SMABS 2004 Jena University
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European Association of Methodology

Department of methodology and evaluation research

Jena University

Contributions: Abstract

A generalized measure of proficiencies variability that is invariant against different parameterization of the discrimination parameter: A reply to H. Müller

Jörg Michael Müller
University of Tübingen

Based on a discussion about the possibility to compare Rasch-scaled variance (1PL) of the person parameter from different questionnaires (Müller, 2003a) this contribution illustrates H. Müller's and the author's positions and presumes a generalized measure of variability. The author assumes that the variance of person proficiency estimates could vary significantly between psychological dimensions (2002). The measure earlier proposed by Müller (2002) to measure variability (also adjusted for the measurement error) assumes discrimination parameters of 1.

A modified 2PL (but with equal discrimination for all items) was used to generate known variabilities that are replicated by a new measure for variability; no matter which parameterization was uses to overcome the scale indeterminancy (fixing discrimination or variance of the person parameter to 1). Additionally, the simulation study reveals systematic artefacts (negative reliability coefficients) from software packages (BILOG-MG) dependent on the approach to determine a scale and proficiency variability. The consequences suppose the manipulation of the proficiency variability in simulation studies, e.g. evaluating estimation algorithms. Applications of the measure of variability had been supposed on earlier presentation, e.g. proofing content validity (Müller 2003b).


Müller, J.M. (2002). Different variation in psychological dimensions; an interpretation of the range of person parameters. Zeitschrift für Differentielle und Diagnostische Psychologie, 261-271.

Müller, J.M. (2003a). The utility for psychological diagnostic from the interpretation of the estimated Rasch-scaled person parameter variances. Positionsreferat auf der 7. Arbeitstagung der Fachgruppe Differentielle Psychologie, Persönlichkeitspsychologie und Psychologische Diagnostik in Halle, 29.-30 September.

Müller, J.M. (2003b). Comparison of the NEO-FFI, EPP, 16PF-R, EPQ-R and TIPI Extraversion Scale: A new approach to proofing content validity by comparing the Rasch-scaled variance of person parameters. 11th Biennial Meeting of the International Society for the Study of Individual Differences in Graz, Austria, 13-17 July.