Alternating imputation posterior estimation of models with crossed random effects
Generalized linear mixed models or latent variable models for categorical data are difficult to estimate if the random effects or latent variables vary at non-nested levels, such as persons and test items.Â Clayton and Rasbash (1999) suggested an Alternating Imputation Posterior (AIP) algorithm for approximate maximum likelihood estimation. For item response models with random item effects, the algorithm iterates between an item wing in which the item mean and variance are estimated for given person effects and a person wing in which the person mean and variance are estimated for given item effects. The person effects used for the item wing are sampled from the conditional posterior distribution estimated in the person wing and vice versa.Â Clayton and Rasbash (1999) used marginal quasi-likelihood (MQL) and penalized quasi-likelihood (PQL) estimation within the AIP algorithm, but this method has been shown to produce biased estimates in many situations, so we use maximum likelihood estimation with adaptive quadrature. We apply the proposed algorithm to the famous salamander mating data, comparing the estimates with many other methods, and to an educational testing dataset. We also present a simulation study to assess performance of the AIP algorithm and the Laplace approximation with different numbers of items and persons and a range of item and person variances.
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- Sophia Rabe-Hesketh & Anders Skrondal, 2012. "Multilevel and Longitudinal Modeling Using Stata, 3rd Edition," Stata Press books, StataCorp LP, edition 3, number mimus2, September.
- Diaz, Rafael E., 2007. "Comparison of PQL and Laplace 6 estimates of hierarchical linear models when comparing groups of small incident rates in cluster randomised trials," Computational Statistics & Data Analysis, Elsevier, vol. 51(6), pages 2871-2888, March.
- R. Darrell Bock & Marcus Lieberman, 1970. "Fitting a response model forn dichotomously scored items," Psychometrika, Springer;The Psychometric Society, vol. 35(2), pages 179-197, June.
- Hua-Hua Chang & William Stout, 1993. "The asymptotic posterior normality of the latent trait in an IRT model," Psychometrika, Springer;The Psychometric Society, vol. 58(1), pages 37-52, March.
- Germán Rodríguez & Noreen Goldman, 2001. "Improved estimation procedures for multilevel models with binary response: a case-study," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 164(2), pages 339-355.
- Joe, Harry, 2008. "Accuracy of Laplace approximation for discrete response mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5066-5074, August.
- Jean-Paul Fox & Cees Glas, 2001. "Bayesian estimation of a multilevel IRT model using gibbs sampling," Psychometrika, Springer;The Psychometric Society, vol. 66(2), pages 271-288, June.
- Butler, J S & Moffitt, Robert, 1982. "A Computationally Efficient Quadrature Procedure for the One-Factor Multinomial Probit Model," Econometrica, Econometric Society, vol. 50(3), pages 761-764, May.
- Stephen Schilling & R. Bock, 2005. "High-dimensional maximum marginal likelihood item factor analysis by adaptive quadrature," Psychometrika, Springer;The Psychometric Society, vol. 70(3), pages 533-555, September.
- Paul Boeck, 2008. "Random Item IRT Models," Psychometrika, Springer;The Psychometric Society, vol. 73(4), pages 533-559, December.
- Robert Mislevy, 1991. "Randomization-based inference about latent variables from complex samples," Psychometrika, Springer;The Psychometric Society, vol. 56(2), pages 177-196, June.
- Rabe-Hesketh, Sophia & Skrondal, Anders & Pickles, Andrew, 2005. "Maximum likelihood estimation of limited and discrete dependent variable models with nested random effects," Journal of Econometrics, Elsevier, vol. 128(2), pages 301-323, October.
- Noh, Maengseok & Lee, Youngjo, 2007. "REML estimation for binary data in GLMMs," Journal of Multivariate Analysis, Elsevier, vol. 98(5), pages 896-915, May.
- W. Albers & R. Does & Tj. Imbos & M. Janssen, 1989. "A stochastic growth model applied to repeated tests of academic knowledge," Psychometrika, Springer;The Psychometric Society, vol. 54(3), pages 451-466, September.
- J. G. Booth & J. P. Hobert, 1999. "Maximizing generalized linear mixed model likelihoods with an automated Monte Carlo EM algorithm," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 265-285.
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