Likelihood-based tests for a class of misspecified finite mixture models for ordinal categorical data

• Roberto Colombi ^[1] ; Sabrina Giordano ^[2]
  1. [1] University of Bergamo

     University of Bergamo

     Bérgamo, Italia

     
  2. [2] University of Calabria

     University of Calabria

     Cosenza, Italia

     
• Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 28, Nº. 4, 2019, págs. 1175-1202
• Idioma: inglés
• DOI: 10.1007/s11749-019-00626-w
• Texto completo no disponible (Saber más ...)
• Resumen

  • The main purpose of this paper is to apply likelihood-based hypothesis testing procedures to a class of latent variable models for ordinal responses that allow for uncertain answers (Colombi et al. in Scand J Stat, 2018. https://doi.org/10.1111/sjos.12366). As these models are based on some assumptions, needed to describe different respondent behaviors, it is essential to discuss inferential issues without assuming that the tested model is correctly specified. By adapting the works of White (Econometrica 50(1):1–25, 1982) and Vuong (Econometrica 57(2):307–333, 1989), we are able to compare nested models under misspecification and then contrast the limiting distributions of Wald, Lagrange multiplier/score and likelihood ratio statistics with the classical asymptotic Chi-square to show the consequences of ignoring misspecification.