B1000
Title: A latent variable approach for dealing with heaping and ``too many to count'' in domestic violence counts
Authors: Brian Francis - Lancaster University (United Kingdom) [presenting]
Sylvia Walby - Lancaster University (United Kingdom)
Jude Towers - Lancaster University (United Kingdom)
Abstract: One recent theory suggests that there are different types of domestic violence. These types are defined by the nature of the behaviour of one partner towards the other. It is hypothesized that one form of domestic violence is likely to lead to repeated acts of violence within a relationship, perhaps escalating in severity. This suggests that a mixture of two count processes may be a good way to model such data. We discuss recent work which has attempted to determine whether there are a number of distinct groups of domestic violence victims, or whether there is a single distribution with overdispersion. Such mixture models however, need to take account not only of capping but of heaping and a ``too many to count'' category. Heaping is the tendency for respondents to report yearly incidents to the nearest rounded number. This will affect the mixture model in introducing modal peaks in the incident distribution. Dealing with both of these leads to a mixture of mixtures problem, where the heaping and too many to count processes mixes on top of a mixture of Poisson or negative binomials. Results will be presented from an analysis of ten years of data on intimate personal violence from the Crime Survey of England and Wales, and analysis problems are identified.
