the issue you're experiencing is just a by-product of an unfortunate choice for the measurement of the dependent variable. In other terms, the assumption that you have a latent variable y* which is normally distributed (conditional on your explanatory variable) is quite difficult to justify. In these cases, you should either re-define your dependent variable (are logs an option, for example?), or re-define your model, by using other densities than the normal (the gamma density, maybe, if your dependent variable is non-negative?). If you choose the latter option, you'll have to code your estimator via mle, or use some other non-parametric alternative. Hope this helps! ------------------------------------------------------- Riccardo (Jack) Lucchetti Dipartimento di Scienze Economiche e Sociali (DiSES) Università Politecnica delle Marche (formerly known as Università di Ancona) r.lucchetti(a)univpm.it http://www2.econ.univpm.it/servizi/hpp/lucchetti -------------------------------------------------------