Semi-nonparametric competing risks analysis of recidivism

Abstract

In this paper we specify a semi-nonparametric competing risks (SNP-CR) model of recidivism, for misdemeanors and felonies. The model is a bivariate mixed proportional hazard model with Weibull baseline hazards and common unobserved heterogeneity. The distribution of the latter is modeled seminonparametrically, using orthonormal Legendre polynomials on the unit interval, and integrated out to make the two durations dependent, conditional on the covariates. The SNP-CR model involved corresponds to a Logit model for felony arrest; hence the validity of the SNP-CR model can be tested by testing the validity of the implied Logit model. The latter will be done by using the integrated conditional moment (ICM) test. In the first instance we have estimated and tested two versions of the SNP-CR model, without and with fixed state effects. However, the ICM test rejects these models. Therefore, we have estimated and tested the model for each state separately. These state models are not rejected by the ICM test. Indeed, the estimation results vary substantially per state.

In this paper we specify a semi-nonparametric competing risks (SNP-CR) model of recidivism, for misdemeanors and felonies. The model is a bivariate mixed proportional hazard model with Weibull baseline hazards and common unobserved heterogeneity. The distribution of the latter is modeled seminonparametrically, using orthonormal Legendre polynomials on the unit interval, and integrated out to make the two durations dependent, conditional on the covariates. The SNP-CR model involved corresponds to a Logit model for felony arrest; hence the validity of the SNP-CR model can be tested by testing the validity of the implied Logit model. The latter will be done by using the integrated conditional moment (ICM) test. In the first instance we have estimated and tested two versions of the SNP-CR model, without and with fixed state effects. However, the ICM test rejects these models. Therefore, we have estimated and tested the model for each state separately. These state models are not rejected by the ICM test. Indeed, the estimation results vary substantially per state.