Diagnostics in nonlinear negative binomial models

Communications in Statistics - Theory and Methods

Volumn 32, Issue 6, 2003, Pages 1227-1250

  Svetliza, Carolina F ^a   Paula, Gilberto A ^a  

^a UNIVERSITY OF SÃO PAULO   (Brazil)

Author keywords

Count data; Influence diagnostic; Lack of fit; Likelihood displacement; Offset facility; Overdispersion; Residual analysis

Indexed keywords

ALGORITHMS; ASYMPTOTIC STABILITY; MATRIX ALGEBRA; MAXIMUM LIKELIHOOD ESTIMATION; NORMAL DISTRIBUTION; PARAMETER ESTIMATION; PROBABILITY DISTRIBUTIONS; REGRESSION ANALYSIS;

COUNT DATA; INFLUENCE DIAGNOSTICS; LACK-OF-FIT; LIKELIHOOD DISPLACEMENT; NONLINEAR NEGATIVE BINOMIAL MODELS; OFFSET-FACILITY; OVERDISPERSION; RESIDUAL ANALYSIS;

MATHEMATICAL MODELS;

EID: 0037868263     PISSN: 03610926     EISSN: None     Source Type: Journal    
DOI: 10.1081/STA-120021329     Document Type: Article

References (41)

1. Atkinson, A. C. (1981). Two graphical display for outlying and influential observations in regression. Biometrika 68:13-20.
2. Bates, D. M., Watts, D. G. (1980). Relative curvature measures of nonlinearity (with discussion). Journal of the Royal Statistical Society B 42:1-25.
3. Beckman, R. J., Nachtsheim, C. J., Cook, R. D. (1987). Diagnostics for mixed-model analysis of variance. Technometrics 29:413-426.
4. Billor, N., Loynes, R. M. (1993). Local influence: a new approach. Communications in Statistics, Theory and Methods 22:1595-1611.
5. Cook, R. D. (1986). Assessment of local influence (with discussion). Journal of the Royal Statistical Society B 48:133-169.
6. Cordeiro, G. M., Paula, G. A. (1989). Fitting non-exponential family nonlinear modelsin GLIM by using the offset facility. In: Gilchrist, et al., ed. Proceedings of the 3rd International Conference on Generalized Linear Models. Lecture Notes in Statistics. Berlin: Springer, 57:105-144.
7. Cordeiro, G. M., Paula, G. A. (1989). Improved likelihood ratio statistics for exponential family nonlinear models. Biometrika 76:93-100.
8. Cox, D. R., Snell, E. J. (1968). A general definition of residuals (with discussion). Journal of the Royal Statistical Society B 30:248-275.
9. Davison, A. C., Gigli, A. (1989). Deviance residuals and normal scores plots. Biometrika 76:211-221.
10. de Souza, F. A. M., Paula, G. A. (2002). Deviance residuals for an angular response. Australian and New Zealand Journal of Statistics 44:345-356.
11. Diggle, P. J. (1990). Time Series. A Biostatistical Introduction. Oxford: Oxford University Press.
12. Escobar, L. A., Meeker, W. Q. (1992). Assessing influence in regression analysis with censored data. Biometrics 48:507-528.
13. Farhrmeir, L., Tutz, G. (1994). Multivariate Statistical Modelling Based on Generalized Linear Models. New York: Springer.
14. Galea, M., Paula, G. A., Bolfarine, H. (1997). Local influence in elliptical linear regression models. The Statistician 46:71-79.
15. Gu, H., Fung, W. K. (1998). Assessing local influence in canonical correlation analysis. Annals of the Institute of Statistical Mathematics 50:755-772.
16. Jørgensen, B. (1997). The Theory of Dispersion Models. London: Chapman and Hall.
17. Kim, M. G. (1995). Local influence in multivariate regression. Communications in Statistics, Theory and Methods 20:1271-1278.
18. Kwan, C. W., Fung, W. K. (1998). Assessing local influence for specific restricted likelihood: applications to factor analysis. Psychometrika 63:35-46.
19. Lambert, P. (1996). Modeling of nonlinear growth curve on series of correlated count data measured at unequally spaced times: a full likelihood based approach. Biometrics 52:50-55.
20. Lawless, J. F. (1987). Negative binomial and mixed poisson regression. Canadian Journal of Statistics 15:209-225.
21. Lawrence, A. J. (1988). Regression transformation diagnostics using local influence. Journal of the American Statistical Association 84:125-141.
22. Lesafre, E., Verbeke, G. (1998). Local influence in linear mixed models. Biometrics 54:570-582.
23. Liu, S. Z. (2000). On local influence for elliptical linear models. Statistical Papers 41:211-224.
24. McCullagh, P. (1987). Tensor Methods in Statistics. London: Chapman and Hall.
25. McCullaghz, P., Nelder, J. A. (1989). Generalized Linear Models. 2nd ed. London: Chapman and Hall.
26. Moolgavkar, S., Lustbader, E., Venzon, D. A. (1984). Geometric approach to nonlinear regression diagnostic with application to matched case-control studies. Annals of Statistics 12:816-826.
27. O'Hara, R. J., Lawless, J. F., Carter, E. M. (1992). Diagnostics for a cumulative multinomial generalized linear model with application to grouped toxicological mortality data. Journal of the American Statistical Association 87:1059-1069.
28. Pan, J. X., Fang, K. T., von Rosen, D. (1997). Local influence assessment in the growth curve model with unstructured covariance. Journal of Statistical Planning and Inference 62:263-278.
29. Paula, G. A. (1993). Assessing local influence in restricted regression models. Computational Statistics and Data Analysis 16:63-79.
30. Paula, G. A. (1995). Influence and residuals in restricted generalized linear models. Journal of Statistical Computation and Simulation 51:315-352.
31. Pettitt, A. N., Bin Daud, I. (1988). Case-weight measures of influence for proportional hazards regression. Applied Statistics 38:51-67.
32. Pregibon, D. (1981). Logistic regression diagnostics. Annals of Statistics 9:705-724.
33. Rancel, M. M. S., Sierra, M. A. G. (2001). Regression diagnostic using local influence: a review. Communications in Statistics, Theory and Methods 30:799-813.
34. Shi, L. (1997). Local influence in principal components analysis. Biometrika 84:175-186.
35. Tang, N. S., Wei, B. C., Wang, X. R. (2001). Local influence in nonlinear reproductive dispersion models. Communications in Statistics, Theory and Methods 30:435-449.
36. Therneau, T. M., Grambsch, P. M., Fleming, T. R. (1990). Martingale-based residuals for survival models. Biometrika 77:147-60.
37. Tsai, C. H., Wu, X. (1992). Assessing local influence in linear regression models with first-order autoregressive or heteroscedastic error structure. Statistics and Probability Letters 14:247-252.
38. Venables, W. N., Ripley, B. D. (1999). Modern Applied Statistics with S-Plus. 3rd ed. New York: Springer.
39. Wei, B. (1998). Eponential family nonlinear models. In: Lecture Notes in Statistics. New York: Springer, 130.
40. Williams, D. A. (1987). Generalized linear model diagnostic using the deviance and single case deletion. Applied Statistics 36:181-191.
41. Wu, X., Luo, L. (1993). Second-order approach to local influence. Journal of the Royal Statistical Society B 55:929-936.