Modeling Uncertainty in Latent Class Membership: a Case Study in Criminology

Kathryn Roeder - Kevin G. Lynch - Daniel S. Nagin


Social scientists are commonly interested in relating a latent trait (e.g., criminal tendency) to measurable individual covariates (e.g., poor parenting) to understand what defines or perhaps causes the latent trait. In this article we develop an efficient and convenient method for answering such questions. The basic model presumes that two types of variables have been measured -- response variables (possibly longitudinal) that partially determine the latent class membership and covariates or risk factors that we wish to relate to these latent class variables. The model assumes that these observable variables are conditionally independent, given the latent class variable. We use a mixture model for the joint distribution of the observables. We apply this model to a longitudinal data set assembled as part of the Cambridge Study of Delinquent Development to test a fundamental theory of criminal development. This theory holds that crime is committed by two distinct groups within the population - adolescent limited offenders and life course persistent offenders. As these labels suggest, the two groups are distinguished by the longevity of their offending careers. The theory also predicts that life course persistent offenders are disproportionately comprised of individuals born with neurological deficits and reared by caregivers without the skills and resources to effectively socialize a difficult child.

Keywords: Classification error, Latent class analysis, Mixture models

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