title: Empirical Correction to the Likelihood Ratio Statistic for Structural Equation Modeling with Many Variables.
abstract: Survey data typically contain many variables. Structural equation modeling (SEM) is commonly used in analyzing such data. The most widely used statistic for evaluating the adequacy of a SEM model is T ML, a slight modification to the likelihood ratio statistic. Under normality assumption, T ML approximately follows a chi-square distribution when the number of observations (N) is large and the number of items or variables (p) is small. However, in practice, p can be rather large while N is always limited due to not having enough participants. Even with a relatively large N, empirical results show that T ML rejects the correct model too often when p is not too small. Various corrections to T ML have been proposed, but they are mostly heuristic. Following the principle of the Bartlett correction, this paper proposes an empirical approach to correct T ML so that the mean of the resulting statistic approximately equals the degrees of freedom of the nominal chi-square distribution. Results show that empirically corrected statistics follow the nominal chi-square distribution much more closely than previously proposed corrections to T ML, and they control type I errors reasonably well whenever N ≥ max(50,2p). The formulations of the empirically corrected statistics are further used to predict type I errors of T ML as reported in the literature, and they perform well.
authors: Department of Psychology, University of Notre Dame, Notre Dame, IN, 46556, USA, kyuan@nd.edu.
authors: Ke-Hai
authors: KH
authors: Yuan
authors: Yubin
authors: Y
authors: Tian
authors: Hirokazu
authors: H
authors: Yanagihara
mesh_terms: D000465:Algorithms; D016009:Chi-Square Distribution; D006801:Humans; D016013:Likelihood Functions; D011594:Psychometrics; D012107:Research Design; D011795:Surveys and Questionnaires