An Isotonic Partial Credit Model for Ordering Subjects on the Basis of Their Sum Scores

Autor/in	Ligtvoet, Rudy
Titel	An Isotonic Partial Credit Model for Ordering Subjects on the Basis of Their Sum Scores
Quelle	In: Psychometrika, 77 (2012) 3, S.479-494 (16 Seiten) PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0033-3123
DOI	10.1007/s11336-012-9272-6
Schlagwörter	Simulation; Item Response Theory; Comparative Analysis; Scores; Models; Observation; Bayesian Statistics; Tests; Data Analysis; Serial Ordering; Evaluation Methods; Computation + Suchen Sie Ihr Suchwort? Simulation program; Simulationsprogramm; Item-Response-Theorie; Analogiemodell; Beobachtung; Examination; Prüfung; Examen; Auswertung; Ordnen; Ordnungsstruktur; Ordnungssystem
Abstract	In practice, the sum of the item scores is often used as a basis for comparing subjects. For items that have more than two ordered score categories, only the partial credit model (PCM) and special cases of this model imply that the subjects are stochastically ordered on the common latent variable. However, the PCM is very restrictive with respect to the constraints that it imposes on the data. In this paper, sufficient conditions for the stochastic ordering of subjects by their sum score are obtained. These conditions define the isotonic (nonparametric) PCM model. The isotonic PCM is more flexible than the PCM, which makes it useful for a wider variety of tests. Also, observable properties of the isotonic PCM are derived in the form of inequality constraints. It is shown how to obtain estimates of the score distribution under these constraints by using the Gibbs sampling algorithm. A small simulation study shows that the Bayesian p-values based on the log-likelihood ratio statistic can be used to assess the fit of the isotonic PCM to the data, where model-data fit can be taken as a justification of the use of the sum score to order subjects. (As Provided).
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Update	2017/4/10