How Should We Assess the Fit of Rasch-Type Models? Approximating the Power of Goodness-of-Fit Statistics in Categorical Data Analysis

Autor/inn/en	Maydeu-Olivares, Alberto; Montano, Rosa
Titel	How Should We Assess the Fit of Rasch-Type Models? Approximating the Power of Goodness-of-Fit Statistics in Categorical Data Analysis
Quelle	In: Psychometrika, 78 (2013) 1, S.116-133 (18 Seiten) PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0033-3123
DOI	10.1007/s11336-012-9293-1
Schlagwörter	Foreign Countries; Item Response Theory; Statistics; Data Analysis; Goodness of Fit; Psychometrics; Test Items; Measurement Techniques; Spain + Suchen Sie Ihr Suchwort? Ausland; Item-Response-Theorie; Statistik; Auswertung; Psychometry; Psychometrie; Test content; Testaufgabe; Messtechnik; Spanien
Abstract	We investigate the performance of three statistics, R [subscript 1], R [subscript 2] (Glas in "Psychometrika" 53:525-546, 1988), and M [subscript 2] (Maydeu-Olivares & Joe in "J. Am. Stat. Assoc." 100:1009-1020, 2005, "Psychometrika" 71:713-732, 2006) to assess the overall fit of a one-parameter logistic model (1PL) estimated by (marginal) maximum likelihood (ML). R [subscript 1] and R [subscript 2] were specifically designed to target specific assumptions of Rasch models, whereas M [subscript 2] is a general purpose test statistic. We report asymptotic power rates under some interesting violations of model assumptions (different item discrimination, presence of guessing, and multidimensionality) as well as empirical rejection rates for correctly specified models and some misspecified models. All three statistics were found to be more powerful than Pearson's X [superscript 2] against two- and three-parameter logistic alternatives (2PL and 3PL), and against multidimensional 1PL models. The results suggest that there is no clear advantage in using goodness-of-fit statistics specifically designed for Rasch-type models to test these models when marginal ML estimation is used. (As Provided).
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Update	2017/4/10