Measurement error modelling with an approximate instrumental variable

Journal of the Royal Statistical Society. Series B: Statistical Methodology

Volumn 69, Issue 5, 2007, Pages 797-815

  Gustafson, Paul ^a  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

Bayesian analysis; Instrumental variable; Measurement error

Indexed keywords

EID: 35648969491     PISSN: 13697412     EISSN: 14679868     Source Type: Journal    
DOI: 10.1111/j.1467-9868.2007.00611.x     Document Type: Article

References (28)

1. Buzas, J. S. Stefanski, L. A. (1996) Instrumental variables estimation in generalized linear measurement error models. J. Am. Statist. Ass., 91, 999 1006.
2. Carroll, R. J., Ruppert, D., Crainiceanu, C. M., Tosteson, T. D. Karagas, M. R. (2004) Nonlinear and nonparametric regression and instrumental variables. J. Am. Statist. Ass., 99, 736 750.
3. Carroll, R. J., Ruppert, D., Stefanski, L. A. Crainiceanu, C. M. (2006) Measurement Error in Nonlinear Models, 2nd edn. Boca Raton : Chapman and Hall-CRC.
4. Chao, J. C. Phillips, P. C. B. (1998) Posterior distributions in limited information analysis of the simultaneous equations models using the Jeffreys' prior. J. Econometr., 111, 251 283.
5. Dendukuri, N., Rahme, E., Belisle, P. Joseph, L. (2004) Bayesian sample size determination for prevalence and diagnostic test studies in the absence of a gold standard test. Biometrics, 60, 388 397.
6. Fernández, C., Osiewalski, J. Steel, M. (1997) On the use of panel data in stochastic frontier models with improper priors. J. Econometr., 79, 169 193.
7. Fuller, W. (1987) Measurement Error Models. New York : Wiley.
8. Gelfand, A. E. Sahu, S. K. (1999) Identifiability, improper priors, and Gibbs sampling for generalized linear models. J. Am. Statist. Ass., 94, 247 253.
9. Greenland, S. (2000) An introduction to instrumental variables for epidemiologists. Int. J. Epidem., 29, 722 729.
10. Greenland, S. (2003) The impact of prior distributions for uncontrolled confounding and response bias: a case study of the relation of wire codes and magnetic fields to childhood leukemia. J. Am. Statist. Ass., 98, 47 54.
11. Greenland, S. (2005) Multiple-bias modelling for analysis of observational data (with discussion). J. R. Statist. Soc. A, 168, 267 306.
12. Gustafson, P. (2003) Measurement Error and Misclassification in Statistics and Epidemiology: Impacts and Bayesian Adjustments. Boca Raton : Chapman and Hall-CRC.
13. Gustafson, P. (2005a) On model expansion, model contraction, identifiability, and prior information: two illustrative scenarios involving mismeasured variables (with discussion). Statist. Sci., 20, 111 140.
14. Gustafson, P. (2005b) The utility of prior information and stratification for parameter estimation with two screening tests but no gold standard. Statist. Med., 24, 1203 1217.
15. Kleibergen, F. Zivot, E. (2003) Bayesian and classical approaches to instrumental variable regression. J. Econometr., 114, 29 72.
16. Kuchenöff, H. (1995) The identification of logistic regression models with errors in the variables. Statist. Pap., 36, 41 48.
17. Lancaster, T. (2004) An Introduction to Modern Bayesian Econometrics. Oxford : Blackwell.
18. Lindley, D. V. (1971) Bayesian Statistics: a Review. Philadelphia : Society for Industrial and Applied Mathematics.
19. Manski, C. F. (2003) Partial Identification of Probability Distributions. New York : Springer.
20. Neath, A. E. Samaniego, F. J. (1997) On the efficacy of Bayesian inference for nonidentifiable models. Am. Statistn, 51, 225 232.
21. Newhouse, J. P. McClellan, M. (1998) Econometrics in outcomes research: the use of instrumental variables. A. Rev. Publ. Hlth, 19, 17 34.
22. Poirier, D. J. (1998) Revising beliefs in nonidentified models. Econometr. Theory, 14, 483 509.
23. Posner, M. A., Ash, A. S., Freund, K. M., Moskowitz, M. A. Shwartz, M. (2001) Comparing standard regression, propensity score matching, and instrumental variable methods for determining the influence of mammography on stage of diagnosis. Hlth Serv. Out. Res. Methodol., 2, 279 290.
24. Richardson, S. Gilks, W. R. (1993) Conditional independence models for epidemiological studies with covariate measurement error. Statist. Med., 12, 1703 1722.
25. Scharfstein, D. O., Manski, C. F. Anthony, J. C. (2004) On the construction of bounds in prospective studies with missing ordinal outcomes: application to the good behavior game trial. Biometrics, 60, 154 164.
26. Stefanski, L. A. Buzas, J. S. (1995) Instrumental variable estimation in binary regression measurement error models. J. Am. Statist. Ass., 90, 541 550.
27. White, H. (1982) Maximum likelihood estimation of misspecified models. Econometrika, 50, 1 25.
28. Xie, Y. Carlin, B. P. (2006) Measures of Bayesian learning and identifiability in hierarchical models. J. Statist. Planng Inf., 136, 3458 3477.