A Latent Markov Model for Detecting Patterns of Criminal Activity

Abstract

The paper investigates the problem of determining patterns of criminal behaviour from official criminal histories, concentrating on the variety and type of offending convictions. The analysis is carried out on the basis of a multivariate latent Markov model which allows for discrete covariates affecting the initial and the transition probabilities of the latent process. We also show some simplifications which reduce the number of parameters substantially; we include a Rasch-like parameterization of the conditional distribution of the response variables given the latent process and a constraint of partial homogeneity of the latent Markov chain. For the maximum likelihood estimation of the model we outline an EM algorithm based on recursions known in the hidden Markov literature, which make the estimation feasible also when the number of time occasions is large. Through this model, we analyse the conviction histories of a cohort of offenders who were born in England and Wales in 1953. The final model identifies five latent classes and specifies common transition probabilities for males and females between 5-year age periods, but with different initial probabilities. Copyright 2007 Royal Statistical Society.

LMest: An R Package for Latent Markov Models for Longitudinal Categorical Data

“…The mixed LM model is illustrated by using a simulated dataset similar to the one analyzed in Bartolucci et al (2007); see also Francis, Liu, and Soothill (2010) and Pennoni (2014). The data are related to the complete conviction histories of a cohort of offenders followed from the age of criminal responsibility, 10 years.…”

“…For every age band, each response variable is equal to 1 if the subject has been convicted for a crime of the corresponding offense group and to 0 otherwise. Then, the data matrix, reported below in long format, has been simulated on the basis of the same parameter estimates reported in Bartolucci et al (2007): R> data("data_criminal_sim", package = "LMest") R> head(data_criminal_sim) id sex time y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 The first column of the data matrix contains the id code of each subject, whereas the covariate gender (second column named sex) is coded as 1 for male and 2 for female, the column named time is referred to the age band, and the last ten columns are related to the binary response variables.…”

“…In particular, the basic LM model, which relies on a homogeneous Markov chain of first order, has been extended in several ways on the basis of parameterizations that allow us to incorporate certain hypotheses in the model. The most relevant extended version includes individual covariates that may affect the distribution of the latent process (Vermunt, Langeheine, and Böckenholt 1999;Bartolucci, Pennoni, and Francis 2007) or the conditional distribution of the response variables given this process (Bartolucci and Farcomeni 2009). LM models may be also formulated to take into account certain types of unobserved heterogeneity.…”

Serious, Violent Young Offenders in South Africa

“…Latent class modeling constructs homogeneous latent groups on the basis of observed variables such that correlation between the observed variables is explained by the latent groups (McCutcheon, 1987). In criminology, latent class modeling has been used to identify different criminal careers (Bartolucci, Pennoni, & Brain, 2007) and to discriminate recidivists from one-time offenders (Bijleveld & Mooijaart, 2003).…”

Group-based Criminal Trajectory Analysis Using Cross-validation Criteria

“…The most common approach is to optimize the Bayesian Information Criterion (BIC) (e.g. Brame, Nagin & Wasserman, 2006;D'Unger, Land, McCall, & Nagin, 1998;Kass & Raftery, 1995;Raftery, 1995;Bartolucci et al, 2007), by computing the corresponding maximum likelihood estimator (MLE) using the software Proc Traj (Jones, 2001;Jones, Nagin, & Roeder, 2001;Jones, & Nagin, 2007). Although versions of this procedure have had much success, it is known that such optimization can be problematic (e.g.…”