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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

Summary. 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.

Suggested Citation

  • Francesco Bartolucci & Fulvia Pennoni & Brian Francis, 2007. "A latent Markov model for detecting patterns of criminal activity," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 170(1), pages 115-132, January.
  • Handle: RePEc:bla:jorssa:v:170:y:2007:i:1:p:115-132
    DOI: 10.1111/j.1467-985X.2006.00440.x
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    File URL: https://doi.org/10.1111/j.1467-985X.2006.00440.x
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    References listed on IDEAS

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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, April.
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    Cited by:

    1. Brian Francis & Jiayi Liu, 2015. "Modelling escalation in crime seriousness: a latent variable approach," METRON, Springer;Sapienza Università di Roma, vol. 73(2), pages 277-297, August.
    2. Francesco Dotto & Alessio Farcomeni & Maria Grazia Pittau & Roberto Zelli, 2019. "A dynamic inhomogeneous latent state model for measuring material deprivation," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 182(2), pages 495-516, February.
    3. 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.
    4. Siem Jan Koopman & Marius Ooms & André Lucas & Kees van Montfort & Victor Van Der Geest, 2008. "Estimating systematic continuous‐time trends in recidivism using a non‐Gaussian panel data model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 62(1), pages 104-130, February.
    5. Kelava, Augustin & Kohler, Michael & Krzyżak, Adam & Schaffland, Tim Fabian, 2017. "Nonparametric estimation of a latent variable model," Journal of Multivariate Analysis, Elsevier, vol. 154(C), pages 112-134.
    6. 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;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 8(2), pages 125-145, June.
    7. 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;The Psychometric Society, vol. 75(4), pages 725-743, December.
    8. 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.
    9. Paas, L.J. & Vermunt, J.K. & Bijmolt, T.H.A., 2007. "Discrete-time discrete-state latent Markov modelling for assessing and predicting household acquisitions of financial products," Other publications TiSEM 5781ab33-6687-4ad5-b57a-3, Tilburg University, School of Economics and Management.
    10. F. Bartolucci & A. Farcomeni & F. Pennoni, 2014. "Latent Markov models: a review of a general framework for the analysis of longitudinal data with covariates," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(3), pages 433-465, September.
    11. Leonard J. Paas & Jeroen K. Vermunt & Tammo H. A. Bijmolt, 2007. "Discrete time, discrete state latent Markov modelling for assessing and predicting household acquisitions of financial products," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 170(4), pages 955-974, October.
    12. Eugene C.X. Ikejemba & Peter C. Schuur, 2018. "Analyzing the Impact of Theft and Vandalism in Relation to the Sustainability of Renewable Energy Development Projects in Sub-Saharan Africa," Sustainability, MDPI, Open Access Journal, vol. 10(3), pages 1-17, March.

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