Conceptual notes on models for discrete polytomous item responses
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Conceptual notes on models for discrete polytomous item responses
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1995
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Abstract
The following types of discrete item responses are distinguished
: nominal-dichotomous, ordinal-dichotomous,
nominal-polytomous, and ordinal-polytomous. Bock
(1972) presented a model for nominal-polytomous item
responses that, when applied to dichotomous responses,
yields Birnbaum’s (1968) two-parameter logistic model.
Applying Bock’s model to ordinal-polytomous items
leads to a conceptual problem. The ordinal nature of
the response variable must be preserved; this can be
achieved using three different methods. A number of existing
models are derived using these three methods. The
structure of these models is similar, but they differ in the
interpretation and qualities of their parameters. Information, parameter invariance, log-odds differences invariance,
and model violation also are discussed. Information
and parameter invariance of dichotomous item
response theory (IRT) also apply to polytomous IRT.
Specific objectivity of the Rasch model for dichotomous
items is a special case of log-odds differences invariance
of polytomous items. Differential item functioning
of dichotomous IRT is a special case of measurement
model violation of polytomous IRT. Index terms: adjacent
categories, continuation ratios, cumulative probabilities,
differential item functioning, log-odds
differences invariance, measurement model violation,
parameter invariance, polytomous IRT models.
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Mellenbergh, Gideon J. (1995). Conceptual notes on models for discrete polytomous item responses. Applied Psychological Measurement, 19, 91-100. doi:10.1177/014662169501900110
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doi:10.1177/014662169501900110
Suggested citation
Mellenbergh, Gideon J.. (1995). Conceptual notes on models for discrete polytomous item responses. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/117441.
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