Continuous-time state-space modelling of delinquent behaviour in adolescence and young adulthood
Sina Mews · 2021
Using data from a longitudinal study on delinquent behaviour of adolescents in Germany, we investigate the persistence of an individual’s delinquency level over time. We assume the latter to be a latent trait underlying the observed trajectories of adolescents' delinquency, thus using a state-space model (SSM) to analyse the data. As the observations are irregularly spaced in time, we formulate the SSM in continuous time and specify the state process as an Ornstein-Uhlenbeck process. We further include the adolescents’ gender and age as covariates in the observation process. Statistical inference is carried out by maximum approximate likelihood estimation, where multiple numerical integration within the likelihood evaluation is performed via a fine discretisation of the state process. The corresponding reframing of the SSM as a continuous-time hidden Markov model enables us to apply the associated efficient algorithms for parameter estimation and state decoding. The results reveal temporal persistence in the deviation of an individual's delinquency level from the population mean.