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Multidimensional Item Response Theory Modeling of Binary Data: Large Sample Properties of NOHARM Estimates

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  • Albert Maydeu-Olivares

Abstract

NOHARM is a program that performs factor analysis for dichotomous variables assuming that these arise from an underlying multinormal distribution. Parameter estimates are obtained by minimizing an unweighted least squares function of the first- and second-order marginal proportions. Here, large sample standard errors for restricted as well as rotated unrestricted factor solutions are given. Also a test of the goodness of fit of the model to the first- and second-order marginals of the contingency table is proposed. In a simulation study, it was found that for small models, accurate parameter estimates, standard errors, and goodness-of-fit tests can be obtained with as few as 100 observations. Furthermore, NOHARM estimates, standard errors, and goodness-of-fit tests are comparable to those obtained using a related LISREL procedure.

Suggested Citation

  • Albert Maydeu-Olivares, 2001. "Multidimensional Item Response Theory Modeling of Binary Data: Large Sample Properties of NOHARM Estimates," Journal of Educational and Behavioral Statistics, , vol. 26(1), pages 51-71, March.
    • Handle: RePEc:sae:jedbes:v:26:y:2001:i:1:p:51-71
    DOI: 10.3102/10769986026001051
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    Cited by:

    1. Mirko Antino & Jesús M. Alvarado & Rodrigo A. Asún & Paul Bliese, 2020. "Rethinking the Exploration of Dichotomous Data: Mokken Scale Analysis Versus Factorial Analysis," Sociological Methods & Research, , vol. 49(4), pages 839-867, November.
    2. Albert Maydeu-Olivares & Harry Joe, 2006. "Limited Information Goodness-of-fit Testing in Multidimensional Contingency Tables," Psychometrika, Springer;The Psychometric Society, vol. 71(4), pages 713-732, December.
    3. Gregory Camilli & Jean-Paul Fox, 2015. "An Aggregate IRT Procedure for Exploratory Factor Analysis," Journal of Educational and Behavioral Statistics, , vol. 40(4), pages 377-401, August.
    4. Harry Joe & Alberto Maydeu-Olivares, 2010. "A General Family of Limited Information Goodness-of-Fit Statistics for Multinomial Data," Psychometrika, Springer;The Psychometric Society, vol. 75(3), pages 393-419, September.
    5. Alexander Robitzsch, 2024. "A Comparison of Limited Information Estimation Methods for the Two-Parameter Normal-Ogive Model with Locally Dependent Items," Stats, MDPI, vol. 7(3), pages 1-16, June.

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