Sample selection bias with multiple selection rules: application with residential relocation, attrition, and activity participation in Puget sound transportation panel

Two sources of sample selection bias emerging simultaneously from panel attrition and residential relocation and their effect on activity participation are examined. The data used were from two time points (Wave 1 in 1989 and Wave 2 in 1990) of the Puget Sound Transportation Panel. Data regarding relocation decisions, taking place between Wave 1 and Wave 2, are available for the households that participated in both waves (participants) and are not available for the households that participated in the first wave only (dropouts). Double selection was associated with the possible simultaneous or sequential decision process underlying participation in the survey and household residential relocation. The method used is based on a bivariate probit model that accounts for selectivity. The method emerges from the unknown relocation status of the dropouts in Wave 2. Subsequent creation of correction terms, needed to account for the lack of data on dropout households' activity participation in Wave 2, uses the probit model. The method, called the Tunali method, is a two-step procedure that follows the usual Heckman method. The models estimated, that is, the bivariate probit model of double-selection and activity participation linear regressions corrected and uncorrected for selection, are provided.