Latent class multi-state quantile regression with a cure fraction: application to jail recidivism in the U.S.

We propose a multi-state quantile regression model that admits a cure-fraction for each possible transition, so that individuals may not experience that event. A discrete latent variable allows us to take into account unobserved heterogeneity. The model is estimated in a Bayesian framework, without specifying the number of latent classes. A simple strategy to scale inference to big data is discussed. We are motivated by an original application to jail recidivism in the U.S. between 2020 and 2023. We find that 20% of the subjects have high cumulative hazard of recidivism; with little association to covariates such as age, gender, crime, and ethnicity. A latent group has been shown to accumulate up to two detentions per year of freedom and represents about 10% of the population.