A flexible model for generalized linear regression with measurement error

Annals of the Institute of Statistical Mathematics

Volumn 58, Issue 1, 2006, Pages 153-169

  Roy, Surupa ^a   Banerjee, Tathagata ^b,c  

^a ST XAVIER S COLLEGE   (India)

^b UNIVERSITY OF CALCUTTA   (India)

^c INDIAN INSTITUTE OF MANAGEMENT   (India)

Author keywords

Canonical link; EM algorithm; Generalized linear model; Logistic regression; Mixture distribution; Structural model; Surrogate; Validation data

Indexed keywords

COMPUTATION THEORY; LINEAR SYSTEMS; MEASUREMENT ERRORS; NUMERICAL ANALYSIS; OPTIMIZATION; PARAMETER ESTIMATION;

CANONICAL LINK; EM ALGORITHM; GENERALIZED LINEAR MODEL; LOGISTIC REGRESSION; MIXTURE DISTRIBUTION; STRUCTURAL MODEL; SURROGATE; VALIDATION DATA;

REGRESSION ANALYSIS;

EID: 33645725822     PISSN: 00203157     EISSN: 15729052     Source Type: Journal    
DOI: 10.1007/s10463-005-0002-z     Document Type: Article

References (21)

1. Abramowitz, M., Stegun, I. (eds) (1972). Handbook of mathematical functions. New York: Dover.
2. Carroll, R.J., Gail, M.H., Lubin, J.H. (1993). Case-control studies with errors in covariates. Journal of the American Statistical Association, 88, 185-199.
3. Carroll, R.J., Ruppert, D., Stefanski, L. A. (1995). Measurement error in non linear models. New York: Chapman & Hall.
4. Carroll, R.J., Maca, J.D., Ruppert, D. (1999a). Non parametric regression in the presence of measurement error. Biometrika, 86 (3), 541-554.
5. Carroll, R.J., Roeder, K., Wassermann, L. (1999b). Flexible parametric measurement error models. Biometrics, 55, 44-54.
6. 2)dt: application to logistic-normal models. Journal of the American Statistical Association, 85, 464-467.
7. Dempster, A.P., Laird, N.M., Rubin, D.B. (1977). Maximum likelihood for incomplete data via EM algorithm. Journal of the Royal Statistical Society, Series B, 39, 1-38.
8. Fuller, W.A. (1980). Measurement error models. New York: John Wiley.
9. Lange, K.L., Little, R.J.A., Taylor, J.M.G. (1989). Robust statistical modeling using the t distribution. Journal of the American Statistical Association, 84, 881-896.
10. Lange, K.L., Sinsheimer, J.S. (1993). Normal independent distributions and their applications in robust regression. Journal Computational Graphical Statistics, 2, 175-198.
11. Liu, C.H., Rubin, D.B. (1994). The ECME algorithm: a simple extension of EM and ECM with fast monotone convergence. Biometrika, 81, 633-648.
12. Liu, C.H., Rubin, D.B. (1995). ML estimation of the t distribution using EM and its extensions, ECM and ECME. Statistica Sinica, 5, 19-40.
13. McCullagh, P., Nelder, J.A. (1989). Generalized linear models. London: Chapman and Hall.
14. Muller, P., Roeder, K. (1997). A Bayesian semi parametric model for case-control studies with errors in variables. Biometrika, 84(3), 523-537.
15. Roeder, K., Carroll, R.J., Lindsay, B.G. (1996). A semi parametric mixture approach to case control studies with errors in covariables. Journal of the American Statistical Association, 91, 722-732.
16. Rosner, B., Willet, W.C., Spiegelman, D. (1989). Correction of logistic regression relative risk estimates and confidence intervals for systematic within-person measurement error. Statistics in Medicine, 8, 1075-1093.
17. Richardson, S., Leblond, L., Jaussent, I., Green, P.J. (2000). Mixture models in measurement error problems, with references to epidemiological studies, in Press.
18. Schafer, D.W. (1987). Covariate measurement error in generalized linear models. Biometrika, 74, 385-391.
19. Stefanski, L.A. (1985). The effects of measurement error on parameter estimation. Biometrika, 72, 385-389.
20. Stefanski, L.A., Carroll, R.J. (1985). Covariate measurement error in logistic regression. Annals of Statistics, 13, 1335-1351.
21. Sutradhar, B.C., Ali, M.M. (1989). A generalization of the Wishart distribution for the elliptical model and its moments for the multivariate t model. Journal of Multivariate Analysis, 29, 155-162.