Investigating non-ignorable drop-out in panel studies of residential mobility

Washbrook. E., Clarke, P.S. and Steele, F. (2014) Investigating non-ignorable drop-out in panel studies of residential mobility. Journal of the Royal Statistical Society, Series C (forthcoming).

Abstract

We consider the impact of non-ignorable drop-out in the analysis of residential mobility in household panel surveys. To investigate the impact of such drop-out, we consider two types of selection model: the first allows drop-out to depend directly on the individual’s potentially missing moving status; and the second is a Heckman-type selection model with correlated errors. We discuss the identification and estimation of these models and use simulations to study the role of exclusion restrictions in minimising the dependence of inferences on unverifiable parametric assumptions. The models are both applied to data from the British Household Panel Survey.

Further details

The use of household panel data has great advantages in the study of residential mobility because it allows moves to be placed in the temporal context of a series of life events, such as changing household composition and employment status. However, any study that relies on prospectively collected longitudinal data must consider the issue of attrition, or the potentially non-random drop-out of participants before the end of the study period. To date, the impact of attrition due to drop-out is a methodological issue that has been neglected in the residential mobility literature. This is perhaps surprising given the evidence that residential mobility is a major cause of drop-out from panel surveys. This situation, in which the probability of drop-out is directly related to the (possibly unobserved) outcome of interest, is one of ‘non-ignorable’ non-response which can lead to systematic differences between the distributions of the remaining sample and the target population. Failure to adjust for these differences can give misleading results and it is well known that valid inferences can be obtained only by jointly modelling the mobility and drop-out processes.

Adjustments for non-ignorable drop-out are also known to be sensitive to the choice of drop-out model. To address this problem, we compare two closely related but conceptually different types of drop-out model. In the first type of model, which we term the ‘direct dependence’ approach, the drop-out probability is allowed to depend directly on moving status. The second type is based on an extension of the Heckman selection model in which the association between mobility and drop out is assumed to be due to omitted variables common to both processes. We favour the direct-dependence model a priori on theoretical grounds because it incorporates the idea that mobility and drop-out are causally related, but the main focus of the article is on investigating whether the results of our BHPS analysis are sensitive to the choice of approach.

In our comparison of these approaches, we also address two methodological issues. First, the focus on local moves raises complications in the presence of non-ignorable drop-out. In the residential mobility literature, short- and long-distance moves are studied separately so that migratory long-distance moves play no role in analyses of local short-distance moves. While in the absence of missing data this approach is justified, we show that the standard direct-dependence drop-out model must be extended to depend on moves of any kind and that migratory moves cannot be ignored.

Second, the methodological literatures on the two types of selection model have both emphasised the importance of ‘exclusion restrictions’, or covariates that predict one of mobility or drop-out but not both; such a variable is often referred to as an instrumental variable. However, it is not always clear under what circumstances valid exclusion restrictions will improve the model in practice. The strength of the instrument, the model it appears in, and the validity of the parametric assumptions made about the latent error distributions may all play a role. Hence, we investigate these questions in the context of the mobility model, first by comparing estimates from the BHPS data with and without the inclusion of instrumental variables, and then using a simulation study to explore the effectiveness of exclusion restriction strategies in scenarios with features similar to our mobility application.