Mixture of measurement errors and their impact on parameter inferences

References

• Carroll , R. J. , Spiegelman , C. , Lan , K. K. , Bailey , K. T. and Abbott , R. D. 1984 . On errors-in-variables for binary regression models . Biometrika , 71 : 19 – 25 . (doi:10.1093/biomet/71.1.19)
   Web of Science ®Google Scholar
• Carroll , R. J. , Ruppert , D. , Stefanske , L. A. and Crainiceanu , C. M. 2006 . Measurement Error in Nonlinear Models: A Modern Perspective , 25 – 36 . Boca Raton , FL : Chapman and Hall/CRC Press . 90–95
   Google Scholar
• Degrace , J. S. and Fuller , W. A. 1972 . Estimation of the slopes and analysis of covariance when the concomitant variable is measured with error . J. Amer. Statist. Assoc , 67 : 930 – 937 . (doi:10.1080/01621459.1972.10481321)
   Web of Science ®Google Scholar
• Jöreskog , K. G. 1970 . A general method for analysis of covariance structures . Biometrika , 57 : 239 – 251 .
   Web of Science ®Google Scholar
• Plewis , I. 1972 . Analysing Change: Measurement and Explanation Using Longitudinal Data , New York : Wiley .
   Google Scholar
• Mallick , B. K. and Gelfand , A. E. 1996 . Semiparametric errors-in-variables models: A Bayesian approach . J. Statist. Plann. Inference , 52 : 307 – 321 . (doi:10.1016/0378-3758(95)00139-5)
   Web of Science ®Google Scholar
• Berkson , J. 1950 . Are there two regressions? . Scand. J. Statist , 12 : 171 – 178 .
   Google Scholar
• Tosteson , T. , Stefamski , L. A. and Schafer , D. W. 1989 . A measurement error model for binary and ordinal regression . Stat. Med , 8 : 1139 – 1147 . (doi:10.1002/sim.4780080914)
   PubMed Web of Science ®Google Scholar
• Kipnis , V. , Carroll , R. J. , Freedman , L. S. and Li , L. 1999 . Implications of a new dietary measurement error model for estimation of relative risk: Application to four calibration studies . Amer. J. Epidemiol , 150 ( 6 ) : 642 – 651 . (doi:10.1093/oxfordjournals.aje.a010063)
   PubMed Web of Science ®Google Scholar
• Kipnis , V. , Midthune , D. , Freedman , L. S. , Bingham , S. , Schatzkin , A. , Subar , A. F. and Carroll , R. J. 2001 . Empirical evidence of correlated biases in dietary assessment instruments and its implications . Amer. J. Epidemiol , 153 ( 4 ) : 394 – 403 . (doi:10.1093/aje/153.4.394)
   PubMed Web of Science ®Google Scholar
• Kipnis , V. , Subar , A. F. , Midthune , D. , Freedman , L. S. , Ballard-Barbash , R. , Troiano , R. P. , Bingham , S. , Schoeller , D. A. , Schatzkin , A. and Carroll , R. J. 2003 . Structure of dietary measurement error: Results of the open biomarker study . Amer. J. Epidemiol , 158 ( 1 ) : 14 – 21 . (doi:10.1093/aje/kwg091)
   PubMed Web of Science ®Google Scholar
• Carroll , R. J. , Midthune , D. , Freedman , L. S. and Kipnis , V. 2006 . Seemingly unrelated measurement error models, with application to nutritional epidemiology . Biometrics , 62 ( 1 ) : 75 – 84 . (doi:10.1111/j.1541-0420.2005.00400.x)
   PubMed Web of Science ®Google Scholar
• Azzalini , A. 1985 . A class of distributions which includes the normal ones . Scand. J. Statist , 12 : 171 – 178 .
   Web of Science ®Google Scholar
• Azzalini , A. 2005 . The skew-normal distribution and related multivariate families . Scand. J. Statist , 32 ( 2 ) : 159 – 188 . (doi:10.1111/j.1467-9469.2005.00426.x)
   Web of Science ®Google Scholar
• Gustafson , P. 2003 . Measurement Error and Misclassification in Statistics and Epidemiology: Impacts and Bayesian Adjustments , FL 9 – 33 . Boca Raton : Chapman and Hall/CRC Press .
   Google Scholar
• VanderWeele , T. J. 2010 . Bias formulas for sensitivity analysis for direct and indirect effects . Epidemiology , 21 : 540 – 551 . (doi:10.1097/EDE.0b013e3181df191c)
   PubMed Web of Science ®Google Scholar
• Rodrigues , J. 2006 . A Bayesian inference for the extended skew-normal measurement error model . Braz. J. Probab. Stat , 20 ( 2 ) : 179 – 190 .
   Google Scholar
• Gelman , A. and Rubin , R. D. 1992 . Inference from iterative simulation using multiple sequences . Statist. Sci , 7 : 457 – 511 . (doi:10.1214/ss/1177011136)
   Google Scholar
• Gelman , A. , Carlin , J. B. and Stern , H. 2003 . Bayesian Data Analysis , 282 – 307 . Boca Raton , FL : Chapman Hall/CRC Press .
   Google Scholar
• Fuller , W. A. 1987 . Measurement Error Models , 1 – 84 . New York : John Wiley & Sons .
   Google Scholar
• Thompson , S. J. , Torres , M. E. , Stevenson , R. E. , Dean , J. H. and Best , R. G. 2003 . Periconceptional multivitamin folic acid use, dietary folate, total folate and risk of neural tube defects in South Carolina . Ann. Epidemiol , 13 : 412 – 418 . (doi:10.1016/S1047-2797(02)00460-X)
   PubMed Web of Science ®Google Scholar
• Willett , W. 1998 . Nutritional Epidemiology , New York : Oxford University Press .
   Google Scholar
• Subar , A. F. , Thompson , F. E. , Kipnis , V. , Midthune , D. , Hurwitz , P. , McNutt , S. , McIntosh , A. and Rosenfeld , S. 2001 . Comparative validation of the Block, Willett, and national cancer institute food frequency questionnaires . Amer. J. Epidemiol , 154 ( 12 ) : 1089 – 1099 . (doi:10.1093/aje/154.12.1089)
   PubMed Web of Science ®Google Scholar