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

  • Roberto Colombi
  • Sabrina GiordanoEmail author
Original Paper


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. 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.


Misspecified models Marginal models Likelihood ratio tests Weighted sum of Chi-squares 

Mathematics Subject Classification

62F03 62H15 



We would like to thank Rocco Servidio of the Department of Languages and Educational Sciences (University of Calabria, Italy) for providing the real data analyzed in Sect. 7. Moreover, we acknowledge two referees for their useful comments that improved the initial version of the paper.


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Copyright information

© Sociedad de Estadística e Investigación Operativa 2019

Authors and Affiliations

  1. 1.Department of Management, Information and Production EngineeringUniversity of BergamoBergamoItaly
  2. 2.Department of Economics, Statistics and Finance “Giovanni Anania”University of CalabriaCosenzaItaly

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