University of Amsterdam, The Netherlands.
Br J Math Stat Psychol. 2010 May;63(Pt 2):293-317. doi: 10.1348/000711009X456935. Epub 2009 Sep 30.
Maximum likelihood estimation in the one-factor model is based on the assumption of multivariate normality for the observed data. This general distributional assumption implies three specific assumptions for the parameters in the one-factor model: the common factor has a normal distribution; the residuals are homoscedastic; and the factor loadings do not vary across the common factor scale. When any of these assumptions is violated, non-normality arises in the observed data. In this paper, a model is presented based on marginal maximum likelihood to enable explicit tests of these assumptions. In addition, the model is suitable to incorporate the detected violations, to enable statistical modelling of these effects. Two simulation studies are reported in which the viability of the model is investigated. Finally, the model is applied to IQ data to demonstrate its practical utility as a means to investigate ability differentiation.
在单因素模型中，极大似然估计基于观察数据的多元正态分布假设。这种一般的分布假设对单因素模型中的参数有三个具体的假设：共同因素具有正态分布；残差具有同方差性；因子负荷在共同因子标度上不变化。当这些假设中的任何一个被违反时，观察数据中就会出现非正态性。本文提出了一种基于边缘极大似然的模型，以能够对这些假设进行明确的检验。此外，该模型适合纳入已检测到的违反情况，以能够对这些影响进行统计建模。报告了两项模拟研究，以调查该模型的可行性。最后，将该模型应用于智商数据，以证明其作为一种调查能力差异的实用工具的实际效用。
