The Heteroscedastic Graded Response Model with a Skewed Latent Trait: Testing Statistical and Substantive Hypotheses Related to Skewed Item Category Functions

Autor/inn/en	Molenaar, Dylan; Dolan, Conor V.; de Boeck, Paul
Titel	The Heteroscedastic Graded Response Model with a Skewed Latent Trait: Testing Statistical and Substantive Hypotheses Related to Skewed Item Category Functions
Quelle	In: Psychometrika, 77 (2012) 3, S.455-478 (24 Seiten) PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0033-3123
DOI	10.1007/s11336-012-9273-5
Schlagwörter	Simulation; Regression (Statistics); Psychometrics; Item Response Theory; Models; Error of Measurement; Feedback (Response); Research; Computation; Scores; Classification; Tests + Suchen Sie Ihr Suchwort? Simulation program; Simulationsprogramm; Regression; Regressionsanalyse; Psychometry; Psychometrie; Item-Response-Theorie; Analogiemodell; Messfehler; Forschung; Classification system; Klassifikation; Klassifikationssystem; Examination; Prüfung; Examen
Abstract	The Graded Response Model (GRM; Samejima, "Estimation of ability using a response pattern of graded scores," Psychometric Monograph No. 17, Richmond, VA: The Psychometric Society, 1969) can be derived by assuming a linear regression of a continuous variable, Z, on the trait, [theta], to underlie the ordinal item scores (Takane & de Leeuw in "Psychometrika," 52:393-408, 1987). Traditionally, a normal distribution is specified for Z implying homoscedastic error variances and a normally distributed [theta]. In this paper, we present the Heteroscedastic GRM with Skewed Latent Trait, which extends the traditional GRM by incorporation of heteroscedastic error variances and a skew-normal latent trait. An appealing property of the extended GRM is that it includes the traditional GRM as a special case. This enables specific tests on the normality assumption of Z. We show how violations of normality in Z can lead to asymmetrical category response functions. The ability to test this normality assumption is beneficial from both a statistical and substantive perspective. In a simulation study, we show the viability of the model and investigate the specificity of the effects. We apply the model to a dataset on affect and a dataset on alexithymia. (As Provided).
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Update	2017/4/10