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An Item Response Model for Multidimensional Analysis of Multiple-Choice Data

An Item Response Model for Multidimensional Analysis of Multiple-Choice Data An item response model, similar to that in test theory, was proposed for multiple-choice questionaire data. In this model both subjects and item categories are represented as points in a multidimensional euclidean space. The probability of a particular subject choosing a particular item category is stated as a decreasing function of the distance between the subject point and the item category point. The subject point is assumed to follow a certain distribution, and is then integrated out to derive marginal probabilities of response patterns. A marginal maximum likelihood (MML) method was developed to estimate coordinates of the item category points as well as distributional properties of the subject point. Bock and Aitkin’s EM algorithm was adapted to the MML estimation of the proposed model. Examples were given to illustrate the method, which we call MAXMC. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Behaviormetrika Springer Journals

An Item Response Model for Multidimensional Analysis of Multiple-Choice Data

Takane, Yoshio
Behaviormetrika , Volume 23 (2) – Sep 15, 1996
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15 pages

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Publisher
Springer Journals
Copyright
Copyright
Subject
Statistics; Statistical Theory and Methods; Statistics for Business, Management, Economics, Finance, Insurance; Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences
ISSN
0385-7417
eISSN
1349-6964
DOI
10.2333/bhmk.23.153
Publisher site
See Article on Publisher Site

Abstract

An item response model, similar to that in test theory, was proposed for multiple-choice questionaire data. In this model both subjects and item categories are represented as points in a multidimensional euclidean space. The probability of a particular subject choosing a particular item category is stated as a decreasing function of the distance between the subject point and the item category point. The subject point is assumed to follow a certain distribution, and is then integrated out to derive marginal probabilities of response patterns. A marginal maximum likelihood (MML) method was developed to estimate coordinates of the item category points as well as distributional properties of the subject point. Bock and Aitkin’s EM algorithm was adapted to the MML estimation of the proposed model. Examples were given to illustrate the method, which we call MAXMC.

Journal

Behaviormetrika – Springer Journals

Published: Sep 15, 1996

References

  • A new look at the statistical model identification
    Akaike, H
  • Baysian statistics
    Akaike, H
  • Latent variable models and factor analysis
    Bartholomew, DJ
  • Discrete multivariate analysis theory and practice
    Bishop, YMM; Fienberg, SE; Holland, PW
  • Estimating item parameters and latent ability when responses are scored in two or more nominal categories
    Bock, RD
  • Marginal maximum likelihood estimation of item parameters: Applications of an EM algorithm
    Bock, RD; Aitkin, M
  • Full information item factor analysis
    Bock, RD; Gibbons, R; Muraki, E
  • Fitting a response model for n dichotomously scored items
    Bock, RD; Lieberman, M
  • A theory of data
    Coombs, CH
  • Confusable and discriminable stimuli: Comment on Nosofsky (1986) and Shepar
    Ennis, DM
  • Theory and applications of correspondence analysis
    Greenacre, MJ
  • On the prediction of phenomena from qualitative data and the quantification of qualitative data from mathematico-statistical point of view
    Hayashi, C
  • Changes in belief systems, quality of life issues and social conditions over 25 years in post-war Japan
    Hayashi, C
  • Parella Measurement of latent traits by proximity items
    Hoijtink, H
  • Obtaining the observed information matrix from the Poisson log linear model with incomplete data
    Lang, J
  • Latent structure analysis
    Lazarsfeld, PF; Henry, N
  • Työntekijäin työasema ja työpaikkaliikkuvuus erikokoisissa teollisuusyrityksissä. [Bluecollar work position and workplace mobility in small and large industial firms, I. Theoretical point of departure and comparison of workers in small and large industrial firms]
    Leimu, H
  • Finding the observed information matrix when using the EM algorithm
    Louis, TA
  • Individual choice behavior
    Luce, RD
  • Analysis of categorical data: dual scaling and its applications
    Nishisato, S
  • Attention, similarity, and the identification-categorization relationship
    Nosofsky, RM
  • Stimulus and response generalization: A stochastic model relating generalization to distance in psychological space
    Shepard, RN
  • Discrimination and generalization in identification and classification: Comment on Nosofsky
    Shepard, RN
  • Kategorikaru deta no inshibunseki [Factor analysis of categorical data]
    Shigemasu, K
  • The relationship between item response theory and factor analysis of discretized variables
    Takane, Y; Leeuw, J
  • Multidimensional data analysis
    Takane, Y; Shibayama, T
  • Multidimensional models of perception and cognition
    Takane, Y; Shibayama, T