### 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.

Original language | English |
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Pages (from-to) | 253-276 |

Number of pages | 24 |

Journal | Applied Psychological Measurement |

Volume | 17 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1 Jan 1993 |

Externally published | Yes |

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*Applied Psychological Measurement*, vol. 17, no. 3, pp. 253-276. https://doi.org/10.1177/014662169301700307

**A Hyperbolic Cosine Latent Trait Model For Unfolding Dichotomous Single-Stimulus Responses.** / Andrich, David; Luo, Guanzhong.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A Hyperbolic Cosine Latent Trait Model For Unfolding Dichotomous Single-Stimulus Responses

AU - Andrich, David

AU - Luo, Guanzhong

PY - 1993/1/1

Y1 - 1993/1/1

N2 - 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.

AB - 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.

KW - Attitude measurement

KW - item response theory

KW - latent trait theory

KW - Rasch models

KW - unfolding data

KW - unidimensional scaling

UR - http://www.scopus.com/inward/record.url?scp=84976936145&partnerID=8YFLogxK

U2 - 10.1177/014662169301700307

DO - 10.1177/014662169301700307

M3 - Article

VL - 17

SP - 253

EP - 276

JO - Applied Pyschological Measurement

JF - Applied Pyschological Measurement

SN - 0146-6216

IS - 3

ER -