Analyzing Multiple-Item Measures of Crime and Deviance II: Tobit Regression Analysis of Transformed Scores - Osgood, D. Wayne (Journal of quantitative criminology, 2002)
The purpose of this article is to inform criminological researchers about tobit regression, an alternative regression model that deserves more attention in this field. Tobit regression is intended for continuous data that are censored, or bounded at a limiting value. The tobit model may be a particularly good match to measures of self-reported offending, provided they have been transformed to reduce skewness. We present empirical analyses that evaluate the match of self-report measures to the assumptions of ordinary least square (OLS) and tobit regression models and that assess the consequences of any violations of assumptions. The analyses use a fourteen-item, self-report measure of delinquency from the Monitoring the Future study, a national survey of high school seniors. These analyses provide clear evidence that (1) transformations to reduce skewness improve the match of OLS to the data but still leave considerable discrepancies, and (2) the tobit model is well suited to the transformed measure. We conclude by assessing the purposes for which tobit offers greater and smaller advantages over OLS regression.