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Dynamic, disaggregate choice models which use longitudinal data are known to have clear advantages over cross-sectional models, but they also have their own unique estimation problems. The correlation among unobserved error components ("heterogeneity") that is likely to exist in such data sets can be the source of apparent state dependence, but true state dependence is also possible. A review of car ownership models reveals that the issue of heterogeneity versus true state dependence has not been adequately addressed in the transportation literature. This paper develops computationally convenient ordered-response probit models for panel data, estimates models of car ownership, and performs tests of heterogeneity versus true state dependence. Conclusions in (the more general) one-factor models are found to differ from those obtained from (the more restricted) components of variance models, and the issue of initial conditions is also found to affect the conclusions.