Uncertainty in Latent Trait Models and Dimensionality Reduction Methods for Complex Data: An Analysis of Taxpayer Perception on the Fiscal System

Collecting data through multiple measurements poses challenges in dealing with ordered categories, especially when several ratings measure one or more latent traits. This chapter proposes a hybrid model as an alternative to the conventional analysis that relies on the sum of individual item scores. Our approach involves synthesizing responses from multiple ordinal items into a single score using a dimension reduction approach. This synthesized score is then used as a predictor in a model designed explicitly for analysing ordinal response variables while accounting for subject-specific uncertainty in respondents’ answers. We implement the hybrid approach in the context of tax compliance models, where multiple ratings assess taxpayers’ perceptions on ordinal scales. Our analysis utilizes multivariate ordinal data models with a specification of latent variables. It has been shown that neglecting subject-specific uncertainty can lead to biased estimates of model parameters, and our proposed approach effectively addresses this concern. Additionally, we discuss the policy implications of our findings, highlighting the importance of incorporating subject-specific uncertainty when designing effective tax compliance strategies.