Pseudo-likelihood estimation of multidimensional response models: Polytomous and dichotomous items

Youngshil Paek, Carolyn Jane Anderson

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Log-multiplicative association (LMA) models have been proposed as uni- and multidimensional item response models for dichotomous and/or polytomous items. A problem that prevents more widespread use of LMA models is that current estimation methods for moderate to large problems are computationally prohibitive. As a special case of a log-linear model, maximum likelihood estimation (MLE) of LMA models requires iteratively computing fitted values for all possible response patterns, the number of which increases exponentially as the number of items and/or response options per item increases. Anderson et al. (J. Stat. Softw. 20, 2007, doi:10.18637/jss.v020.i06) used pseudo-likelihood estimation for linear-by-linear models, which are special cases of LMA models, but in their proposal, the category scores are fixed to specific values. The solution presented here extends pseudo-likelihood estimation to more general LMA models where category scores are estimated. Our simulation studies show that parameter estimates from the new algorithm are nearly identical to parameter estimates from MLE, work for large numbers of items, are insensitive to starting values, and converge in a small number of iterations.

Original languageEnglish (US)
Title of host publicationQuantitative Psychology - 81st Annual Meeting of the Psychometric Society, 2016
EditorsWen-Chung Wang, Marie Wiberg, Steven A. Culpepper, Jeffrey A. Douglas, L. Andries van der Ark
PublisherSpringer New York LLC
Pages21-30
Number of pages10
ISBN (Print)9783319562933
DOIs
StatePublished - Jan 1 2017
Event81st annual meeting of the Psychometric Society, 2016 - Asheville, United States
Duration: Jul 11 2016Jul 15 2016

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume196
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Other

Other81st annual meeting of the Psychometric Society, 2016
CountryUnited States
CityAsheville
Period7/11/167/15/16

Fingerprint

Association Model
Multiplicative Model
Pseudo-likelihood
Maximum Likelihood Estimation
Log-linear Models
Model
Estimate
Linear Model
Simulation Study
Converge
Iteration
Computing

Keywords

  • Formative measurement models
  • Log linear-by-linear models
  • Log-multiplicative association models
  • Multidimensional item response theory
  • Second-order exponential models

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Paek, Y., & Anderson, C. J. (2017). Pseudo-likelihood estimation of multidimensional response models: Polytomous and dichotomous items. In W-C. Wang, M. Wiberg, S. A. Culpepper, J. A. Douglas, & L. A. van der Ark (Eds.), Quantitative Psychology - 81st Annual Meeting of the Psychometric Society, 2016 (pp. 21-30). (Springer Proceedings in Mathematics and Statistics; Vol. 196). Springer New York LLC. https://doi.org/10.1007/978-3-319-56294-0_3

Pseudo-likelihood estimation of multidimensional response models : Polytomous and dichotomous items. / Paek, Youngshil; Anderson, Carolyn Jane.

Quantitative Psychology - 81st Annual Meeting of the Psychometric Society, 2016. ed. / Wen-Chung Wang; Marie Wiberg; Steven A. Culpepper; Jeffrey A. Douglas; L. Andries van der Ark. Springer New York LLC, 2017. p. 21-30 (Springer Proceedings in Mathematics and Statistics; Vol. 196).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Paek, Y & Anderson, CJ 2017, Pseudo-likelihood estimation of multidimensional response models: Polytomous and dichotomous items. in W-C Wang, M Wiberg, SA Culpepper, JA Douglas & LA van der Ark (eds), Quantitative Psychology - 81st Annual Meeting of the Psychometric Society, 2016. Springer Proceedings in Mathematics and Statistics, vol. 196, Springer New York LLC, pp. 21-30, 81st annual meeting of the Psychometric Society, 2016, Asheville, United States, 7/11/16. https://doi.org/10.1007/978-3-319-56294-0_3
Paek Y, Anderson CJ. Pseudo-likelihood estimation of multidimensional response models: Polytomous and dichotomous items. In Wang W-C, Wiberg M, Culpepper SA, Douglas JA, van der Ark LA, editors, Quantitative Psychology - 81st Annual Meeting of the Psychometric Society, 2016. Springer New York LLC. 2017. p. 21-30. (Springer Proceedings in Mathematics and Statistics). https://doi.org/10.1007/978-3-319-56294-0_3
Paek, Youngshil ; Anderson, Carolyn Jane. / Pseudo-likelihood estimation of multidimensional response models : Polytomous and dichotomous items. Quantitative Psychology - 81st Annual Meeting of the Psychometric Society, 2016. editor / Wen-Chung Wang ; Marie Wiberg ; Steven A. Culpepper ; Jeffrey A. Douglas ; L. Andries van der Ark. Springer New York LLC, 2017. pp. 21-30 (Springer Proceedings in Mathematics and Statistics).
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