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Optimal designs for the generalized partial credit model
Author(s) -
Bürkner PaulChristian,
Schwabe Rainer,
Holling Heinz
Publication year - 2019
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1111/bmsp.12148
Subject(s) - context (archaeology) , mathematics , optimal design , bayes' theorem , polytomous rasch model , bayesian probability , ordinal scale , econometrics , point (geometry) , scale (ratio) , logistic regression , computer science , mathematical optimization , statistics , item response theory , psychometrics , quantum mechanics , biology , paleontology , physics , geometry
Analysing ordinal data is becoming increasingly important in psychology, especially in the context of item response theory. The generalized partial credit model ( GPCM ) is probably the most widely used ordinal model and has found application in many large‐scale educational assessment studies such as PISA . In the present paper, optimal test designs are investigated for estimating persons’ abilities with the GPCM for calibrated tests when item parameters are known from previous studies. We find that local optimality may be achieved by assigning non‐zero probability only to the first and last categories independently of a person's ability. That is, when using such a design, the GPCM reduces to the dichotomous two‐parameter logistic (2 PL ) model. Since locally optimal designs require the true ability to be known, we consider alternative Bayesian design criteria using weight distributions over the ability parameter space. For symmetric weight distributions, we derive necessary conditions for the optimal one‐point design of two response categories to be Bayes optimal. Furthermore, we discuss examples of common symmetric weight distributions and investigate under what circumstances the necessary conditions are also sufficient. Since the 2 PL model is a special case of the GPCM , all of these results hold for the 2 PL model as well.