## Measurement Error in Nonlinear ModelsThis monograph provides an up-to-date discussion of analysis strategies for regression problems in which predictor variables are measured with errors. The analysis of nonlinear regression models includes generalized linear models, transform-both-sides models and quasilikelihood and variance function problems. The text concentrates on the general ideas and strategies of estimation and inference rather than being concerned with a specific problem. Measurement error occurs in many fields, such as biometry, epidemiology and economics. In particular, the book contains a large number of epidemiological examples. An outline of strategies for handling progressively more difficult problems is also provided. |

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### Contents

REGRESSION AND ATTENUATION | 21 |

Error Structure | 23 |

REGRESSION CALIBRATION | 40 |

SIMULATION EXTRAPOLATION | 79 |

INSTRUMENTAL VARIABLES | 107 |

FUNCTIONAL METHODS | 122 |

LIKELIHOOD AND QUASILIKELIHOOD | 141 |

BAYESIAN METHODS | 165 |

UNKNOWN LINK FUNCTIONS | 199 |

HYPOTHESIS TESTING | 206 |

DENSITY ESTIMATION AND NONPARAMET | 215 |

RESPONSE VARIABLE ERROR | 229 |

OTHER TOPICS | 243 |

A FITTING METHODS AND MODELS | 257 |

280 | |

298 | |

### Common terms and phrases

algorithm analysis applied assumed assumption attenuation bias biased bootstrap Carroll Chapter coefficient complete data components compute consistent estimate covariance matrix deconvoluting define denote density estimates depends described differential measurement error discussed distributed with mean effects of measurement estimating equations estimating function Exam example extrapolant Framingham data functional modeling Gibbs sampler given heteroscedastic homoscedastic independent instrumental variable intake least squares linear models linear regression logistic regression M-estimator maximum likelihood mean and variance measured with error measurement error models measurement error variance missing data naive test nondifferential measurement error nonlinear nonparametric regression normally distributed observed data obtained plot posterior predictor problem pseudolikelihood quadratic quasilikelihood random variables regression calibration regression calibration approximation regression calibration model regression model replicates resampling response sample sandwich saturated fat SIMEX estimator standard errors statistical Stefanski structural modeling surement error surrogate techniques tion unbiased estimating validation data variance estimator variance function vector

### Popular passages

Page 290 - Blood pressure, stroke, and coronary heart disease. Part 1. Prolonged differences in blood pressure: prospective observational studies corrected for the regression dilution bias.

Page 297 - Willett WC, Sampson L, Stampfer MJ, Rosner B, Bain C, Witschi J, Hennekens CH, Speizer FE. 1985. Reproducibility and validity of a semiquantitative food frequency questionnaire. Am J Epidemiol 122:51-65.