Global, local, and graphical person-fit analysis using person-response functions.
Person-fit statistics test whether the likelihood of a respondent's complete vector of item scores on a test is low given the hypothesized item response theory model. This binary information may be insufficient for diagnosing the cause of a misfitting item-score vector. The authors propose a comprehensive methodology for person-fit analysis in the context of nonparametric item response theory. The methodology (a) includes H. Van der Flier's (1982) global person-fit statistic U3 to make the binary decision about fit or misfit of a person's item-score vector, (b) uses kernel smoothing (J. O. Ramsay, 1991) to estimate the person-response function for the misfitting item-score vectors, and (c) evaluates unexpected trends in the person-response function using a new local person-fit statistic (W. H. M. Emons, 2003). An empirical data example shows how to use the methodology for practical person-fit analysis.
Emons
Wilco H M
WH
Department of Methodology and Statistics, Tilburg University, Tilburg, Netherlands. w.h.m.emons@uvt.nl
Sijtsma
Klaas
K
Meijer
Rob R
RR
D006801:Humans; D008960:Models, Psychological; D011584:Psychology / Q000379:methods*; D018709:Statistics, Nonparametric