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Measurement Error Models (measurement + error_models)

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Mathematics and Statistics100%

Selected Abstracts

On Latent-Variable Model Misspecification in Structural Measurement Error Models for Binary Response

BIOMETRICS, Issue 3 2009
Xianzheng Huang
Summary We consider structural measurement error models for a binary response. We show that likelihood-based estimators obtained from fitting structural measurement error models with pooled binary responses can be far more robust to covariate measurement error in the presence of latent-variable model misspecification than the corresponding estimators from individual responses. Furthermore, despite the loss in information, pooling can provide improved parameter estimators in terms of mean-squared error. Based on these and other findings, we create a new diagnostic method to detect latent-variable model misspecification in structural measurement error models with individual binary response. We use simulation and data from the Framingham Heart Study to illustrate our methods. [source]

Estimation in Semiparametric Transition Measurement Error Models for Longitudinal Data

BIOMETRICS, Issue 3 2009
Wenqin Pan
Summary We consider semiparametric transition measurement error models for longitudinal data, where one of the covariates is measured with error in transition models, and no distributional assumption is made for the underlying unobserved covariate. An estimating equation approach based on the pseudo conditional score method is proposed. We show the resulting estimators of the regression coefficients are consistent and asymptotically normal. We also discuss the issue of efficiency loss. Simulation studies are conducted to examine the finite-sample performance of our estimators. The longitudinal AIDS Costs and Services Utilization Survey data are analyzed for illustration. [source]

Assessing interaction effects in linear measurement error models

JOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES C (APPLIED STATISTICS), Issue 1 2005
Li-Shan Huang
Summary., In a linear model, the effect of a continuous explanatory variable may vary across groups defined by a categorical variable, and the variable itself may be subject to measurement error. This suggests a linear measurement error model with slope-by-factor interactions. The variables that are defined by such interactions are neither continuous nor discrete, and hence it is not immediately clear how to fit linear measurement error models when interactions are present. This paper gives a corollary of a theorem of Fuller for the situation of correcting measurement errors in a linear model with slope-by-factor interactions. In particular, the error-corrected estimate of the coefficients and its asymptotic variance matrix are given in a more easily assessable form. Simulation results confirm the asymptotic normality of the coefficients in finite sample cases. We apply the results to data from the Seychelles Child Development Study at age 66 months, assessing the effects of exposure to mercury through consumption of fish on child development for females and males for both prenatal and post-natal exposure. [source]

A unified approach to estimation of nonlinear mixed effects and Berkson measurement error models

THE CANADIAN JOURNAL OF STATISTICS, Issue 2 2007
Liqun Wang
Abstract Mixed effects models and Berkson measurement error models are widely used. They share features which the author uses to develop a unified estimation framework. He deals with models in which the random effects (or measurement errors) have a general parametric distribution, whereas the random regression coefficients (or unobserved predictor variables) and error terms have nonparametric distributions. He proposes a second-order least squares estimator and a simulation-based estimator based on the first two moments of the conditional response variable given the observed covariates. He shows that both estimators are consistent and asymptotically normally distributed under fairly general conditions. The author also reports Monte Carlo simulation studies showing that the proposed estimators perform satisfactorily for relatively small sample sizes. Compared to the likelihood approach, the proposed methods are computationally feasible and do not rely on the normality assumption for random effects or other variables in the model. Une stratégie d'estimation commune pour les modèles non linéaires à effets mixtes et les modèles d'erreur de mesure de Berkson Les modèles à effets mixtes et les modèles d'erreur de mesure de Berkson sont très usités. Ils par-tagent certaines caractéristiques que l'auteur met à profit pour élaborer une stratégie d'estimation commune. II considère des modèles dans lesquels la loi des effets aléatoires (ou des erreurs de mesure) est paramé-trique tandis que celles des coefficients de régression aléatoires (ou de variables exogènes non observées) et des termes d'erreur ne le sont pas. II propose une estimation des moindres carrés au second ordre et une approche par simulation fondées sur les deux premiers moments conditionnels de la variable endogène, sachant les variables exogènes observées. Les deux estimateurs s'avèrent convergents et asymptotiquement gaussiens sous des conditions assez générales. L'auteur fait aussi état d'études de Monte-Carlo attestant du bon comportement des deux estimations dans des échantillons relativement petits. Les méthodes proposées ne posent aucune difficulté particulière au plan numérique et au contraire de l'approche par vraisemblance, ne supposent ni la normalité des effets aléatoires, ni celle des autres variables du modèle. [source]

Regression Calibration in Semiparametric Accelerated Failure Time Models

BIOMETRICS, Issue 2 2010
Menggang Yu
Summary In large cohort studies, it often happens that some covariates are expensive to measure and hence only measured on a validation set. On the other hand, relatively cheap but error-prone measurements of the covariates are available for all subjects. Regression calibration (RC) estimation method (Prentice, 1982,,Biometrika,69, 331,342) is a popular method for analyzing such data and has been applied to the Cox model by Wang et al. (1997,,Biometrics,53, 131,145) under normal measurement error and rare disease assumptions. In this article, we consider the RC estimation method for the semiparametric accelerated failure time model with covariates subject to measurement error. Asymptotic properties of the proposed method are investigated under a two-phase sampling scheme for validation data that are selected via stratified random sampling, resulting in neither independent nor identically distributed observations. We show that the estimates converge to some well-defined parameters. In particular, unbiased estimation is feasible under additive normal measurement error models for normal covariates and under Berkson error models. The proposed method performs well in finite-sample simulation studies. We also apply the proposed method to a depression mortality study. [source]

On Latent-Variable Model Misspecification in Structural Measurement Error Models for Binary Response

BIOMETRICS, Issue 3 2009
Xianzheng Huang
Summary We consider structural measurement error models for a binary response. We show that likelihood-based estimators obtained from fitting structural measurement error models with pooled binary responses can be far more robust to covariate measurement error in the presence of latent-variable model misspecification than the corresponding estimators from individual responses. Furthermore, despite the loss in information, pooling can provide improved parameter estimators in terms of mean-squared error. Based on these and other findings, we create a new diagnostic method to detect latent-variable model misspecification in structural measurement error models with individual binary response. We use simulation and data from the Framingham Heart Study to illustrate our methods. [source]

Estimation in Semiparametric Transition Measurement Error Models for Longitudinal Data

BIOMETRICS, Issue 3 2009
Wenqin Pan
Summary We consider semiparametric transition measurement error models for longitudinal data, where one of the covariates is measured with error in transition models, and no distributional assumption is made for the underlying unobserved covariate. An estimating equation approach based on the pseudo conditional score method is proposed. We show the resulting estimators of the regression coefficients are consistent and asymptotically normal. We also discuss the issue of efficiency loss. Simulation studies are conducted to examine the finite-sample performance of our estimators. The longitudinal AIDS Costs and Services Utilization Survey data are analyzed for illustration. [source]

A Semiparametric Joint Model for Longitudinal and Survival Data with Application to Hemodialysis Study

BIOMETRICS, Issue 3 2009
Liang Li
Summary In many longitudinal clinical studies, the level and progression rate of repeatedly measured biomarkers on each subject quantify the severity of the disease and that subject's susceptibility to progression of the disease. It is of scientific and clinical interest to relate such quantities to a later time-to-event clinical endpoint such as patient survival. This is usually done with a shared parameter model. In such models, the longitudinal biomarker data and the survival outcome of each subject are assumed to be conditionally independent given subject-level severity or susceptibility (also called frailty in statistical terms). In this article, we study the case where the conditional distribution of longitudinal data is modeled by a linear mixed-effect model, and the conditional distribution of the survival data is given by a Cox proportional hazard model. We allow unknown regression coefficients and time-dependent covariates in both models. The proposed estimators are maximizers of an exact correction to the joint log likelihood with the frailties eliminated as nuisance parameters, an idea that originated from correction of covariate measurement error in measurement error models. The corrected joint log likelihood is shown to be asymptotically concave and leads to consistent and asymptotically normal estimators. Unlike most published methods for joint modeling, the proposed estimation procedure does not rely on distributional assumptions of the frailties. The proposed method was studied in simulations and applied to a data set from the Hemodialysis Study. [source]

Measurement Error in a Random Walk Model with Applications to Population Dynamics

BIOMETRICS, Issue 4 2006
John Staudenmayer
Summary Population abundances are rarely, if ever, known. Instead, they are estimated with some amount of uncertainty. The resulting measurement error has its consequences on subsequent analyses that model population dynamics and estimate probabilities about abundances at future points in time. This article addresses some outstanding questions on the consequences of measurement error in one such dynamic model, the random walk with drift model, and proposes some new ways to correct for measurement error. We present a broad and realistic class of measurement error models that allows both heteroskedasticity and possible correlation in the measurement errors, and we provide analytical results about the biases of estimators that ignore the measurement error. Our new estimators include both method of moments estimators and "pseudo"-estimators that proceed from both observed estimates of population abundance and estimates of parameters in the measurement error model. We derive the asymptotic properties of our methods and existing methods, and we compare their finite-sample performance with a simulation experiment. We also examine the practical implications of the methods by using them to analyze two existing population dynamics data sets. [source]