Alternating imputation posterior estimation of models with crossed random effects
AbstractGeneralized 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Elsevier in its journal Computational Statistics & Data Analysis.
Volume (Year): 55 (2011)
Issue (Month): 1 (January)
Contact details of provider:
Web page: http://www.elsevier.com/locate/csda
Adaptive quadrature Crossed random effects Generalized linear mixed model Item response theory Laplace approximation Random cross-classification Salamander mating data Two-way error components;
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Joe, Harry, 2008. "Accuracy of Laplace approximation for discrete response mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5066-5074, August.
- 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 761-64, May.
- 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.
- 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.
- Robert Mislevy, 1991. "Randomization-based inference about latent variables from complex samples," Psychometrika, Springer, vol. 56(2), pages 177-196, June.
- 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.
- W. Albers & R. Does & Tj. Imbos & M. Janssen, 1989. "A stochastic growth model applied to repeated tests of academic knowledge," Psychometrika, Springer, vol. 54(3), pages 451-466, September.
- Martijn G. De Jong & Jan-Benedict E. M. Steenkamp & Jean-Paul Fox, 2007. "Relaxing Measurement Invariance in Cross-National Consumer Research Using a Hierarchical IRT Model," Journal of Consumer Research, University of Chicago Press, vol. 34(2), pages 260-278, 06.
- 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.
- Noh, Maengseok & Lee, Youngjo, 2007. "REML estimation for binary data in GLMMs," Journal of Multivariate Analysis, Elsevier, vol. 98(5), pages 896-915, May.
- Paul Boeck, 2008. "Random Item IRT Models," Psychometrika, Springer, vol. 73(4), pages 533-559, December.
- Hua-Hua Chang & William Stout, 1993. "The asymptotic posterior normality of the latent trait in an IRT model," Psychometrika, Springer, vol. 58(1), pages 37-52, March.
- Jean-Paul Fox & Cees Glas, 2001. "Bayesian estimation of a multilevel IRT model using gibbs sampling," Psychometrika, Springer, vol. 66(2), pages 271-288, June.
- Sophia Rabe-Hesketh & Anders Skrondal, 2012. "Multilevel and Longitudinal Modeling Using Stata, 3rd Edition," Stata Press books, StataCorp LP, edition 3, number mimus2, March.
- Stephen Schilling & R. Bock, 2005. "High-dimensional maximum marginal likelihood item factor analysis by adaptive quadrature," Psychometrika, Springer, vol. 70(3), pages 533-555, September.
- R. Darrell Bock & Marcus Lieberman, 1970. "Fitting a response model forn dichotomously scored items," Psychometrika, Springer, vol. 35(2), pages 179-197, June.
- Susan Embretson & Xiangdong Yang, 2013. "A Multicomponent Latent Trait Model for Diagnosis," Psychometrika, Springer, vol. 78(1), pages 14-36, January.
- Sun-Joo Cho & Allan Cohen & Brian Bottge, 2013. "Detecting Intervention Effects Using a Multilevel Latent Transition Analysis with a Mixture IRT Model," Psychometrika, Springer, vol. 78(3), pages 576-600, July.
- Hanneke Geerlings & Cees Glas & Wim Linden, 2011. "Modeling Rule-Based Item Generation," Psychometrika, Springer, vol. 76(2), pages 337-359, April.
- Sun-Joo Cho & Jennifer Gilbert & Amanda Goodwin, 2013. "Explanatory Multidimensional Multilevel Random Item Response Model: An Application to Simultaneous Investigation of Word and Person Contributions to Multidimensional Lexical Representations," Psychometrika, Springer, vol. 78(4), pages 830-855, October.
- Sun-Joo Cho & Paul Boeck & Susan Embretson & Sophia Rabe-Hesketh, 2014. "Additive Multilevel Item Structure Models with Random Residuals: Item Modeling for Explanation and Item Generation," Psychometrika, Springer, vol. 79(1), pages 84-104, January.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.