A Third Moment Adjusted Test Statistic for Small Sample Factor Analysis

Autor/inn/en	Lin, Johnny; Bentler, Peter M.
Titel	A Third Moment Adjusted Test Statistic for Small Sample Factor Analysis
Quelle	In: Multivariate Behavioral Research, 47 (2012) 3, S.448-462 (15 Seiten) PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0027-3171
DOI	10.1080/00273171.2012.673948
Schlagwörter	Factor Analysis; Statistical Analysis; Scaling; Sample Size; Simulation; Error of Measurement; Robustness (Statistics); Goodness of Fit + Suchen Sie Ihr Suchwort? Faktorenanalyse; Statistische Analyse; Scale construction; Skalenkonstruktion; Simulation program; Simulationsprogramm; Messfehler; Widerstandsfähigkeit
Abstract	Goodness-of-fit testing in factor analysis is based on the assumption that the test statistic is asymptotically chi-square, but this property may not hold in small samples even when the factors and errors are normally distributed in the population. Robust methods such as Browne's (1984) asymptotically distribution-free method and Satorra Bentler's (1988, 1994) mean scaling statistic were developed under the presumption of nonnormality in the factors and errors. This article finds new application to the case where factors and errors are normally distributed in the population but the skewness of the obtained test statistic is still high due to sampling error in the observed indicators. An extension of Satorra Bentler's statistic is proposed that not only scales the mean but also adjusts the degrees of freedom based on the skewness of the obtained test statistic in order to improve its robustness under small samples. A simple simulation study shows that this third moment adjusted statistic asymptotically performs on par with previously proposed methods and at a very small sample size offers superior Type I error rates under a properly specified model. Data from Mardia, Kent, and Bibby's (1980) study of students tested for their ability in 5 content areas that were either open or closed book were used to illustrate the real-world performance of this statistic. (Contains 1 table and 2 figures.) (As Provided).
Anmerkungen	Psychology Press. Available from: Taylor & Francis, Ltd. 325 Chestnut Street Suite 800, Philadelphia, PA 19106. Tel: 800-354-1420; Fax: 215-625-2940; Web site: http://www.tandf.co.uk/journals
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10