Analyzing the continuity of attitudinal and perceptual indicators in hybrid choice models

The main objective of this paper is to compare the consequences of treating the attitudinal and perceptual indicators of hybrid discrete choice (HDC) models as continuous or ordinal outcomes. Based on tradition and computational reasons, such indicators are still predominantly treated as continuous outcomes in practice. This usually neglects their nature (as respondents are normally asked to state their preferences, or level of agreement with a set of statements, using a discrete scale) and may induce bias. We conducted an analysis based on simulated data and real information (two case studies) and were able to find that the distribution of the indicators (especially when associated with non-uniformly spaced thresholds) may lead to a clear deterioration of the model's overall predictive capacity, when assuming continuous indicators. This, however, does not translate to the goodness-of-fit of the discrete-choice component of the HDC model. Along the same line, a higher relative variability of the latent variables increases the differences between both approaches (ordinal and continuous outcomes), especially concerning the goodness-of-fit of the discrete-choice component of the model. It was not possible to identify a relation between the predictive capacity of both approaches and the amount of available information. Considering more indicators tend to reduce the gap between both approaches, but the effect is significantly smaller than the effect of the relative variability. Finally, two case studies using real data confirmed that no major differences, regarding the predictability of the discrete choices can be observed when the relative variability of the latent variables is low. Thus, we recommend analyzing this relative variability in order to decide on the suitability of the continuous assumption as a suitable alternative to the more onerous but correct ordinal treatment.