title: Asymptotic Robustness Study of the Polychoric Correlation Estimation.
abstract: Asymptotic robustness against misspecification of the underlying distribution for the polychoric correlation estimation is studied. The asymptotic normality of the pseudo-maximum likelihood estimator is derived using the two-step estimation procedure. The t distribution assumption and the skew-normal distribution assumption are used as alternatives to the normal distribution assumption in a numerical study. The numerical results show that the underlying normal distribution can be substantially biased, even though skewness and kurtosis are not large. The skew-normal assumption generally produces a lower bias than the normal assumption. Thus, it is worth using a non-normal distributional assumption if the normal assumption is dubious.
authors.affiliation: Department of Statistics, Uppsala University, 751 20 , Uppsala, Sweden. shaobo.jin@statistik.uu.se.
authors.forename: Shaobo
authors.initials: S
authors.lastname: Jin
authors.affiliation: Department of Statistics, Uppsala University, 751 20 , Uppsala, Sweden.
authors.forename: Fan
authors.initials: F
authors.lastname: Yang-Wallentin
mesh_terms: D000704:Analysis of Variance; D015982:Bias; D006801:Humans; D016013:Likelihood Functions; D015233:Models, Statistical; D016011:Normal Distribution; D011594:Psychometrics
keywords: asymptotic covariance matrix; non-normality; pseudo-maximum likelihood; underlying distribution