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A latent Markov model for detecting patterns of criminal activity

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  • Francesco Bartolucci
  • Fulvia Pennoni
  • Brian Francis

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.

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Bibliographic Info

Article provided by Royal Statistical Society in its journal Journal of the Royal Statistical Society: Series A (Statistics in Society).

Volume (Year): 170 (2007)
Issue (Month): 1 ()
Pages: 115-132

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Handle: RePEc:bla:jorssa:v:170:y:2007:i:1:p:115-132

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  1. Francesco Bartolucci, 2006. "Likelihood inference for a class of latent Markov models under linear hypotheses on the transition probabilities," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(2), pages 155-178.
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Cited by:
  1. Siem Jan Koopman & André Lucas & Marius Ooms & Kees van Montfort & Victor van der Geest, 2007. "Estimating Systematic Continuous-time Trends in Recidivism using a Non-Gaussian Panel Data Model," Tinbergen Institute Discussion Papers 07-027/4, Tinbergen Institute.
  2. Bartolucci, Francesco & Farcomeni, Alessio, 2009. "A Multivariate Extension of the Dynamic Logit Model for Longitudinal Data Based on a Latent Markov Heterogeneity Structure," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 816-831.
  3. Bartolucci, Francesco & Farcomeni, Alessio & Pennoni, Fulvia, 2012. "Latent Markov models: a review of a general framework for the analysis of longitudinal data with covariates," MPRA Paper 39023, University Library of Munich, Germany.
  4. S. Bacci & S. Pandolfi & F. Pennoni, 2014. "A comparison of some criteria for states selection in the latent Markov model for longitudinal data," Advances in Data Analysis and Classification, Springer, vol. 8(2), pages 125-145, June.
  5. Francesco Bartolucci & Ivonne Solis-Trapala, 2010. "Multidimensional Latent Markov Models in a Developmental Study of Inhibitory Control and Attentional Flexibility in Early Childhood," Psychometrika, Springer, vol. 75(4), pages 725-743, December.
  6. De Angelis, L & Paas, L.J., 2009. "The dynamic analysis and prediction of stock markets through the latent Markov model," Serie Research Memoranda 0053, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.

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