A hyperbolic cosine latent trait model for unfolding dichotomous single-stimulus responses
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A hyperbolic cosine latent trait model for unfolding dichotomous single-stimulus responses
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1993
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Abstract
Social-psychological variables are typically
measured using either cumulative or unfolding
response processes. In the former, the greater the
location of a person relative to the location of a
stimulus on the continuum, the greater the probability
of a positive response; in the latter, the
closer the location of the person to the location of
the statement, irrespective of direction, the greater
the probability of a positive response. Formal
probability models for these processes are, respectively,
monotonically increasing and single-peaked
as a function of the location of the person relative
to the location of the statement. In general, these
models have been considered to be independent of
each other. However, if statements constructed on
the basis of a cumulative model have three ordered
response categories, the response function within
the statement for the middle category is in fact
single-peaked. Using this observation, a unidimensional
model for responses to statements that have
an unfolding structure was constructed from the
cumulative Rasch model for ordered response
categories. A location and unit of measurement
parameter exist for each statement. A joint maximum
likelihood estimation procedure was investigated.
Analysis of a small simulation study and a
small real dataset showed that the model is readily
applicable. Index terms: attitude measurement, item
response theory, latent trait theory, latent trait theory, Rasch models, unfolding data,
unidimensional scaling.
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Andrich, David & Luo, Guanzhong. (1993). A hyperbolic cosine latent trait model for unfolding dichotomous single-stimulus responses. Applied Psychological Measurement, 17, 253-276. doi:10.1177/014662169301700307
Suggested citation
Andrich, David; Luo, Guanzhong. (1993). A hyperbolic cosine latent trait model for unfolding dichotomous single-stimulus responses. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/116369.
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