Treating the Deviant Y: An Examination of Regression Methods for Censored, Non-Normal Variables in Criminological Research

Censored, or Tobit, regression provides criminologists with a useful tool for the estimation of models with limited dependent variables. Recent research has demonstrated advantages of this approach. At the same time, caution, and potential adjustment, is required in utilizing these techniques. This study looks at the problems presented by recalcitrant, censored variables; focusing specifically on the issue of normality in the specified latent dependent variable. Some have previously suggested that censored, non-normal distributions in conjunction with the Tobit model are more problematic than equivalent violations in assumptions of linear regression. Examples abound of such dependent variables in criminological inquiry (e.g., seriousness scales, length of prison sentence) making it necessary to consider methods for properly incorporating them into regression models. This work discusses issues related to analysis of these variables and offers some preliminary solutions for ensuring proper inference. Semi-parametric estimators previously utilized in econometric research will be discussed as one possible option for dealing with the difficulties presented by censored, non-normal outcome variables.

crime, criminal justice, research, regression, deviant, criminology