Jin Shaobo, Yang-Wallentin Fan
Department of Statistics, Uppsala University, 751 20 , Uppsala, Sweden.
Psychometrika. 2017 Mar;82(1):67-85. doi: 10.1007/s11336-016-9512-2. Epub 2016 Sep 22.
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.
研究了针对多列相关估计中潜在分布误设的渐近稳健性。使用两步估计程序推导了伪最大似然估计量的渐近正态性。在数值研究中，使用t分布假设和偏态正态分布假设作为正态分布假设的替代。数值结果表明，即使偏度和峰度不大，潜在的正态分布也可能存在显著偏差。偏态正态假设通常比正态假设产生的偏差更低。因此，如果正态假设存疑，使用非正态分布假设是值得的。
