This project is concerned with methodology for investigating the development of criminal activity throughout the life course, specifically focussing on the nature and type of activity which offenders are involved in, as well as the frequency of such behaviour. There are four interrelated themes.

THEME 1. focuses on the changing patterns of criminal activity through the statistical modelling of court conviction data. This will investigate dynamic offending typologies through the nature of the convictions rather than the number. The nature of criminal activity and the number of different types of activity will also change over time and as an offender ages, and transitions between groups are also of interest.

THEME 2. is developing models for length of criminal career . We are interested in three issues - how to best estimate the length of criminal career from official criminal records, detecting changes in length of career over time and across birth cohorts and investigation of male-female differences in estimated length are changing for more recent cohorts.

THEME 3.is concerned with methodology for investigating the interrelationships between offences. We focus on six major serious offences: arson, threats to kill, blackmail, kidnap, homicide and rape (serious sexual assault).

THEME 4. is developing methods for assessing offence seriousness- that is, the seriousness level of an average offence type. We contrast several different approaches, including average length of custodial sentence and a bilinear modelling approach. This will enable researchers to measure degrees of offending escalation through the criminal life course.

Duration: 1st April 2005 to 30 September 2008

Researchers: Keith Soothill, Brian Francis, Elizabeth Ackerley, Jiayi Liu, Les Humphreys, Audrienne Bezzina

Ranked and partially ranked data are typically produced through social surveys, with respondents asked to rank a set of items into an order or partial order. However, longitudinal ranked data models have been relatively neglected. Here the correlation between responses over time needs to be taken into account, and other correlation structures between responses within a time point can also be considered. We aim to examine measures of world values and longitudinal changes. We will specifically focus on the Inglehart scale of post-materialism which is collected as a partially ranked dataset and is present in most social surveys, including the Euro-barometer and the BHPS.

Our focus is on the Bradley Terry model for paired comparisons. A paired comparison experiment is where each of a set of individuals is asked to judge a number of pairs of objects, choosing which object is preferred. We have shown that we can convert ranked data and partially ranked data into a set of paired comparison responses for each individual.

It is also possible to consider Likert data. If Likert questions are all measured on the same scale, with similar wording, then we can look at differences between items and analyse these as paired comparisons.

Longitudinal data is being modelled in two ways. One method is through a random effects formulation to account for individual specific factors over time. We use a non-parametric mass-point approach for the random effect, which becomes a mixture of Bradley Terry models. Another approach under development with our Vienna colleagues is the inclusion of specific Markov-dependence terms for paired responses across time.

Duration: April 2005 to September 2008

Researchers: Brian Francis, David Firth, Roger Penn collaborating with Regina Dittrich, Reinhold Hatzinger and Walter Katzenbeisser at Wirtschaftsuniversität-Vienna

This project focuses on the statistical modelling of developmental change in early childhood. Studies in Developmental Psychology typically acquire data of distinct kinds: measurements may be continuous, discrete or categorical and are taken at a pre-specified set of follow-up times. We are developing likelihood-based statistical inference to assess change in performance of young children on repeated measures of executive functions -i.e., tests of working memory, set shifting and inhibitory control. To do this we build random-effect-transition regression models that take into account variability between individuals, dependence between results on successive testing occasions and inter-relationships between tests. We aim to address many substantive questions once methodological work is complete. How do cognitive skills develop in young children? Can we distinguish between competing psychological models? For example, when preschoolers develop skills in executive function, what causes such change?

Duration: April 2005 to September 2008

Researchers: Peter Diggle, Charlie Lewis, John Copas, Ivonne Solis-Trapala

This project is exploring approximate likelihood approaches to inference in models which involve complex structures of random effects. These arise in longitudinal data, including data on competition, on networks of relationships, on multi-item test performance, on legislative voting, and many other modern social-research contexts. The essence of the "random" effects is to capture variation that is not predicted perfectly by available explanatory variables. This is crucial as neglecting important sources of variation typically results in non-negligible bias and/or substantial over-statement of the precision of estimates.

The technical difficulties are of two kinds: computational complexity arising from the need to calculate high-dimensional integrals repeatedly and accurately; and sensitivity of conclusions to secondary modelling assumptions - those which are needed in order to specify a full likelihood function. The focus of this project is on some recently-suggested approximate likelihood methods which aim to overcome one or both of these types of difficulty; "composite likelihood" methods, based on low-order marginal or conditional views of the full dataset, are particularly promising. The aims are to investigate the statistical properties of such methods in some "leading case" contexts of interest in social research, and to implement the methods in open-source softwareso that they become available to the wider research community.

Progress has been mostly on the technical aspects. Some models studied are inherently non-linear, and this has led to implementation of some of the methods as extensions to the "gnm" (generalized nonlinear models) software package, written by theteam and which won the prestigious John M Chambers Statistical Software Award in 2007.

Duration: April 2005 to September 2008

Researchers: David Firth, Mohand Feddag, Heather Turner, John Copas