Defining Interalternative Error Structures for Joint Revealed Preference-Stated Preference Modeling

Joint model estimation with revealed (RP) and stated preference (SP) data has become popular in the past few years, and it is now considered common practice. Many theoretical issues related to estimation and prediction with joint RP-SP data are far from being fully explored. Given the ample diffusion of RP-SP modeling in practice, its misuse can have severe consequences on policy analysis and evaluation of transport investments; thus, it is crucial to continue research on this problem to try to give a theoretical justification to the many relevant issues that remain uncovered. One particularly interesting issue, which has not been well explored, is the effect of partial data enrichment on the correlation structure of alternatives (i.e., when different correlation structures are revealed in the RP and SP data sets). This problem, which is often found in practice, has no trivial solution and raises new interesting theoretical questions about estimation and prediction. In this paper, theoretical and practical implications of this problem are discussed and then empirical evidence is provided, from a real case, of the errors that may creep in when these models are not applied correctly. Finally some guidelines to help fill this important gap in the proper use of RP-SP data are provided.