This article describes the gologit2 program for generalized ordered logit models. gologit2 is inspired by Vincent Fu's gologit routine (Stata Technical Bulletin Reprints 8: 160-164) and is backward compatible with it but offers several additional powerful options. A major strength of gologit2 is that it can fit three special cases of the generalized model: the proportional odds/parallel-lines model, the partial proportional odds model, and the logistic regression model. Hence, gologit2 can fit models that are less restrictive than the parallel-lines models fitted by ologit (whose assumptions are often violated) but more parsimonious and interpretable than those fitted by a nonordinal method, such as multinomial logistic regression (i.e., mlogit). Other key advantages of gologit2 include support for linear constraints, survey data estimation, and the computation of estimated probabilities via the predict command.

Many researchers and journals place a strong emphasis on the sign and statistical significance of effects-but often there is very little emphasis on the substantive and practical significance of the findings. As Long and Freese (2006, Regression Models for Categorical Dependent Variables Using Stata [Stata Press]) show, results can often be made more tangible by computing predicted or expected values for hypothetical or prototypical cases. Stata 11 introduced new tools for making such calculations-factor variables and the margins command. These can do most of the things that were previously done by Stata's own adjust and mfx commands, and much more. Unfortunately, the complexity of the margins syntax, the daunting 50-page reference manual entry that describes it, and a lack of understanding about what margins offers over older commands that have been widely used for years may have dissuaded some researchers from examining how the margins command could benefit them. In this article, therefore, I explain what adjusted predictions and marginal effects are, and how they can contribute to the interpretation of results. I further explain why older commands, like adjust and mfx, can often produce incorrect results, and how factor variables and the margins command can avoid these errors. The relative merits of different methods for setting representative values for variables in the model (marginal effects at the means, average marginal effects, and marginal effects at representative values) are considered. I shows how the marginsplot command (introduced in Stata 12) provides a graphical and often much easier means for presenting and understanding the results from margins, and explain why margins does not present marginal effects for interaction terms.

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Allison (1999) notes that comparisons of logit and probit coefficients across groups can be invalid and misleading, proposes a procedure by which these problems can be corrected, and argues that ``routine use [of this method] seems advisable'' and that ``it is hard to see how [the method] can be improved.'' In this article, the author argues that as originally proposed, Allison's method can have serious problems and should not be applied on a routine basis. However, this study also shows that his model belongs to a larger class of models variously known as heterogeneous choice or location-scale models. Several advantages of this broader and more flexible class of models are illustrated. Dependent variables can be ordinal in addition to binary, sources of heterogeneity can be better modeled and controlled for, and insights can be gained into the effects of group characteristics on outcomes that would be missed by other methods.

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Panel data make it possible both to control for unobserved confounders and allow for lagged, reciprocal causation. Trying to do both at the same time, however, leads to serious estimation difficulties. In the econometric literature, these problems have been solved by using lagged instrumental variables together with the generalized method of moments (GMM). Here we show that the same problems can be solved by maximum likelihood (ML) estimation implemented with standard software packages for structural equation modeling (SEM). Monte Carlo simulations show that the ML-SEM method is less biased and more efficient than the GMM method under a wide range of conditions. ML-SEM also makes it possible to test and relax many of the constraints that are typically embodied in dynamic panel models.

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