caa a22 4500 606242295 CHVBK 20210128101318.0 cr unu---uuuuu 210128e20150601xx s 000 0 eng 10.1007/s11336-013-9386-5 doi (NATIONALLICENCE)springer-10.1007/s11336-013-9386-5 Empirical Correction to the Likelihood Ratio Statistic for Structural Equation Modeling with Many Variables [Elektronische Daten] [Ke-Hai Yuan, Yubin Tian, Hirokazu Yanagihara] 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 typeI errors reasonably well whenever N≥max(50,2p). The formulations of the empirically corrected statistics are further used to predict typeI errors of T ML as reported in the literature, and they perform well. The Psychometric Society, 2013 Bartlett correction nationallicence Bayesian information criterion nationallicence maximum likelihood nationallicence typeI errors nationallicence Yuan Ke-Hai Department of Psychology, University of Notre Dame, 46556, Notre Dame, IN, USA aut Tian Yubin Department of Psychology, University of Notre Dame, 46556, Notre Dame, IN, USA aut Yanagihara Hirokazu Department of Psychology, University of Notre Dame, 46556, Notre Dame, IN, USA aut Psychometrika Springer US; http://www.springer-ny.com 80/2(2015-06-01), 379-405 0033-3123 80:2<379 2015 80 11336 https://doi.org/10.1007/s11336-013-9386-5 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s11336-013-9386-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Yuan Ke-Hai Department of Psychology, University of Notre Dame, 46556, Notre Dame, IN, USA aut NATIONALLICENCE 700 1- Tian Yubin Department of Psychology, University of Notre Dame, 46556, Notre Dame, IN, USA aut NATIONALLICENCE 700 1- Yanagihara Hirokazu Department of Psychology, University of Notre Dame, 46556, Notre Dame, IN, USA aut NATIONALLICENCE 773 0- Psychometrika Springer US; http://www.springer-ny.com 80/2(2015-06-01), 379-405 0033-3123 80:2<379 2015 80 11336