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

This paper addresses the continuity of attitudinal and perceptual indicators in hybrid discrete choice models and the main objective of this work is to compare the consequences of treating the indicators as continuous or ordinal outcomes, given different assumptions about the way in which these are stated. Based on tradition and for computational reasons, such indicators are predominantly treated as continuous outcomes. 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 important bias. We conducted an analysis based on simulated data and real data (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 predictive capacity, especially when assuming continuous indicators. Along the same line, higher relative variability among the latent variables increases the differences between both approaches (ordinal and continuous outcomes), especially concerning goodness-offit of the discrete-choice component. It was not possible to identify a relation between the predictive capacity of both approaches and the amount of available information. Finally, both case studies using real data show an improvement in overall goodness-of-fit when considering the indicators as ordinal outcomes, but this does not translate in a better predictability of the discrete choices.