Journal article
A hyperbolic cosine latent trait model for unfolding dichotomous single-stimulus responses
Applied Psychological Measurement, Vol.17(3), pp.253-276
1993
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 proba bility 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, respec tively, 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 unidimen sional 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 maxi mum likelihood estimation procedure was inves tigated. Analysis of a small simulation study and a small real dataset showed that the model is readily applicable.
Details
- Title
- A hyperbolic cosine latent trait model for unfolding dichotomous single-stimulus responses
- Authors/Creators
- D. Andrich (Author/Creator) - Murdoch UniversityG. Luo (Author/Creator) - South China Normal University
- Publication Details
- Applied Psychological Measurement, Vol.17(3), pp.253-276
- Publisher
- SAGE Publications
- Identifiers
- 991005545131607891
- Copyright
- © 1993, Sage Publications
- Murdoch Affiliation
- School of Psychology and Exercise Science
- Language
- English
- Resource Type
- Journal article
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- Collaboration types
- Domestic collaboration
- International collaboration
- Citation topics
- 6 Social Sciences
- 6.73 Social Psychology
- 6.73.685 Item Response Theory
- Web Of Science research areas
- Psychology, Mathematical
- Social Sciences, Mathematical Methods
- ESI research areas
- Psychiatry/Psychology