Covariate Measurement Error Research Articles

Functional partially linear single index models with measurement error in both functional and real covariates

In this paper, we investigate the functional partially linear single index models with contaminated functional and real covariates when the functional sample grid is dense. To eliminate the influence of measurement error on the estimations of the proposed models, a two-stage estimation procedure is introduced. In the first stage, we utilize a kernel presmoothing regression to denoise the corrupted functional curves. In the second stage, the fitted functional curves are applied to replace the original ones to obtain the predictor of unknown parameter in parametric component with the attenuation correction method and then we derive the predictor of unknown link function in nonparametric part with kernel method. Meanwhile, in order to improve computational efficiency, functional slice inverse regression method is employed to estimate the functional single index parameter. The asymptotic properties are also stated in this process at the situation of independent and identical distribution sample under some mild conditions. A simulation study and real data analysis are further explored to illustrate the good performance of our methodology.

Nonstationary longitudinal autoregressive mixed model for count data with measurement error in covariates: Estimation and asymptotics

Several methods have been proposed in the literature for computing unbiased and efficient estimates of the parameters of generalized linear models when the covariates are measured with error. However, to our knowledge, no documented research on computational techniques for parameter estimation currently exist in the literature when the data is a longitudinal count data influenced by an unobservable latent variable and observable covariates that are measured with error. In this paper, we propose a nonstationary conditionally Poisson mixed model for such data and develop unbiased estimating equations with iterative methods for computing estimates of the effect of the covariates, variance of the latent variable, and the correlation index parameter. The performance of the iterative methods is examined through extensive simulation studies. The results show that the methods performed well when the magnitude of the measurement error is not so large as to dominate or mask the effect of the true covariates. Using observed longitudinal count data on the number of patents awarded to 168 firms in the United States from 1974 to 1979 along with associated covariate information on the type of firm, log of the book value of capital in 1972 and research and development (R & D) expenditures we have demonstrated how the methods proposed in this paper can be applied to a real data. In addition, we derive the influence function of the estimator of the covariate effect and discuss the asymptotic properties of the estimator. Journal of Statistical Research 2024, Vol. 58, No. 1, pp. 151-180.

Instrumental Variable Method for Regularized Estimation in Generalized Linear Measurement Error Models

Regularized regression methods have attracted much attention in the literature, mainly due to its application in high-dimensional variable selection problems. Most existing regularization methods assume that the predictors are directly observed and precisely measured. It is well known that in a low-dimensional regression model if some covariates are measured with error, then the naive estimators that ignore the measurement error are biased and inconsistent. However, the impact of measurement error in regularized estimation procedures is not clear. For example, it is known that the ordinary least squares estimate of the regression coefficient in a linear model is attenuated towards zero and, on the other hand, the variance of the observed surrogate predictor is inflated. Therefore, it is unclear how the interaction of these two factors affects the selection outcome. To correct for the measurement error effects, some researchers assume that the measurement error covariance matrix is known or can be estimated using external data. In this paper, we propose the regularized instrumental variable method for generalized linear measurement error models. We show that the proposed approach yields a consistent variable selection procedure and root-n consistent parameter estimators. Extensive finite sample simulation studies show that the proposed method performs satisfactorily in both linear and generalized linear models. A real data example is provided to further demonstrate the usage of the method.

A Bayesian semi-parametric scalar-on-function regression with measurement error using instrumental variables.

Wearable devices such as the ActiGraph are now commonly used in research to monitor or track physical activity. This trend corresponds with the growing need to assess the relationships between physical activity and health outcomes, such as obesity, accurately. Device-based physical activity measures are best treated as functions when assessing their associations with scalar-valued outcomes such as body mass index. Scalar-on-function regression (SoFR) is a suitable regression model in this setting. Most estimation approaches in SoFR assume that the measurement error in functional covariates is white noise. Violating this assumption can lead to underestimating model parameters. There are limited approaches to correcting measurement errors for frequentist methods and none for Bayesian methods in this area. We present a non-parametric Bayesian measurement error-corrected SoFR model that relaxes all the constraining assumptions often involved with these models. Our estimation relies on an instrumental variable allowing a time-varying biasing factor, a significant departure from the current generalized method of moment (GMM) approach. Our proposed method also permits model-based grouping of the functional covariate following measurement error correction. This grouping of the measurement error-corrected functional covariate allows additional ease of interpretation of how the different groups differ. Our method is easy to implement, and we demonstrate its finite sample properties in extensive simulations. Finally, we applied our method to data from the National Health and Examination Survey to assess the relationship between wearable device-based measures of physical activity and body mass index in adults in the United States.

Measurement error–tolerant Poisson regression for Valley Fever incidence prediction

The incidence of Valley Fever can be predicted using a Poisson regression model, which links the expected incidence count to influential covariates with model coefficients. In real-world practice, the estimated model coefficients are sensitive to the inevitable measurement errors in the covariates, which are usually manifested as classical errors and/or Berkson errors. While conventional methods have separately addressed each type of error, the joint consideration of both, referred to as mixture measurement error in this article, is currently absent from the existing literature, leaving model coefficient estimators with significant biases. This article presents a measurement-error tolerant Poisson regression to mitigate the impacts of the mixture measurement error in covariates of health-care data analysis. An error-structureadapted quasi-likelihood estimation method is proposed to enhance the accuracy of model estimation. The effectiveness of the proposed method is demonstrated through a numerical case study built upon a Valley Fever investigation, validating its improved estimation accuracy and robustness.

Order‐restricted hypothesis tests for nonlinear mixed‐effects models with measurement errors in covariates

AbstractOrder‐restricted hypothesis testing problems frequently arise in practice, including studies involving regression models for longitudinal data. These tests are known to be more powerful than tests that ignore such restrictions. In this article, we consider order‐restricted tests for nonlinear mixed‐effects models with measurement errors in time‐dependent covariates. We propose to use a multiple imputation method to address measurement errors, since this approach allows us to use existing complete‐data methods for order‐restricted tests. Some theoretical results are presented. We evaluate our proposed methods via simulation studies that demonstrate they are more powerful than either a competing naive method or a two‐step approach to testing hypotheses. We illustrate the use of our proposed approach by analyzing data from an HIV/AIDS study.

Kalman‐based multiple sinusoids identification from intermittently missing measurements of the superimposed signal

SummaryWe consider the problem of stochastic identification of multiple sinusoids from intermittently missing measurements of superimposed signal. An alternate problem formulation is presented as estimation of amplitude and frequency of the sinusoids from missing measurements. The popularly known estimation methods, such as the extended Kalman filter (EKF) and cubature Kalman filter (CKF) may fail or suffer from poor accuracy if the measurements are missing. In this paper, we redesign the EKF to handle this irregularity in measurements and apply the modified EKF for the formulated estimation problem. In this regard, we introduce a modified measurement model incorporating the possibility of missing measurements. Subsequently, we rederive the relevant parameters of the EKF, such as measurement estimate, measurement error covariance, and state‐measurement cross‐covariance, for the modified measurement model. Furthermore, we rederive the posterior covariance with minimized trace and study the stability of the resulting extension of the EKF. The results reveal the superior performance of the modified EKF compared with the ordinary Gaussian filters and existing filters‐based estimation of the sinusoids in the presence of intermittently missing measurements.

Semiparametric analysis of competing risks data with covariate measurement error

Semiparametric analysis of competing risks data with covariate measurement error

Statistical inference for linear quantile regression with measurement error in covariates and nonignorable missing responses

Statistical inference for linear quantile regression with measurement error in covariates and nonignorable missing responses

Measurement errors and implications for preprocessing in miniaturised near-infrared spectrometers: Classification of sweet and bitter almonds as a case of study

Near-infrared (NIR) spectroscopy is a well-established analytical technique that has been used in many applications over the years. Due to the advancements in the semiconductor industry, NIR instruments have evolved from benchtop instruments to miniaturised portable devices. The miniaturised NIR instruments have gained more interest in recent years because of the fast and robust measurements they provide with almost no sample pretreatments.However, due to the very different configurations and characteristics of these instruments, they need a dedicated optimization of the measurement conditions, which is crucial for obtaining reliable results. To comprehensively grasp the capabilities and potentials offered by these sensors, it is imperative to examine errors that can affect the raw data, which is a facet frequently overlooked. In this study, measurement error covariance and correlation matrices were calculated and then visually inspected to gain insight into the error structures associated with the devices, and to find the optimal preprocessing technique that may result in the improvement of the models built.This strategy was applied to the classification of sweet and bitter almonds, which were measured with the three portable low-cost NIR devices (SCiO, FlameNIR+ and NeoSpectra Micro Development Kit) after removing the shelled, since their classification is of utmost importance for the almond industry. The results showed that bitter almonds can be classified from sweet almonds using any of the instruments after selecting the optimal preprocessing, obtained through inspection of covariance and correlation matrices. Measurements obtained with FlameNIR + device provided the best classification models with an accuracy of 98 %. The chosen strategy provides new insight into the performance characterization of the fast-growing miniaturised NIR instruments.

Parameter Estimation in Spatial Autoregressive Models with Missing Data and Measurement Errors

This study addresses the problem of parameter estimation in spatial autoregressive models with missing data and measurement errors in covariates. Specifically, a corrected likelihood estimation approach is employed to rectify the bias in the log-maximum likelihood function induced by measurement errors. Additionally, a combination of inverse probability weighting (IPW) and mean imputation is utilized to mitigate the bias caused by missing data. Under several mild conditions, it is demonstrated that the proposed estimators are consistent and possess oracle properties. The efficacy of the proposed parameter estimation process is assessed through Monte Carlo simulation studies. Finally, the applicability of the proposed method is further substantiated using the Boston Housing Dataset.

A new kernel two-parameter prediction under multicollinearity in partially linear mixed measurement error model

A Partially linear mixed effects model relating a response Y to predictors ( X , Z , T ) with the mean function X T β + Zb + g ( T ) is considered in this paper. When the parametric parts' variable X are measured with additive error and there is ill-conditioned data suffering from multicollinearity, a new kernel two-parameter prediction method using the kernel ridge and Liu regression approach is suggested. The kernel two parameter estimator of β and the predictor of b are derived by modifying the likelihood and Henderson methods. Matrix mean square error comparisons are calculated. We also demonstrate that under suitable conditions, the resulting estimator of β is asymptotically normal. The situation with an unknown measurement error covariance matrix is handled. A Monte Carlo simulation study, together with an earthquake data example, is compiled to evaluate the effectiveness of the proposed approach at the end of the paper.

Estimation for partially linear single-index spatial autoregressive model with covariate measurement errors

Estimation for partially linear single-index spatial autoregressive model with covariate measurement errors

Simultaneous variable selection and parameters estimation for longitudinal data subject to missingness and covariates measurement error

Longitudinal studies are indispensable to study the change over time in a response variable. The main challenge of such studies is the presence of missing values. Another challenge in these studies is that covariates may be subject to measurement error. In such studies, variable selection, especially if the data are subject to measurement error and missingness, is crucial. Variable selection may lead to biased results in case of ignoring the missing values. Also, measurement error in covariates can negatively affect the accuracy of the estimates if not treated properly. Variable selection for longitudinal data that suffers from missing values and measurement error in covariates is not well explored in literature. In this article, we propose and develop a simultaneous variable selection and parameter estimation method for longitudinal data that suffers from intermittent missing values and covariates measurement error. The penalized weighted generalized estimating equations is used to account for the missingness in the longitudinal response, and simulation selection extrapolation techniques is used to account for the covariate measurement error. A simulation study is conducted to assess the performance of the proposed method. Also, the applicability of the proposed method is demonstrated using the Longitudinal Internet Studies for Social sciences data.

Robust Bayesian small area estimation using the sub-Gaussian $$\alpha$$-stable distribution for measurement error in covariates

Robust Bayesian small area estimation using the sub-Gaussian $$\alpha$$-stable distribution for measurement error in covariates

Cluster-weighted modeling with measurement error in covariates

The cluster-weighted model (CWM) is a model-based clustering approach that utilizes a mixture of regression models to cluster data points based on both a response variable Y and covariates 𝑿, where the covariates are assumed to be random. The Gaussian CWM (GCWM) is the most commonly used member of the CWM family, where the Gaussian distribution is adopted for both the covariates and the response given the covariates. In mixture of regression, assignment of data points to the clusters is based on the conditional distribution of the response variable given covariates and is independent of the covariates’ distribution. In CWM, to increase clustering performance, the covariates’ distribution is also used to assign data points to the clusters. Existing researches on CWMs are limited to the directly observed covariates, which may not reflect real-world scenarios where measurement errors (MEs) occur. The measurement error can lead to inconsistent estimates, consequently, produce spurious or obscure clusters. In this article, we assume that random covariates 𝑿 are latent, observed with an independent ME that has the Gaussian distribution. A new generalized expectation maximization algorithm is defined for estimating model parameters. The performance of the proposal is illustrated and compared with the GCWM using both simulated and real data.

Generalized Linear Models with Covariate Measurement Error and Zero-Inflated Surrogates.

Epidemiological studies often encounter a challenge due to exposure measurement error when estimating an exposure-disease association. A surrogate variable may be available for the true unobserved exposure variable. However, zero-inflated data are encountered frequently in the surrogate variables. For example, many nutrient or physical activity measures may have a zero value (or a low detectable value) among a group of individuals. In this paper, we investigate regression analysis when the observed surrogates may have zero values among some individuals of the whole study cohort. A naive regression calibration without taking into account a probability mass of the surrogate variable at 0 (or a low detectable value) will be biased. We developed a regression calibration estimator which typically can have smaller biases than the naive regression calibration estimator. We propose an expected estimating equation estimator which is consistent under the zero-inflated surrogate regression model. Extensive simulations show that the proposed estimator performs well in terms of bias correction. These methods are applied to a physical activity intervention study.

Adjusting for bias due to measurement error in functional quantile regression models with error-prone functional and scalar covariates

Wearable devices enable the continuous monitoring of physical activity (PA) but generate complex functional data with poorly characterized errors. Most work on functional data views the data as smooth, latent curves obtained at discrete time intervals with some random noise with mean zero and constant variance. Viewing this noise as homoscedastic and independent ignores potential serial correlations. Our preliminary studies indicate that failing to account for these serial correlations can bias estimations. In dietary assessments, epidemiologists often use self-reported measures based on food frequency questionnaires that are prone to recall bias. With the increased availability of complex, high-dimensional functional, and scalar biomedical data potentially prone to measurement errors, it is necessary to adjust for biases induced by these errors to permit accurate analyzes in various regression settings. However, there has been limited work to address measurement errors in functional and scalar covariates in the context of quantile regression. Therefore, we developed new statistical methods based on simulation extrapolation (SIMEX) and mixed effects regression with repeated measures to correct for measurement error biases in this context. We conducted simulation studies to establish the finite sample properties of our new methods. The methods are illustrated through application to a real data set.

Parametric modal regression with error in covariates.

An inference procedure is proposed to provide consistent estimators of parameters in a modal regression model with a covariate prone to measurement error. A score-based diagnostic tool exploiting parametric bootstrap is developed to assess adequacy of parametric assumptions imposed on the regression model. The proposed estimation method and diagnostic tool are applied to synthetic data generated from simulation experiments and data from real-world applications to demonstrate their implementation and performance. These empirical examples illustrate the importance of adequately accounting for measurement error in the error-prone covariate when inferring the association between a response and covariates based on a modal regression model that is especially suitable for skewed and heavy-tailed responsedata.

Estimation for single-index spatial autoregressive model with covariate measurement errors

This paper explores the estimators of parameters for a spatial data single-index model which has measurement errors of covariates in the nonparametric part. The related estimations are considered to combine a local-linear smoother based simulation-extrapolation (SIMEX) algorithm, the estimation equation and the estimation method for profile maximum likelihood. Under regular conditions, asymptotic properties of the link function and uncertain estimators are derived. As verified in simulations, the performance of the estimators is satisfactory. Finally, an application to a real dataset is illustrated.