Maximum likelihood methods for a generalized class of log-linear models

Annals of Statistics

Volumn 24, Issue 2, 1996, Pages 726-752

  Lang, Joseph B ^a  

^a UNIVERSITY OF IOWA   (United States)

Author keywords

Asymptotics; Constraint equation; Freedom equation; Marginal model; Multinomial distribution; Multivariate categorical data; Simultaneous model

Indexed keywords

EID: 0030502155     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1032894462     Document Type: Article

References (25)

1. AGRESTI, A. (1990). Categorical Data Analysis. Wiley, New York.
2. AITCHISON, J. (1962). Large-sample restricted parametric tests. J. Roy. Statist. Soc. Ser. B 24 234-250.
3. AITCHISON, J. and SILVEY, S. D. (1958). Maximum-likelihood estimation of parameters subject to restraints. Ann. Math. Statist. 29 813-828.
4. AITCHISON, J. and SILVEY, S. D. (1960). Maximum-likelihood estimation procedures and associated tests of significance. J. Roy. Statist. Soc. Ser. B 22 154-171.
5. BECKER, M. P. and BALAGTAS, C. C. (1993). A log-nonlinear model for binary cross-over data. Biometrics 49 997-1009.
6. BISHOP, Y., FIENBERG, S. E. and HOLLAND, P. (1975). Discrete Multivariate Analysis. MIT Press.
7. DALE, J. R. (1986). Global cross-ratio models for bivariate, discrete, ordered responses. Biometrics 42 909-917.
8. GILULA, Z. and HABERMAN, S. J. (1986). Canonical analysis of contingency tables by maximum likelihood. J. Amer. Statist. Assoc. 81 780-798.
9. GLONEK, G. F. V. and MCCULLAGH, P. (1995). Multivariate logistic models. J. Roy. Statist. Soc. Ser. B 57 533-546
10. HABER, M. (1985a). Maximum likelihood methods for linear and log-linear models in categorical data. Comput. Statist. Data Anal. 3 1-10.
11. HABER, M. (1985b). Log-linear models for correlated marginal totals of a contingency table. Comm. Statist. Theory Methods 14 2845-2856.
12. HABER, M. and BROWN, M. (1986). Maximum likelihood methods for log-linear models when expected frequencies are subject to linear constraints. J. Amer. Statist. Assoc. 81 477-482.
13. HABERMAN, S. J. (1973). The analysis of residuals in cross-classification tables. Biometrics 29 205-220.
14. HABERMAN, S. J. (1974). The Analysis of Frequency Data. Univ. Chicago Press.
15. LAIRD, N. M. (1991). Topics of likelihood-based methods for longitudinal data analysis. Statist. Sinica 1 33-50.
16. LANG, J. B. (1996). On the comparison of multinomial and Poisson loglinear models. J. Roy. Statist. Soc. Ser. B 58 253-266.
17. LANG, J. B. and AGRESTI, A. (1994). Simultaneously modeling joint and marginal distributions of multivariate categorical responses. J. Amer. Statist. Assoc. 89 625-632.
18. MACRAE, E. C. (1974). Matrix derivatives with an application to an adaptive linear decision problem. Ann. Statist. 2 337-346.
19. MCCULLAGH, P. and NELDER, J. A. (1989). Generalized Linear Models. Chapman and Hall, London.
20. MOLENBERGHS, G. and LESAFFRE, E. (1994). Marginal modelling of multivariate categorical data. Unpublished manuscript.
21. PALMGREN, J. (1981). The Fisher information matrix for log linear models arguing conditionally on observed explanatory variables. Biometrika 68 563-566.
22. PIERCE, D. A. and SCHAFER, D. W. (1986). Residuals in generalized linear models. J. Amer. Statist. Assoc. 81 977-986.
23. PRATT, J. W. (1981). Concavity of the log likelihood. J. Amer. Statist. Assoc. 76 103-106.
24. SERFLING, R. J. (1980). Approximation Theorems of Mathematical Statistics. Wiley, New York.
25. SILVEY, S. D. (1959). The Lagrange-multiplier test. Ann. Math. Statist. 30 389-407.