Distinctive and incompatible properties of two common classes of IRT models for graded responses
1995
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Distinctive and incompatible properties of two common classes of IRT models for graded responses
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1995
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Abstract
Two classes of models for graded responses, the first
based on the work of Thurstone and the second based on
the work of Rasch, are juxtaposed and shown to satisfy
important, but mutually incompatible, criteria and to reflect
different response processes. Specifically, in the
Thurstone models if adjacent categories are joined to
form a new category, either before or after the data are
collected, then the probability of a response in the new
category is the sum of the probabilities of the responses
in the original categories. However, the model does not
have the explicit property that if the categories are so
joined, then the estimate of the location of the entity or
object being measured is invariant before and after the
joining. For the Rasch models, if a pair of adjacent categories
are joined and then the data are collected, the estimate
of the location of the entity is the same before
and after the joining, but the probability of a response in
the new category is not the sum of the probabilities of
the responses in the original categories. Furthermore, if
data satisfy the model and the categories are joined after
the data are collected, then they no longer satisfy the
same Rasch model with the smaller number of categories.
These differences imply that the choice between
these two classes of models for graded responses is not
simply a matter of preference; they also permit a better
understanding of the choice of models for graded response
data as a function of the underlying processes
they are intended to represent. Index terms: graded responses,
joining assumption, polytomous IRT models,
Rasch model, Thurstone model.
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Previously Published Citation
Andrich, David. (1995). Distinctive and incompatible properties of two common classes of IRT models for graded responses. Applied Psychological Measurement, 19, 101-119. doi:10.1177/014662169501900111
Suggested citation
Andrich, David. (1995). Distinctive and incompatible properties of two common classes of IRT models for graded responses. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/117442.
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