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

Roberto Colombi () and Sabrina Giordano ()
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Roberto Colombi: University of Bergamo
Sabrina Giordano: University of Calabria

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2019, vol. 28, issue 4, No 11, 1175-1202

Abstract: Abstract 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.

Keywords: Misspecified models; Marginal models; Likelihood ratio tests; Weighted sum of Chi-squares; 62F03; 62H15 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s11749-019-00626-w

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