A Cautionary Note on Using G[squared](dif) to Assess Relative Model Fit in Categorical Data Analysis

Autor/inn/en	Maydeu-Olivares, Albert; Cai, Li
Titel	A Cautionary Note on Using G[squared](dif) to Assess Relative Model Fit in Categorical Data Analysis
Quelle	In: Multivariate Behavioral Research, 41 (2006) 1, S.55-64 (10 Seiten) PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0027-3171
DOI	10.1207/s15327906mbr4101_4
Schlagwörter	Goodness of Fit; Data Analysis; Simulation; Item Response Theory; Robustness (Statistics); Maximum Likelihood Statistics + Suchen Sie Ihr Suchwort? Auswertung; Simulation program; Simulationsprogramm; Item-Response-Theorie; Widerstandsfähigkeit
Abstract	The likelihood ratio test statistic G[squared](dif) is widely used for comparing the fit of nested models in categorical data analysis. In large samples, this statistic is distributed as a chi-square with degrees of freedom equal to the difference in degrees of freedom between the tested models, but only if the least restrictive model is correctly specified. Yet, this statistic is often used in applications without assessing the adequacy of the least restrictive model. This may result in incorrect substantive conclusions as the above large sample reference distribution for G[squared](dif) is no longer appropriate. Rather, its large sample distribution will depend on the degree of model misspecification of the least restrictive model. To illustrate this, a simulation study is performed where this statistic is used to compare nested item response theory models under various degrees of misspecification of the least restrictive model. G[squared](dif) was found to be robust only under small model misspecification of the least restrictive model. Consequently, we argue that some indication of the absolute goodness of fit of the least restrictive model is needed before employing G[squared](dif) to assess relative model fit. (Author).
Anmerkungen	Lawrence Erlbaum Associates, Inc. 10 Industrial Avenue, Mahwah, NJ 07430. Tel: 800-926-6579; Tel: 201-258-2200; Fax: 201-236-0072; e-mail: journals@erlbaum.com; Web site: https://www.erlbaum.com.
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10