International Choice Modelling Conference, International Choice Modelling Conference 2017

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Modelling state dependence in rare life course events: Introducing the Accumulative Hybrid Choice Skew Multivariate Probit
Romain Crastes dit Sourd, Matthew Beck, Charisma Choudhury, Thijs Dekker, Stephane Hess

Last modified: 28 March 2017


A key limitation of the majority of work in choice modelling is the reliance on data collected at a single point in time, limiting the generalisability of the findings as well as preventing a study of the evolution of preferences over time. Either of these aims requires the use of longitudinal data. The recent increase in popularity of survey methods for collecting longitudinal data such as the life-course calendar approach (Schoenduwe et al., 2015) has shed a new light on the causal relationships between certain life events (relocation, birth of a child, etc.) and other activities, for example travel and energy consumption behaviour. A growing stream of literature has studied the distribution of key events over the life course and the relationship between such events and changes in day to day activities.

Key events, also named life course events, can be characterized by two salient features:

(i)            they are rare events, therefore their distribution over the life-course potentially exhibits non-normal features such as asymmetry or long tails; and

(ii)          they induce state dependence, which means that the conditional probability that an individual will experience a given life-course event in the future is a function of both past experiences and unmeasured variables that vary at the individual level (Heckman, 1981).

To our knowledge, only a small number of choice modelling studies have attempted to move away from normality (Bhat et al., 2015). Moreover, state dependence is typically accounted for by adding random effects and lagged covariates in choice models, thus ignoring the fact that people accumulate experience about their choices and develop and attitude about their current state over time. In the current paper, we propose a model structure which jointly accounts for non-normality and state dependence and introduce an Accumulative Hybrid Choice Skew Multivariate Probit (AHC-SMP) model.

The AHC-SMP model features a Skew Multivariate Probit component for the joint probability of triggering a given set of life-course events at time t for an individual i. The model allows for correlated unobserved heterogeneity and non-normal errors and accounts for state dependence (as defined above) by the mean of lagged dependent variables and multivariate normal random effects. Finally, in a departure from standard techniques to measure state dependence, we also introduce “latent” state dependence. More precisely, we recognise that the number of events an individual has experienced over their life course (number of children, number of different jobs, etc.) has an impact on their capacity and/or willingness to engage in more events. For example an individual who has changed residential location five times over their life course may have a different attitude towards relocating another time in comparison to an individual who has changed only once. We treat the number of events experienced by an individual as indicators of latent attitudes toward life course changes, using them as dependent variables in a measurement equations component within a Hybrid Choice Model structure. We treat the number of events as count data and make use of a negative binomial structure (thus accounting for the over-dispersed nature of the indicators).

In the context of the above discussion, the empirical focus of this paper is on timing of long term choices. We apply the proposed framework to the British Household Panel Survey (BHPS) dataset (Taylor et al., 2010). The BHPS is a longitudinal study that was carried out by the Institute for Social and Economic Research from 1991 to 2009. It follows the same representative sample of individuals over 18 years and most notably addresses topics such as household composition, car purchases, relocations, changes of the work place but also provides information on life satisfaction by means of a series of attitudinal questions. As a result, this dataset also allows us to account for changes in attitudes over time, which can be naturally implemented within the AHC-SMP framework.

In our specification application, four long term choices will be considered: changing car ownership status, buying a property, changing job and getting married. After screening for missing data and other inconsistencies, the final sample size includes 13 years of contiguous data for a total of 2,133 respondents (27,729 observations). Further, we follow the approach suggested by Bhat et al., (2015) and split the sample into 70% for estimation and 30% for prediction. We will also compare the relative performances of the AHC-SMP model against more traditional approaches such as the Random Effect multivariate Probit or survival analysis models. We will use suitable indicators to compare hybrid and non-hybrid choice models such as the predictive adjusted likelihood ratio index.

From a policy point of view, the current paper contributes to a better understanding of choices over time, particularly with respect to key life choices. Finally, the BHPS reports extremely detailed sociodemographic data, which will allow us to investigate whether individuals make different decisions depending on their gender, religion or ethnic group, with the intent of supporting policy development aimed at reducing prevalent differences in mobility across diverse populations.



Bhat, C.R., Dubey, S.K. and Nagel, K., (2015), Introducing non-normality of latent psychological constructs in choice modeling with an application to bicyclist route choice, Transportation Research Part B: Methodological 78, issue C, p. 341-363

Heckman, J.J., (1981), Heterogeneity and State Dependence, in Sherwin Rosen, ed., Studies in labor markets. Chicago: University of Chicago Press, p. 91-139.

Schoenduwe, R., Mueller, M.G., Peters, A., and Lanzendorf, M., (2015), Analysing mobility biographies with the life course calendar: a retrospective survey methodology for longitudinal data collection, Journal of Transport Geography 42, p. 98-109

Taylor, M.F., Brice, J., Buck, N., and Prentice-Lane, E., (2010) British Household Panel Survey User Manual Volume A: Introduction, Technical Report and Appendices. Colchester: University of Essex.

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