Performance of empirical Bayes estimators of random coefficients in multilevel analysis: Some results for the random intercept-only model

Statistica Neerlandica

Volumn 58, Issue 2, 2004, Pages 197-219

  Candel, Math J J M ^a  

^a MAASTRICHT UNIVERSITY   (Netherlands)

Author keywords

(Restricted) maximum likelihood; (Un)balanced designs; Bayes risk; Mean squared error; Monte Carlo simulations; Ordinary least squares estimator

Indexed keywords

EID: 1842733358     PISSN: 00390402     EISSN: None     Source Type: Journal    
DOI: 10.1046/j.0039-0402.2003.00256.x     Document Type: Conference Paper

References (35)

1. ALBERT, P. S. (1999), Tutorial in biostatistics: longitudinal data analysis (repeated measures) in clinical trials, Statistics in Medicine 18, 1707-1732.
2. BRYK, A. S. and S. W. RAUDENBUSH (1992), Hierarchical linear models: applications and data analysis methods, Sage, Newbury Park.
3. BRYK, A. S., S. W. RAUDENBUSH and R.T. CONGDON Jr. (1996), HLM: hierarchical linear and nonlinear modeling with the HLM/2L and HLM/3L programs, Scientific Software International, Chicago.
4. CANDEL, M. J. J. M. (2001), External analysis of preferences: multilevel modeling and some alternatives, Kwantitatieve Methoden 66, 5-32.
5. CANDEL, M. J. J. M. and B. WINKENS (2003), Performance of empirical Bayes estimators of level-2 random parameters in multilevel analysis: a Monte Carlo study for longitudinal designs, Journal of Educational and Behavioral Statistics, accepted for publication.
6. CARLIN, B. P. and T. A. Louis (2000), Bayes and empirical Bayes methods for data analysis, Chapman and Hall, Boca Raton.
7. CASELLA, G. (1985), An introduction to empirical Bayes data analysis, American Statistician 39, 83-87.
8. CASTRO, M. and J.-L. GAVIRIA (2000), Application of hierarchical linear models to metaanalysis: study of the Monte Carlo simulation on the functioning of traditional and empirical-Bayes effect size, Quality and Quantity 34, 33-50.
9. CHARNOCK, D. M. (1996), National uniformity and state and local effects on Australian voting: a multilevel approach, Australian Journal of Political Science 31, 86-97.
10. CHRISTENSEN, R. (1996), Plane answers to complex questions: the theory of linear models, Springer, New York.
11. CNAAN, A., N. M. LAIRD and P. SLASOR (1997), Using the general linear mixed model to analyse unbalanced repeated measures and longitudinal data, Statistics in Medicine 16, 2349-2380.
12. DEGROOT, M. H. (1970), Optimal statistical decisions. McGraw-Hill, New York.
13. EFRON, B. and C. MORRIS (1975), Data analysis using Stein's estimator and its generalizations, Journal of the American Statistical Association 70, 311-319.
14. GOLDSTEIN, H., J. RASBASH, I. PLEWIS, D. DRAPER, W. BROWNE, M. YANG, G. WOODHOUSE and M. HEALY (1998), A user's guide to MLwiN, Multilevel Models Project, Institute of Education, University of London, London.
15. GOLDSTEIN, H., J. RASBASH, M. YANG, G. Woodhouse, H. PAN, D. NUTTALL and S. THOMAS (1993), A multilevel analysis of school examination results, Oxford Review of Education 19, 425-433.
16. HARDY, M. A. and L. E. HAZELRIGG (1999), A multilevel model of early retirement decisions among autoworkers in plants with different futures, Research on Aging 21, 275-303.
17. HEDEKER, D. and R. D. GIBBONS (1996), MIXREG: a computer program for mixed-effects regression analysis with autocorrelated errors, Computer Methods and Programs in Biomedicine 49, 229-252.
18. HEDEKER, D. and R. D. GIBBONS (1997), Application of random-effects pattern-mixture models for missing data in longitudinal studies, Psychological Methods 2, 64-78.
19. Hox, J.J. (1994), Hierarchical regression models for interviewer and respondent effects, Sociological Methods and Research 22, 300-318.
20. JOHNSON, R. A. and D. W. WICHERN (2002), Applied multivariate statistical analysis, Prentice Hall, Upper Saddle River, NJ.
21. MARITZ, J. S. and T. LWIN (1989), Empirical Bayes methods, Chapman and Hall, London.
22. MOOD, A. M., F. A. GRAYBILL and D. C. BOES (1974), Introduction to the theory of statistics, 3rd edn, McGraw-Hill, Tokyo.
23. MORRIS, C. N. (1983), Parametric empirical Bayes inference: theory and applications, Journal of the American Statistical Association 78, 47-55.
24. PITUCH, K. (2001), Using multilevel modeling in large-scale planned variation educational experiments: improving understanding of intervention effects, Journal of Experimental Education 69, 347-372.
25. PLEWIS, I. (2000), Evaluating educational interventions using multilevel growth curves: the case of reading recovery, Educational Research and Evaluation 6, 83-101.
26. PLEWIS, I. and J. HURRY (1998), A multilevel perspective on the design and analysis of intervention studies, Educational Research and Evaluation 4, 13-26.
27. RAO, C. R. (1975), Simultaneous estimation of parameters in different linear models and applications to biometric problems, Biometrics 31, 545-554.
28. RAUDENBUSH, S.W. and A.S. BRYK (1986), A hierarchical model for studying school effects, Sociology of Education 59, 1-17.
29. SAMPSON, R. J., S. W. RAUDENBUSH and F. EARLS (1997), Neighborhoods and violent crime: a multilevel study of collective efficacy, Science 277, 918-924.
30. SEARLE, S. R. (1987), Linear models for unbalanced data, Wiley, New York.
31. SEARLE, S. R., G. CASELLA and C.E. MCCULLOCH (1992), Variance components, Wiley, New York.
32. SNIJDERS, T. A. B. (1996), Analysis of longitudinal data using the hierarchical linear model, Quality and Quantity 30, 405-426.
33. SNIJDERS, T. A. B. and R. J. BOSKER (1999), Multilevel analysis: an introduction to basic and advanced multilevel modeling, Sage, London.
34. TATE, R. L. and J. E. HOKANSON (1993), Analyzing individual status and change with hierarchical linear models: illustration with depression in college students, Journal of Personality 61, 181-206.
35. VERBEKE, G. and G. MOLENBERGHS (2000), Linear mixed models for longitudinal data, Springer, New York.