Electronic Thesis and Dissertation Repository


Doctor of Philosophy


Statistics and Actuarial Sciences


Dr. Charmaine Dean


Understanding the patterns and mechanisms of the process of desistance from criminal activity is imperative for the development of effective sanctions and legal policy. Methodological challenges in the analysis of longitudinal criminal behaviour data include the need to develop methods for multivariate longitudinal discrete data, incorporating modulating exposure variables and several possible sources of zero-inflation. We develop new tools for zero-heavy joint outcome analysis which address these challenges and provide novel insights on processes related to offending patterns. Comparisons with existing approaches demonstrate the benefits of utilizing modeling frameworks which incorporate distinct sources of zeros. An additional concern in this context is heaping of self-reported counts where recorded counts are rounded to different levels of precision. Alternatively, more accurate data that is less burdensome on participants to record may be obtained by collecting information on presence/absence of events at periodic assessments. We compare these two study designs in the context of self-reported data related to criminal behaviour and provide insights on choice of design when heaping is expected.

The contributions of this research work include the following: (i) Developing a general framework for joint modeling of multiple longitudinal zero-inflated count outcomes which incorporates a variety of probabilistic structures on the zero counts. (ii) Accommodating a subgroup of subjects who are not at-risk to engage in a particular outcome (iii) Incorporating the effect of a time-dependent exposure variable in settings where some outcomes are prohibited during exposure to a treatment. (iv) Illustrating the extent to which heaping of zero-inflated counts, arising from a variety of heaping mechanisms, can introduce bias, impeding the identification of important risk factors (v) Identifying situations where there is very little loss of efficiency in the analysis of presence/absence data, depending on the partition of the time for the presence/absence records and the underlying rate of events. (vi) Providing recommendations on the design of studies when heaping is a concern. (vii) Modeling of multiple longitudinal binary outcomes where a mixture model approach allows differential rates of recurrence of events, and where the underlying process generating events may resolve.