Modelling escalation in crime seriousness: a latent variable approach


This paper investigates the use of latent variable models in assessing escalation in crime seriousness. It has two aims. The first is to contrast a mixed-effects approach to modelling crime escalation with a latent variable approach. The paper therefore examines whether there are specific subgroups of offenders with distinct seriousness trajectory shapes. The second is methodological—to compare mixed-effects modelling used in previous work on escalation with group-based trajectory modelling and growth mixture modelling (mixture of mixed-effects models). The availability of software is an issue, and comparisons of fit across software packages is not straightforward. We suggest that mixture models are necessary in modelling crime seriousness, that growth mixture models rather than group-based trajectory models provide the best fit to the data, and that R gives the best software environment for comparing models. Substantively, we identify three latent groups, with the largest group showing crime seriousness increases with criminal justice experience (measured through number of conviction occasions) and decreases with increasing age. The other two groups show more dramatic non-linear effects with age, and non-significant effects of criminal justice experience. Policy considerations of these results are briefly discussed.

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  1. 1.

    For identifiability,the lcmm package in R estimates the variance–covariance matrix of the last latent class, and then a set of estimated class-specific proportional parameters is used to multiply the variance–covariance matrix in order to compute the variances and covariances of each of the other classes.

  2. 2.

    Note that age is treated as piecewise linear through a one breakpoint representation as described in Sect. 6.1

  3. 3.

    The posterior probability is the probability of each individual belongs to certain class k given data \({\varvec{X}}\), \(P(c_{i}=k\mid {\varvec{X}}_{it})\).


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This work was supported by the UK Economic and Social Research Council (ESRC) who funded this work under the AQMEN Phase 2 Initiative (Grant Number ES/K006460/1). This study was a re-analysis of existing data that are publicly available from the UK Data Service at

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Correspondence to Brian Francis.



See Table 5.

Table 5 List of terminologies in mixed-effects and mixture modelling, and the available software for the analysis of a continuous response variable

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Francis, B., Liu, J. Modelling escalation in crime seriousness: a latent variable approach. METRON 73, 277–297 (2015).

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  • Escalation
  • Aggravation
  • Longitudinal data analysis
  • Latent variable methods
  • Heterogeneity
  • Group-based trajectory modelling
  • Growth mixture modelling
  • Criminal careers
  • Comparative study