Generalized score test of homogeneity for mixed effects models

Annals of Statistics

Volumn 34, Issue 3, 2006, Pages 1545-1569

  Zhu, Hongtu ^a,c   Zhang, Heping ^b,d,e  

^a Columbia University ^*  (United States)

^b YALE UNIVERSITY   (United States)

^c NEW YORK STATE PSYCHIATRIC INSTITUTE   (United States)

^d YALE UNIVERSITY SCHOOL OF MEDICINE   (United States)

^e JIANGXI NORMAL UNIVERSITY   (China)

Author keywords

Functional central limit theorem; Latent variable; Random quadratic form; Score test; Variance component

Indexed keywords

EID: 33747190564     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/009053606000000380     Document Type: Article

References (38)

1. ANDREWS, D. W. K. (2001). Testing when a parameter is on the boundary of the maintained hypothesis. Econometrica 69 683-734. MR1828540
2. BENTLER, P. M. and DUDGEON, P. (1996). Covariance structure analysis: Statistical practice, theory and directions. Ann. Review Psychology 47 563-592.
3. BRESLOW, N. E. and CLAYTON, D. G. (1993). Approximate inference in generalized linear mixed models. J. Amer. Statist. Assoc. 88 9-25.
4. CHEN, H. and CHEN, J. (2003). Tests for homogeneity in normal mixtures in the presence of a structural parameter. Statist. Sinica 13 351-365. MR1977730
5. CHEN, H., CHEN, J. and KALBFLEISCH, J. D. (2001). A modified likelihood ratio test for homogeneity in finite mixture models. J. R. Stat. Soc. Ser. B Stat. Methodol. 63 19-29. MR1811988
6. CHEN, H., CHEN, J. and KALBFLEISCH, J. D. (2004). Testing for a finite mixture model with two components. J. R. Stat. Soc. Ser. B Stat. Methodol. 66 95-115. MR2035761
7. CHEN, Z. and DUNSON, D. B. (2003). Random effect selection in linear mixed models. Biometrics 59 762-769. MR2025100
8. COMMENGES, D. and JACQMIN-GADDA, H. (1997). Generalized score test of homogeneity based on correlated random effects models. J. Roy. Statist. Soc. Ser. B 59 157-171. MR1436561
9. Cox, D. R. (1983). Some remarks on overdispersion. Biometrika 70 269-274. MR0742997
10. CRAINICEANU, C. M. and RUPPERT, D. (2004). Likelihood ratio tests in linear mixed models with one variance component. J. R. Stat. Soc. Ser. B Stat. Methodol. 66 165-185. MR2035765
11. DANIELS, M. J. and POURAHMADI, M. (2002). Bayesian analysis of covariance matrices and dynamic models for longitudinal data. Biometrika 89 553-566. MR1929162
12. DE JONG, P. (1987). A central limit theorem for generalized quadratic forms. Probab. Theory Related Fields 75 261-277. MR0885466
13. DELHING, H., MIKOSCH, T. and SØRENSEN, M., eds. (2002). Empirical Process Techniques for Dependent Data. Birkhäuser, Boston. MR1958776
14. FAN, J. (1996). Test of significance based on wavelet thresholding and Neyman's truncation. J. Amer. Statist. Assoc. 91 674-688. MR1395735
15. GUTTORP, P. and LOCKHART, R. A. (1988). On the asymptotic distribution of quadratic forms in uniform order statistics. Ann. Statist. 16 433-449. MR0924879
16. HALL, D. B. and PRÆSTGAARD, J. T. (2001). Order-restricted score tests for homogeneity in generalised linear and nonlinear mixed models. Biometrika 88 739-751. MR1859406
17. JACQMIN-GADDA, H. and COMMENGES, D. (1995). Tests of homogeneity for generalized linear models. J. Amer. Statist. Assoc. 90 1237-1246. MR1379466
18. JIANG, J. (1996). REML estimation: Asymptotic behavior and related topics. Ann. Statist. 24 255-286. MR1389890
19. JØRGENSEN, B. (1987). Exponential dispersion models (with discussion). J. Roy. Statist. Soc. Ser. B 49 127-162. MR0905186
20. KOSOROK, M. R. (2003). Bootstraps of sums of independent but not identically distributed stochastic processes. J. Multivariate Anal. 84 299-318. MR1965224
21. LIANG, K. (1987). A locally most powerful test for homogeneity with many strata. Biometrika 74 259-264. MR0903126
22. LIN, X. (1997). Variance component testing in generalised linear models with random effects. Biometrika 84 309-326. MR1467049
23. MERIKANGAS, K. R., STEVENS, D. E., FENTON, B., STOLAR, M., O'MALLEY, S., WOODS, S. and RISCH, N. (1998). Co-morbidity and familial aggregation of alcoholism and anxiety disorders. Psychological Medicine 28 773-788.
24. MIKOSCH, T. (1991). Functional limit theorems for random quadratic forms. Stochastic Process. Appl. 37 81-98. MR1091696
25. POLLARD, D. (1990). Empirical Processes: Theory and Applications. IMS, Hayward, CA. MR1089429
26. SEN, P. K. and SILVAPULLE, M. J. (2002). An appraisal of some aspects of statistical inference under inequality constraints. J. Statist. Plann. Inference 107 3-43. MR1927753
27. SILVAPULLE, M. J. and SILVAPULLE, P. (1995). A score test against one-sided alternatives. J. Amer. Statist. Assoc. 90 342-349. MR1325141
28. TSAI, M. (1992). On the power superiority of likelihood ratio tests for restricted alternatives. J. Multivariate Anal. 42 102-109. MR1177520
29. VAN DER VAART, A. W. and WELLNER, J. A. (1996). Weak Convergence and Empirical Processes. With Applications to Statistics. Springer, New York. MR1385671
30. VAIDA, F. and XU, R. (2000). Proportional hazards model with random effects. Statistics in Medicine 19 3309-3324.
31. VARBERG, D. E. (1968). Almost sure convergence of quadratic forms in independent random variables. Ann. Math. Statist. 39 1502-1506. MR0230359
32. VERBEKE, G. and MOLENBERGHS, G. (2003). The use of score tests for inference on variance components. Biometrics 59 254-262. MR1987392
33. WEI, B. (1998). Exponential Family Nonlinear Models. Springer, Berlin.
34. ZHANG, H., FENG, R. and ZHU, H. (2003). A latent variable model of segregation analysis for ordinal traits. J. Amer. Statist. Assoc. 98 1023-1034. MR2041490
35. ZHANG, H. and MERIKANGAS, K. (2000). A frailty model of segregation analysis: Understanding the familial transmission of alcoholism. Biometrics 56 815-823.
36. ZHENG, G. and CHEN, Z. (2005). Comparison of maximum statistics for hypothesis testing when a nuisance parameter is present only under the alternative. Biometrics 61 254-258. MR2135868
37. ZHU, H. and ZHANG, H. (2004). Hypothesis testing in mixture regression models. J. R. Stat. Soc. Ser. B Stat. Methodol. 66 3-16. MR2035755
38. ZHU, H. and ZHANG, H. (2005). Generalized score test of homogeneity for mixed effects models: Supplement. Technical report, Yale Univ. School of Medicine. Available at peace.med.yale.edu.