Modeling the Deviant Y in Criminology: An Examination of the Assumptions of Censored Normal Regression and Potential Alternatives

Many dependent variables of criminological interest have censored distributions. Investigations that use such variables increasingly have turned to the Tobit model, a censored regression technique that is specified based on a latent dependent variable. When used under suitable circumstances, this model provides appropriate estimates. This paper discusses key assumptions of the Tobit model. It then highlights the risk of violating these assumptions and reviews alternative flexible parametric and semiparametric modeling techniques, currently used sparingly in criminology, which researchers may find helpful when assumptions regarding the error terms are untenable. By using an empirical example focused on sentencing outcomes and comparing estimates across analytic methods, this study illustrates the potential utility of simultaneously estimating the Tobit model along with some alternatives.