Profile-Likelihood Approach for Estimating Generalized Linear Mixed Models With Factor Structures

Journal of Educational and Behavioral Statistics

Volumn 37, Issue 4, 2012, Pages 518-542

  Jeon, Minjeong ^a   Rabe Hesketh, Sophia ^a,b  

^a University of California Berkeley   (United States)

^b UNIVERSITY OF LONDON   (United Kingdom)

Author keywords

crossed random effects; factor structures; generalized linear mixed models; gllamm; item response theory (IRT); ML estimation; multilevel IRT; persistence parameters; R software

Indexed keywords

EID: 84864348503     PISSN: 10769986     EISSN: None     Source Type: Journal    
DOI: 10.3102/1076998611417628     Document Type: Article

References (56)

1. Adams R.,Wilson M.,Wu M.Multilevel item response models: An approach to errors in variables regression.Journal of Educational and Behavioral Statistics. 1997;22:47-76.
2. BatesD.MaechlerM. (2009). lme4: Linear mixed-effects models using S4 classes R package version 0.999375-31. Retrieved fromhttp://CRAN.Rproject.org/package=lme4.
3. Berkhof J.,Snijders T.A. B.Variance component testing in multilevel models.Journal of Educational and Behavioral Statistics. 2001;26:132-152.
4. Browne W.J.MCMC estimation in MLwiN. Bristol, UK: Centre for Multilevel Modelling; 2009:.
5. Browne W.J.,Draper D.A comparison of Bayesian and likelihood methods for fitting multilevel models.Bayesian Analysis. 2006;1:473-514.
6. Browne W.J.,Goldstein H.,Rasbash J.Multiple membership multiple classification (MMMC) models.Statistical Modelling. 2001;1:103-124.
7. Byrd R.H.,Lu P.,Nocedal J.,Zhu C.A limited memory algorithm for bound constrained optimization.SIAM Journal on Scientific Computing. 1995;16:1190-1208.
8. Cai L.,Yang J.S.,Hansen M.P.Generalized full-information item bifactor analysis.Psychological Methods. 2011;16:221-248.
9. Cho S.-J.,Rabe-Hesketh S.Alternating imputation posterior estimation of models with crossed random effects.Computational Statistics and Data Analysis. 2011;55:12-25.
10. De Boeck P.,Bakker M.,Zwitser R.,Nivard M.,Hofman A.,Tuerlinckx F.,Partchev I.The estimation of item response models with the lmer function from the lme4 package in R.Journal of Statistical Software. 2011;39:1-28.
11. De Boeck P.,Wilson M.Explanatory item response models: A generalized and nonlinear approach. New York, NY: Springer; 2004:.
12. Doolaard S.Schools in change or school in chain. Enschede, Netherlands: University of Twente; 1999:.
13. Doran H.,Bates D.,Bliese P.,Dowling M.Estimating the multilevel Rasch model: With the lme4 package.Journal of Statistical Software. 2007;20:1-18.
14. Embretson S.Generating items during testing: Psychometric issues and models.Psychometrika. 1999;64:407-433.
15. Fisher G.H.Logistic latent trait models with linear constraints.Psychometrika. 1983;48:3-26.
16. Fox J.P.Multilevel IRT modeling in practice with the package mlirt.Journal of Statistical Software. 2007;20:1-16.
17. Fox J.P.,Glas A.C.Bayesian estimation of a multilevel IRT model using Gibbs sampling.Psychometrika. 2001;66:271-288.
18. Gibbons R.D.,Hedeker D.Full-information item bi-factor analysis.Psychometrika. 1992;57:423-436.
19. Goldstein H.Multilevel covariance component models.Biometrika. 1987;74:430-431.
20. Goldstein H.Multilevel statistical models. 2003). Multilevel statistical models. 3rd ed.London, England: Arnold.London, England: Arnold; 2003:.
21. Goldstein H.,Bonnet G.,Rocher T.Multilevel structural equation models for the analysis of comparative data on educational performance.Journal of Educational and Behavioral Statistics. 2007;32:252-286.
22. Goldstein H.,Browne J.W.Contemporary psychometrics: A festschrift for Roderick P. McDonald. Maydeu-Olivares A.McArdle J.J., ed. Mahwah, New Jersey: Lawrence Erlbaum; 2005:453-475.
23. Goldstein H.,Burgess S.,McConnell B.Modelling the effect of pupil mobility on school differences in educational achievement.Journal of the Royal Statistical Society Series A. 2007;170:841-954.
24. Greenland S.A counterexample to the test-based principle of setting confidence limits.American Journal of Epidemiology. 1984;120:4-7.
25. Halperin M.Estimability and estimation in case-referent studies. Letters to the Editor.American Journal of Epidemiology. 1977;105:496-498.
26. Hill P.,Goldstein H.Multilevel modeling of educational data with cross-classification and missing identification for units.Journal of Educational and Behavioral Statistics. 1998;23:117-128.
27. Jeon M.,Rijmen F.,Rabe-Hesketh S.Modeling differential item functioning using a generalized multiple-group bifactor model.Journal of Educational and Behavioral Statistics. in press;:.
28. Joe H.Accuracy of Laplace approximation for discrete response mixed models.Computational Statistics and Data Analysis. 2008;52:5066-5074.
29. Kamata A.Item analysis by the hierarchical generalized linear model.Applied Psychological Measurement. 2001;38:79-93.
30. Li D.,Oranje A.,Jiang Y.On the estimation of hierarchical latent regression models for large-scale assessments.Journal of Educational and Behavioral Statistics. 2009;34:433-463.
31. Lockwood J.,McCaffrey D.,Mariano L.,Setodji C.Bayesian methods for scalable multivariate value-added assessment.Journal of Educational and Behavioral Statistics. 2007;32:125-150.
32. Maas C.M.,Snijders T.A. B.The multilevel approach to repeated measures for complete and incomplete data.Quality & Quantity. 2003;37:71-89.
33. Maier K.S.A Rasch hierarchical measurement model.Journal of Educational and Behavioral Statistics. 2001;26:307-330.
34. Mariano L.,McCaffrey D.,Lockwood J.A model for teacher effects from longitudinal data without assuming vertical scaling.Journal of Educational and Behavioral Statistics. 2010;35:253-279.
35. McCaffrey D.F.,Lockwood J.R.,Koretz D.,Louis T.A.,Hamilton L.Models for value-added modeling of teacher effects.Journal of Educational and Behavioral Statistics. 2004;29:67-101.
36. Mellenbergh J.G.Generalized linear item response theory.Psychological Bulletin. 1994;115:300-307.
37. Meredith W.,Tisak J.Latent curve analysis.Psychometrika. 1988;55:107-122.
38. Miettinen O.Estimability and estimation in case-referent studies.American Journal of Epidemiology. 1976;103:226-235.
39. Muthén L.,Muthén B.Mplus user's guide. Los Angeles, CA: Muthen & Muthen; 2008:.
40. Natarajan R.,Kass R.E.Reference Bayesian methods for generalized linear mixed models.Journal of the American Statistical Association. 2000;95:227-237.
41. Parke R.W.Pseudo maximum likelihood estimation: The asymptotic distribution.Annals of Statistics. 1986;14:355-357.
42. Pawitan Y.In all likelihood: Statistical modeling and inference using likelihood. New York, NY: Oxford; 2001:.
43. Rabe-Hesketh S.,Skrondal A.,Pickles A.Generalized multilevel structural equation modelling.Psychometrika. 2004;69:167-190.
44. Rabe-Hesketh S.,Skrondal A.,Pickles A.Maximum likelihood estimation of limited and discrete dependent variable models with nested random effects.Journal of Econometrics. 2005;128:301-323.
45. Raudenbush S.W.A crossed random effects model for unbalanced data with applications in cross-sectional and longitudinal research.Journal of Educational Statistics. 1993;18:321-349.
46. Raudenbush S.W.,Bryk A.Hierarchical linear models: Applications and data analysis methods. Thousand Oaks, CA: Sage; 2002:.
47. Raudenbush S.W.,Rowan B.,Kang S.J.A multilevel, multivariate model for studying school climate with estimation via the EM algorithm and application to U.S. high-school data.Journal of Educational Statistics. 1991;16:295-330.
48. Raudenbush S.W.,Sampson R.Ecometrics: Toward a science of assessing ecological settings, with application to the systematic social observation of neighborhoods.Sociological Methodology. 1999;29:1-41.
49. Skrondal A.,Rabe-Hesketh S.W.Generalized latent variable modeling: Multilevel, longitudinal, and structural equation models. Boca Raton, FL: Chapman & Hall/CRC; 2004:.
50. Skrondal A.,Rabe-Hesketh S.W.Latent variable modelling: A survey.Scandinavian Journal of Statistics. 2007;34:712-745.
51. SpiegelhalterD. J.ThomasA.BestN. G.GilksW. R. (1996). BUGS 0.5 Bayesian analysis using Gibbs sampling. Manual (version ii).Cambridge, UK: MRC-Biostatistics Unit. Retrieved fromhttp://www.mrc-bsu.cam.ac.uk/bugs/documentation/contents.shtml.
52. Stata statistical software: Release 11. College Station, TX: Author; 2009:.
53. Swaminathan H.,Rogers H.J.Detecting differential item functioning using logistic regression procedures.Journal of Educational Measurement. 1990;27:361-370.
54. Vermunt J.Multilevel latent variable modeling: An application in education testing.Austrian Journal of Statistics. 2007;38:285-299.
55. Wolfinger R.D.Fitting non-linear mixed models with the new NLMIXED procedure (Technical Report). Cary, NC: SAS Institute; 1999:.
56. Zheng X.,Rabe-Hesketh S.Estimating parameters of dichotomous and ordinal item response models with gllamm.The Stata Journal. 2007;7:313-333.