Handling Measurement Error Research Articles

MAXIMUM EXPONENTIALLY WEIGHTED MOVING AVERAGE WITH MEASUREMENT ERROR (USING COVARIATE METHOD) USING AUXILIARY INFORMATION FOR CEMENT QUALITY CONTROL

The main quality characteristic at XYZ Inc. that should be observed is Compressive Strength. Cement production quality control is carried out on the average and process variability jointly with the Max-EWMA control chart. Measurement error can be found in the Compressive Strength. It can affect the sensitivity of the control chart, so quality control will be carried out by considering the presence of measurement error. Handling measurement errors can be done through three approaches (covariate method, multiple measurements, and linearly increasing variance). This research only focuses on the covariate method. Auxiliary variables also explain variance in the production process, so they are also considered in this research, with Blaine used as an auxiliary variable. Therefore, the control chart that will be formed is the Max-EWMA ME (Covariate) AI. The Max-EWMA and Max-EWMA ME (Covariate) AI control charts show that the XYZ Inc. cement production process based on variability and process averages is simultaneously statistically controlled. The controlled Max-EWMA control chart has an upper control limit of UCL=1.503018, and parameters dan . Max-EWMA ME (Covariate) AI has in-control parameters . The Max-EWMA ME (Covariate) AI control chart is more sensitive than the Max-EWMA control chart. Cement production capabilities based on Compressive Strength have a Cpl and Cpk capability index of 1.54, which means that the cement production process is capable, consistent, and has high accuracy so that the quality has reached the target.

Estimation of population mean using ranked set sampling in the presence of measurement errors

Ranked set sampling is widely acknowledged for its superior efficiency compared with simple random sampling. Only a small amount of work has been conducted using ranked set sampling when measurement errors are present. This study introduces innovative estimators utilizing ranked set sampling to assess the population mean when faced with both correlated and uncorrelated measurement errors. The expressions for the bias and mean squared error of the proposed estimators are derived up to the first-order approximation, revealing their superior performance compared to the other examined estimators. The efficacy of the suggested estimators in handling measurement errors was demonstrated through numerical illustration and simulation study investigations. The recommended estimators are further compared to the existing ones using the percentage relative efficiency and mean squared error, and the impact of measurement errors on the results is highlighted through the percentage computation of measurement errors. The innovative estimators suggested were formulated by judiciously incorporating ratio, exponential, and log estimators. Numerical examples involving expenditure and income, as well as simulated data generated from a normal population using R software, affirm the superior performance of the proposed estimators over existing ones such as the usual mean estimator and those proposed by Vishwakarma and Singh (2022), as evidenced by the higher percent relative efficiency and lower mean squared error. The evaluation of the percentage contribution of measurement error values confirms the impact of measurement errors on the properties of the estimators.

Handling Measurement Error and Omitted Confounders Considering Informativeness of the Confounding Effect under Mediation Modeling

In the article, we focused on the issues of measurement error and omitted confounders while conducting mediation analysis under experimental studies. Depending on informativeness of the confounders between the mediator (M) and outcome (Y), we described two approaches. When researchers are confident that primary confounders are included (e.g., based on theory, literature), mediation effects can be estimated using Bayesian estimation with informative priors for the correlation of residuals between latent M and Y (ρ). Simulation study results showed that mediation analysis without accounting for secondary confounders yielded inaccurate inferences about mediation effects. Without prior knowledge about the primary confounders between M and Y, we suggest using sensitivity analysis to probe robustness of mediation analysis results. ρ was used as the sensitivity parameter and an R shiny app was developed to conduct sensitivity analysis: https://qwang17.shinyapps.io/sensitivity/. Both unidimensional and multidimensional models are allowed under our developed R shiny app to conduct sensitivity analysis. Two real data examples were used for illustrating the procedure of sensitivity analysis. We ended the article by making recommendations and entertaining future directions in mediation analysis.

A comparative analysis of multivariate approaches for data analysis in management sciences

The researchers use the SEM-based multivariate approach to analyze the data in different fields, including management sciences and economics. Partial least square structural equation modeling (PLS-SEM) and covariance-based structural equation modeling (CB-SEM) are powerful data analysis techniques. This paper aims to compare both models, their efficiencies and deficiencies, methodologies, procedures, and how to employ the models. The outcomes of this paper exhibited that the PLS-SEM is a technique that combines the strengths of structural equation modeling and partial least squares. It is imperative to know that the PLS-SEM is a powerful technique that can handle measurement error at the highest levels, trim and unbalanced datasets, and latent variables. It is beneficial for analyzing relationships among latent constructs that may not be candidly witnessed and might not be applied in situations where traditional SEM would be infeasible. However, the CB-SEM approach is a procedure that pools the strengths of both structural equation modeling and confirmatory factor analysis. The CB-SEM is a dominant multivariate technique that can grip multiple groups and indicators; it is beneficial for analyzing relationships among latent variables and multiple manifest variables, which can be directly observed. The paper concluded that the PLS-SEM is a more suitable technique for analyzing relations among latent constructs, generally for a small dataset, and the measurement error is high. However, the CB-SEM is suitable for analyzing compound latent and manifest constructs, mainly when the goal is to generalize results to specific population subgroups. The PLS-SEM and CB-SEM have specific efficiencies and deficiencies that determine which technique to use depending on resource availability, the research question, the dataset, and the available time.

Stochastic EM Algorithm for Joint Model of Logistic Regression and Mechanistic Nonlinear Model in Longitudinal Studies

We study a joint model where logistic regression is applied to binary longitudinal data with a mismeasured time-varying covariate that is modeled using a mechanistic nonlinear model. Multiple random effects are necessary to characterize the trajectories of the covariate and the response variable, leading to a high dimensional integral in the likelihood. To account for the computational challenge, we propose a stochastic expectation-maximization (StEM) algorithm with a Gibbs sampler coupled with Metropolis–Hastings sampling for the inference. In contrast with previous developments, this algorithm uses single imputation of the missing data during the Monte Carlo procedure, substantially increasing the computing speed. Through simulation, we assess the algorithm’s convergence and compare the algorithm with more classical approaches for handling measurement errors. We also conduct a real-world data analysis to gain insights into the association between CD4 count and viral load during HIV treatment.

Logistic regression with correlated measurement error and misclassification in covariates.

Many areas of research, such as nutritional epidemiology, may encounter measurement errors of continuous covariates and misclassification of categorical variables when modeling. It is well known that ignoring measurement errors or misclassification can lead to biased results. But most research has focused on solving these two problems separately. Addressing both measurement error and misclassification simultaneously in a single analysis is less actively studied. In this article, we propose a new correction method for a logistic regression to handle correlated error variables involved in multivariate continuous covariates and misclassification in a categorical variable simultaneously. It is not computationally intensive since a closed-form of the approximate likelihood function conditional on observed covariates is derived. The asymptotic normality of this proposed estimator is established under regularity conditions and its finite-sample performance is empirically examined by simulation studies. We apply this new estimation method to handle measurement error in some nutrients of interest and misclassification of a categorical variable named physical activity in the European Prospective Investigation into Cancer and Nutrition-InterAct Study data. Analyses show that fruit is negatively associated with type 2 diabetes for a group of women doing active physical activity, protein has positive association with type 2 diabetes for the group of less active physical activity, and actual physical activity has a greater effect on reducing the risk of type 2 diabetes than observed physical activity.

Comparing methods for assessing a difference in correlations with dependent groups, measurement error, nonnormality, and incomplete data.

I compared multiple methods to estimate and test a difference in correlations (ρdiff) between two variables that are repeatedly measured or originate from dyads. Fisher's z transformed correlations are often used for testing ρdiff. However, raw scores are typically used directly to compute correlations under this popular method, whose performance has not been evaluated with measurement error or nonnormality in data. Structural equation modeling (SEM) can handle measurement error via latent-variable modeling. To handle nonnormality for testing a difference in correlations in dependent groups, when measurement error was of no concern, I discussed SEM using maximum likelihood estimation (ML) with sandwich-type standard errors, ML with bootstrap percentile or bias-corrected confidence intervals, and Bayesian credible intervals. In addition, I also examined a mean- and variance-adjusted likelihood ratio test and the Bollen-Stine bootstrapping model fit test. When measurement error existed, ρdiff was tested under a latent variable model. Furthermore, under the same SEM frameworks with complete data, I also assessed ρdiff with ignorable missing data. A simulation study was conducted considering whether measurement error existed, whether data were normal, and whether data were complete. Empirical examples were used for illustration. Recommendations were then given based on the findings. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

UAV Attitude Angle Measurement Method Based on Magnetometer-Satellite Positioning System

To improve the measurement accuracy of unmanned aerial vehicles (UAVs), in this study, we proposed a method for measuring the attitude angle of a UAV by the combination of a magnetometer and satellite positioning system. Based on the measurement principle, we established a combined measurement error model, analyzed the root cause of the measurement error, and calibrated the magnetometer using the least-squares algorithm. For handling external or system interference effects, we designed a compensation algorithm that does not depend on environmental information. For handling measurement errors, a “current” statistical model was established, and the continuous-discrete Kalman filter algorithm was used to eliminate measurement errors. The test results showed that after using the compensation algorithm, the measurement error was reduced from 17.80% to 6.86% compared to the average absolute error of the local magnetic field intensity, and the absolute measurement error was reduced by 61.49%. The absolute measurement error was compared after using the compensation + filtering algorithm, and the error after compensation was further reduced by 42.36%. Hence, we proved the feasibility and effectiveness of our method.

Marginal analysis of bivariate mixed responses with measurement error and misclassification.

Bivariate responses with mixed continuous and binary variables arise commonly in applications such as clinical trials and genetic studies. Statistical methods based on jointly modeling continuous and binary variables have been available. However, such methods ignore the effects of response mismeasurement, a ubiquitous feature in applications. It has been well studied that in many settings, ignorance of mismeasurement in variables usually results in biased estimation. In this paper, we consider the setting with a bivariate outcome vector which contains a continuous component and a binary component both subject to mismeasurement. We propose estimating equation approaches to handle measurement error in the continuous response and misclassification in the binary response simultaneously. The proposed estimators are consistent and robust to certain model misspecification, provided regularity conditions. Extensive simulation studies confirm that the proposed methods successfully correct the biases resulting from the error-in-variables under various settings. The proposed methods are applied to analyze the outbred Carworth Farms White mice data arising from a genome-wide association study.

Data Integration by Combining Big Data and Survey Sample Data for Finite Population Inference

SummaryThe statistical challenges in using big data for making valid statistical inference in the finite population have been well documented in literature. These challenges are due primarily to statistical bias arising from under‐coverage in the big data source to represent the population of interest and measurement errors in the variables available in the data set. By stratifying the population into a big data stratum and a missing data stratum, we can estimate the missing data stratum by using a fully responding probability sample and hence the population as a whole by using a data integration estimator. By expressing the data integration estimator as a regression estimator, we can handle measurement errors in the variables in big data and also in the probability sample. We also propose a fully nonparametric classification method for identifying the overlapping units and develop a bias‐corrected data integration estimator under misclassification errors. Finally, we develop a two‐step regression data integration estimator to deal with measurement errors in the probability sample. An advantage of the approach advocated in this paper is that we do not have to make unrealistic missing‐at‐random assumptions for the methods to work. The proposed method is applied to the real data example using 2015–2016 Australian Agricultural Census data.

Locally efficient semiparametric estimator for zero-inflated Poisson model with error-prone covariates

Overdispersion is a common phenomenon in count or frequency responses in Poisson models. For example, number of car accidents on a highway during a year period. A similar phenomenon is observed in electric power systems, where cascading failures often follows some distribution with inflated zero. When the response contains an excess amount of zeros, zero-inflated Poisson (ZIP) is the most favourable model. However, during the data collection process, some of the covariates cannot be accessed directly or are measured with error among numerous disciplines. To the best of our knowledge, little existing work is available in the literature that tackles the population heterogeneity in the count response while some of the covariates are measured with error. With the increasing popularity of such outcomes in modern studies, it is interesting and timely to study zero-inflated Poisson models in which some of the covariates are subject to measurement error while some are not. We propose a flexible partial linear single index model for the log Poisson mean to correct bias potentially due to the error in covariates or the population heterogeneity. We derive consistent and locally efficient semiparametric estimators and study the large sample properties. We further assess the finite sample performance through simulation studies. Finally, we apply the proposed method to a real data application and compare with existing methods that handle measurement error in covariates.

Genetic association studies with bivariate mixed responses subject to measurement error and misclassification

In genetic association studies, mixed effects models have been widely used in detecting the pleiotropy effects which occur when one gene affects multiple phenotype traits. In particular, bivariate mixed effects models are useful for describing the association of a gene with a continuous trait and a binary trait. However, such models are inadequate to feature the data with response mismeasurement, a characteristic that is often overlooked. It has been well studied that in univariate settings, ignorance of mismeasurement in variables usually results in biased estimation. In this paper, we consider the setting with a bivariate outcome vector which contains a continuous component and a binary component both subject to mismeasurement. We propose an induced likelihood approach and an EM algorithm method to handle measurement error in continuous response and misclassification in binary response simultaneously. Simulation studies confirm that the proposed methods successfully remove the bias induced from the response mismeasurement.

Performance of the MEWMA‐CoDa control chart in the presence of measurement errors

AbstractThis paper can be considered as an extension of the work of Tran et al (for monitoring compositional data using a multivariate exponentially weighted moving average MEWMA‐compositional data [CoDa] chart) by taking into account potential measurement errors that are known to highly affect production processes. A linearly covariate error model with a constant error variance is used to study the impact of measurement errors on the MEWMA‐CoDa control chart. In particular, the influence of the device parameters (σM,b), the number of independent observations m, and the the number of variables p are investigated in terms of the MEWMA optimal couples (r,H) as well as in terms of their corresponding ARLs. A comparison between the Hotelling‐CoDa T2 and the proposed chart is made in order to show that the MEWMA‐CoDa chart is more efficient in detecting shifts in the presence of measurement errors. A real‐life example of muesli production, using multiple measurements for each composition, is used to estimate the parameters and also to demonstrate how the MEWMA‐CoDa can handle measurement errors to detect shifts in the process.

Sensor Network Robustness Using Model-Based Data Reconciliation for Continuous Tablet Manufacturing

Advances in continuous manufacturing in the pharmaceutical industry necessitate reliable process monitoring systems that are capable of handling measurement errors inherent in all sensor technologies and detecting measurement outliers to ensure operational reliability. The purpose of this work was to demonstrate data reconciliation (DR) and gross error detection methods as real-time process management tools to accomplish robust process monitoring. DR mitigates the effects of random measurement errors, while gross error detection identifies nonrandom sensor malfunctions. DR is an established methodology in other industries (i.e., oil and gas) and was recently investigated for use in drug product continuous manufacturing. This work demonstrates the development and implementation of model-based steady-state data reconciliation on 2 different end-to-end continuous tableting lines: direct compression and dry granulation. These tableting lines involve different equipment and sensor configurations, with sensor network redundancy achieved using equipment-embedded sensors and in-line process analytical technology tools for the critical process parameters and critical quality attributes. The nonlinearity of the process poses additional challenges to solve the steady-state data reconciliation optimization problem in real time. At-line and off-line measurements were used to validate the framework results.

Robust estimation in linear regression models for longitudinal data with covariate measurement errors and outliers

Measurement errors and outliers commonly arise during the process of longitudinal data collection and ignoring them in data analysis can lead to large deviations in estimates. Therefore, it is important to take into account the effect of measurement errors and outliers in longitudinal data analysis. In this paper, a robust estimating equation method for analyzing longitudinal data with covariate measurement errors and outliers is proposed. Specifically, the biases caused by measurement errors are reduced via using the independence between replicate measurements and the biases caused by outliers are corrected via centralizing the observed covariate matrix. The proposed method does not require specifying the distributions of the true covariates, response and measurement errors. In practice, it can be easily implemented via the standard generalized estimating equations algorithms. The asymptotic normality of the proposed estimator is established under regularity conditions. Extensive simulation studies show that the proposed method performs better in handling measurement errors and outliers than several existing methods. For illustration, the proposed method is applied to a data set from the Lifestyle Education for Activity and Nutrition (LEAN) study.

Integrating Covariates into Social Relations Models: A Plausible Values Approach for Handling Measurement Error in Perceiver and Target Effects

ABSTRACTThe Social Relations Model (SRM) is a conceptual and analytical approach to examining dyadic behaviors and interpersonal perceptions within groups. In an SRM, the perceiver effect describes a person's tendency to perceive other group members in a certain way, whereas the target effect measures the tendency to be perceived by others in certain ways. In SRM research, it is often of interest to relate these individual SRM effects to covariates. However, the estimated individual SRM effects might not provide a very reliable measure of the true, unobserved SRM effects, resulting in distorted estimates of associations with other variables. This article introduces a plausible values approach that allows users to correct for measurement error when assessing the association of individual SRM effects with other individual difference variables. In the plausible values approach, the latent, true individual SRM effects are treated as missing values and are imputed from an imputation model by applying Bayesian estimation techniques. In a simulation study, the statistical properties of the plausible values approach are compared with two approaches that have been used in previous research. A data example from educational psychology is presented to illustrate how the plausible values approach can be implemented with the software WinBUGS.

Accounting for measurement error in human life history trade-offs using structural equation modeling.

Revealing causal effects from correlative data is very challenging and a contemporary problem in human life history research owing to the lack of experimental approach. Problems with causal inference arising from measurement error in independent variables, whether related either to inaccurate measurement technique or validity of measurements, seem not well-known in this field. The aim of this study is to show how structural equation modeling (SEM) with latent variables can be applied to account for measurement error in independent variables when the researcher has recorded several indicators of a hypothesized latent construct. As a simple example of this approach, measurement error in lifetime allocation of resources to reproduction in Finnish preindustrial women is modelled in the context of the survival cost of reproduction. In humans, lifetime energetic resources allocated in reproduction are almost impossible to quantify with precision and, thus, typically used measures of lifetime reproductive effort (e.g., lifetime reproductive success and parity) are likely to be plagued by measurement error. These results are contrasted with those obtained from a traditional regression approach where the single best proxy of lifetime reproductive effort available in the data is used for inference. As expected, the inability to account for measurement error in women's lifetime reproductive effort resulted in the underestimation of its underlying effect size on post-reproductive survival. This article emphasizes the advantages that the SEM framework can provide in handling measurement error via multiple-indicator latent variables in human life history studies.

Entropy-Based Experimental Design for Optimal Model Discrimination in the Geosciences

Choosing between competing models lies at the heart of scientific work, and is a frequent motivation for experimentation. Optimal experimental design (OD) methods maximize the benefit of experiments towards a specified goal. We advance and demonstrate an OD approach to maximize the information gained towards model selection. We make use of so-called model choice indicators, which are random variables with an expected value equal to Bayesian model weights. Their uncertainty can be measured with Shannon entropy. Since the experimental data are still random variables in the planning phase of an experiment, we use mutual information (the expected reduction in Shannon entropy) to quantify the information gained from a proposed experimental design. For implementation, we use the Preposterior Data Impact Assessor framework (PreDIA), because it is free of the lower-order approximations of mutual information often found in the geosciences. In comparison to other studies in statistics, our framework is not restricted to sequential design or to discrete-valued data, and it can handle measurement errors. As an application example, we optimize an experiment about the transport of contaminants in clay, featuring the problem of choosing between competing isotherms to describe sorption. We compare the results of optimizing towards maximum model discrimination with an alternative OD approach that minimizes the overall predictive uncertainty under model choice uncertainty.

A doubly robust estimator for the average treatment effect in the context of a mean-reverting measurement error.

One of the main limitations of causal inference methods is that they rely on the assumption that all variables are measured without error. A popular approach for handling measurement error is simulation-extrapolation (SIMEX). However, its use for estimating causal effects have been examined only in the context of an additive, non-differential, and homoscedastic classical measurement error structure. In this article we extend the SIMEX methodology, in the context of a mean reverting measurement error structure, to a doubly robust estimator of the average treatment effect when a single covariate is measured with error but the outcome and treatment and treatment indicator are not. Throughout this article we assume that an independent validation sample is available. Simulation studies suggest that our method performs better than a naive approach that simply uses the covariate measured with error.

Statistical issues related to dietary intake as the response variable in intervention trials.

The focus of this paper is dietary intervention trials. We explore the statistical issues involved when the response variable, intake of a food or nutrient, is based on self‐report data that are subject to inherent measurement error. There has been little work on handling error in this context. A particular feature of self‐reported dietary intake data is that the error may be differential by intervention group. Measurement error methods require information on the nature of the errors in the self‐report data. We assume that there is a calibration sub‐study in which unbiased biomarker data are available. We outline methods for handling measurement error in this setting and use theory and simulations to investigate how self‐report and biomarker data may be combined to estimate the intervention effect. Methods are illustrated using data from the Trial of Nonpharmacologic Intervention in the Elderly, in which the intervention was a sodium‐lowering diet and the response was sodium intake. Simulations are used to investigate the methods under differential error, differing reliability of self‐reports relative to biomarkers and different proportions of individuals in the calibration sub‐study. When the reliability of self‐report measurements is comparable with that of the biomarker, it is advantageous to use the self‐report data in addition to the biomarker to estimate the intervention effect. If, however, the reliability of the self‐report data is low compared with that in the biomarker, then, there is little to be gained by using the self‐report data. Our findings have important implications for the design of dietary intervention trials. © 2016 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd.