Measurement Error Model Research Articles

Weighted and partial total least squares method for the EIV model with linear equality and inequality constraints

A weighted and partial total least squares method for the errors-in-variables (EIV) model with linear equality and inequality constraints is presented. A collected observation vector is formed by the independent variables both in the observation vector and the design matrix. The proposed model is solved based on the Lagrange method and by transforming the problem into a linear complementary problem. The performance of the proposed method is studied by two numerical experiments. The results show that, the proposed method is capable of solving the linearly constrained EIV model efficiently.

Spatial regression of multi-fidelity meteorological observations using a proxy-based measurement error model

Abstract. High-resolution weather maps are fundamental components of early warning systems, since they enable the (near) real-time tracking of extreme weather events. In this context, crowd-sourced weather networks producing low-fidelity observations are often the only type of data available at local (e.g. neighborhood) scales. In this work, we demonstrate that we can provide such maps by combining high-fidelity official weather data with low-fidelity crowd-sourced weather data and high-resolution covariate information. Because the crowd-sourced data contains significant bias and noise, we develop an approach to include a bias budget and noise budget in the multi-fidelity Bayesian spatial data analysis. The weights of the different components of these bias and noise budgets are tuned to the data set. We apply this approach to 24 hours of weather data in the Netherlands, for a day that had a “code orange” (i.e. “be prepared for extreme weather with high risk of impact”) weather warning for heavy precipitation. From our analysis, we see a significant – qualitative and quantitative – synergy effect when introducing low-fidelity data and high-resolution covariate information.

A spline-assisted semiparametric approach to nonparametric measurement error models

A spline-assisted approach is proposed to handle the measurement error problem in treating the pollution and asthma data. It is well known that the minimax rate of convergence in nonparametric regression function estimation of a random variable measured with error is much slower than the rate in the error free case. A different problem is considered. It is shown that if one is willing to impose a relatively mild assumption in requiring that the error-prone variable has a compact support, then standard nonparametric results are obtainable for measurement error models. New and constructive methods to take full advantage of the compact support assumption via spline-assisted semiparametric methods are proposed. It is proven that the new estimator achieves the usual nonparametric rate as if there were no measurement error. Furthermore it is shown that similar spline approach can be used to assess the probability density function on a compact set, using observations with error, and the resulting estimator differs from the true density function only by a constant scale. In addition, it retains the nonparametric density convergence properties of the error free case. The performance of the new methods is demonstrated through simulations and the methods are implemented to analyze the relation between asthma and pollution.

Conformal normal curvature and detection of masked observations in multivariate null intercept measurement error models

Measurement errors occur very commonly in practice. After fitting the model, influence diagnostics is an important step in statistical data analysis. The most frequently used diagnostic method for measurement error models is the local influence. However, this methodology may fail to detect masked influential observations. To overcome this limitation, we propose the use of the conformal normal curvature with the forward search algorithm. The results are presented through easy to interpret plots considering different perturbation schemes. The proposed methodology is illustrated with three real data sets and one simulated data set, two of which have been previously analyzed in the literature. The third data set deals with the stability of the hygroscopic solid dosage in pharmaceutical processes to ensure the maintenance of product safety quality. In this application, the analytical mass balance is subject to measurement errors, which require attention in the modeling process and diagnostic analysis.

Crime Prediction and Analysis against women Using LRSRI-Missing Value Imputation and FIPSO - Optimum Feature Selection Methods

Data investigation is the method of considering crude measurements in arrange to draw conclusions around them. Many statistics evaluation techniques and tendencies had been automated into mechanical techniques and algorithms in such a manner that they provided raw statistics for human consumption. Machine learning could be a portion of artificial intelligence that permits computer frameworks to "analyze" their own statistics and improve them over time without being explicitly programmed. Machine learning algorithms can understand patterns in statistics and analyze them to make their own predictions. Lost esteem ascription is one of the foremost vital procedures in data pre-processing and it is additionally the most prepare of information examination. Ascription of lost information for a variable replaces lost information with a esteem inferred from an assess of the dispersion of that variable. Basic accusation employments as it were one suspicion. Numerous ascriptions employments diverse gauges to reflect the instability in evaluating this dispersion. In this article, The proposed method LRSRI used for impute the missing values on Crime against Women Data-set(CAW).The Linear Regression Imputation and Stochastic regression imputations are used in this method.Feature selection is another important data preprocessing techniques.This is often called attribute selection or feature selection. The most important problem in predictive modeling is the mechanical selection of features in the data. In this work,the proposed method FIPSO implemented for feature selection.This is feature importance and Particle Swarm Optimization based method.The main objective of this work is predict the crime rate against women in India based on 2001 to 2021 crime recorded against women in India.This Data set is collected from Data.gov.in.Finally The predicted result is compared with recent NCRB crime report.The proposed method LRSRI and FIPSO has given 98.34% accuracy of crime prediction.In feature,This outcome will be valuable for the crime office to control the CAW in India.

Measurement error models for spatial network lattice data: Analysis of car crashes in Leeds

Abstract Road casualties represent an alarming concern for modern societies. During the last years, several authors proposed sophisticated approaches to help authorities implement new policies. These models were usually developed considering a set of socio-economic variables and ignoring the measurement error, which can bias the statistical inference. This paper presents a Bayesian model to analyse car crash occurrences at the network-lattice level, taking into account measurement error in the spatial covariate. The suggested methodology is exemplified by considering the collisions in the road network of Leeds (UK) during 2011–2019. Traffic volumes are approximated using an extensive set of counts obtained from mobile devices and the estimates are adjusted using a spatial measurement error correction.

Bayesian instrumental variable estimation in linear measurement error models

AbstractIn this article, we study the problem of parameter estimation for measurement error models by combining the Bayes method with the instrumental variable approach, deriving the posterior distribution of parameters under different priors with known and unknown variance parameters, respectively, and calculating the Bayes estimator (BE) of the parameters under quadratic loss. However, it is difficult to obtain an explicit expression for BE because of the complex multiple integrals involved. Therefore, we adopt the linear Bayes method, which does not specify the form of the prior and avoids these complicated integral calculations, to obtain an expression for the linear Bayes estimator (LBE) for different priors. We prove that this LBE is superior to the two‐stage least squares estimator under the mean squared error matrix criterion. Numerical simulations show that our LBE is very close to the real parameter whether the variance parameters are known or unknown, and it gradually approaches BE as the sample size increases. Our results indicate that this instrumental variable approach is valid for measurement error models.

Local influence in linear mixed measurement error models with ridge estimation

This paper deals with the assessment of the effects of minor perturbations of data in the linear mixed measurement error models with Ridge estimation, based on the corrected score function. The local influence approach is used for assessing the influence of small perturbations on the parameter estimates. We examine different types of perturbation schemes including the covariance matrix of the conditional errors, case weight, response, and explanatory perturbation, to identify influential observations. A real data application and a simulation study illustrate the performance of the proposed diagnostics.

Variance matrix estimation in multivariate classical measurement error models

Variance matrix estimation in multivariate classical measurement error models

A Comprehensive Review of GNSS/INS Integration Techniques for Land and Air Vehicle Applications

Navigation systems are of interest for applications in both civilian and military vehicles. Satellite navigation systems and inertial navigation systems are the most applied in this area. They have complementary properties, which has led to a trend of integrating these systems. At present, there are several approaches to GNSS/INS integration: loosely coupled, tightly coupled and deeply coupled and many approaches to their modifications in dependence of application and arising problems with measurements, such as lack of GNSS measurements or poor quality of GNSS and INS measurements. This article presents an extensive review of the available modern approaches and their modifications for integrating INS and GNSS measurements, arranging them and highlights the main problems arising for the considered type of integration approach. The article includes a review of various integration tools based on the Kalman filter and intelligent systems, INS mechanization and features of development of an INS measurement error model that is necessary for integration, the main problems of GNSS/INS integration and a comparative description of the solutions proposed by the authors for solving these problems. The findings of this work are useful for further research in the field of inertial and satellite navigation, as well as for engineers involved in the practical implementation of integrated GNSS/INS systems.

A general algorithm for error-in-variables regression modelling using Monte Carlo expectation maximization.

In regression modelling, measurement error models are often needed to correct for uncertainty arising from measurements of covariates/predictor variables. The literature on measurement error (or errors-in-variables) modelling is plentiful, however, general algorithms and software for maximum likelihood estimation of models with measurement error are not as readily available, in a form that they can be used by applied researchers without relatively advanced statistical expertise. In this study, we develop a novel algorithm for measurement error modelling, which could in principle take any regression model fitted by maximum likelihood, or penalised likelihood, and extend it to account for uncertainty in covariates. This is achieved by exploiting an interesting property of the Monte Carlo Expectation-Maximization (MCEM) algorithm, namely that it can be expressed as an iteratively reweighted maximisation of complete data likelihoods (formed by imputing the missing values). Thus we can take any regression model for which we have an algorithm for (penalised) likelihood estimation when covariates are error-free, nest it within our proposed iteratively reweighted MCEM algorithm, and thus account for uncertainty in covariates. The approach is demonstrated on examples involving generalized linear models, point process models, generalized additive models and capture-recapture models. Because the proposed method uses maximum (penalised) likelihood, it inherits advantageous optimality and inferential properties, as illustrated by simulation. We also study the model robustness of some violations in predictor distributional assumptions. Software is provided as the refitME package on R, whose key function behaves like a refit() function, taking a fitted regression model object and re-fitting with a pre-specified amount of measurement error.

Optimal Design of a Surface Precipitation Network in Canada

Abstract The surface precipitation network in Canada suffers from large data gaps due to the challenge of covering a large country with a low population density. A proof-of-concept for an optimal network design is proposed to more efficiently estimate precipitation in Canada with the design goal of minimizing the interpolation uncertainty. The network design is based on a statistical model of precipitation that accounts for intermittency and non-Gaussianity of precipitation. Our results indicate that the greatest needs for new stations are in British Columbia, where coastal and mountain climate leads to more uncertainty in precipitation amounts, while the Prairie Provinces (Alberta, Saskatchewan, and Manitoba) could gain efficiencies by reducing their network size. Despite the current low density of stations in the territories north of Canada, these drier and colder regions only have a moderate need for more stations, mostly in the mountainous regions of Yukon. However, from a spatially varying wind undercatch measurement error model, it is shown that these northern regions have greatest need for higher-accuracy measurements. Significance Statement The proposed methodology can guide in the optimal placement of precipitation gauges across a large country such as Canada, which will provide value for money in how rain and snow are monitored.

Nexus Between Urbanization, Industrialization, Natural Resources Rent, and Anthropogenic Carbon Emissions in South Asia: CS-ARDL Approach

Rapid population growth and economic expansion affect environmental sustainability by raising emissions from increased urbanization, industrialization, and energy consumption in South Asia. Therefore, the current research aims to scrutinize the dynamic impacts of urbanization, industrialization, and energy consumption on carbon dioxide (CO2) emissions in five South Asian countries (Bangladesh, Pakistan, India, Nepal, and Sri Lanka) under the umbrella of the famous stochastic regression for impact for technology, population, and asset on environmental condition (STIRPAT) model. This research employed the second-generation unit root and cointegration tests by applying the data from 1972 to 2021 to investigate the existence of slope heterogeneity (SH) and cross-sectional dependence (CSD) problem. After checking CSD, SH, unit root, and cointegration tests, the research utilized cross-sectional autoregressive distributive lag (CS-ARDL) as a baseline model and augmented mean group (AMG), mean group (MG), and common correlated effects mean group (CCEMG) as a robustness check. The evidence shows that the economic boom, urbanization, and industrialization increase CO2 emissions. CO2 emissions in South Asian nations have been reduced due to population growth, natural resources rent, and electrification. All estimators point to urbanization’s negative effects, being far more severe than any other environmental impact. Conversely, natural resource rent prevents environmental degradation more effectively than electricity. Therefore, it is recommended that South Asian economies adopt consistent, sustainable economic policies to reap the benefits of industrialization, urbanization, and increased electricity use. The findings are generally consistent with the policy implications.

The trouble with triples: Examining the impact of measurement error in mediation analysis.

Mediation analysis is used in genetic mapping studies to identify candidate gene mediators of quantitative trait loci (QTL). We consider genetic mediation analysis of triplets-sets of three variables consisting of a target trait, the genotype at a QTL for the target trait, and a candidate mediator that is the abundance of a transcript or protein whose coding gene co-locates with the QTL. We show that, in the presence of measurement error, mediation analysis can infer partial mediation even in the absence of a causal relationship between the candidate mediator and the target. We describe a measurement error model and a corresponding latent variable model with estimable parameters that are combinations of the causal effects and measurement errors across all three variables. The relative magnitudes of the latent variable correlations determine whether or not mediation analysis will tend to infer the correct causal relationship in large samples. We examine case studies that illustrate the common failure modes of genetic mediation analysis and demonstrate how to evaluate the effects of measurement error. While genetic mediation analysis is a powerful tool for identifying candidate genes, we recommend caution when interpreting mediation analysis findings.

Analysis and Projection of Transport Sector Demand for Energy and Carbon Emission: An Application of the Grey Model in Pakistan

The incredible increase in carbon emissions is a major global concern. Thus, academicians and policymakers at COP26 are continuously urging to devise strategies to reduce carbon and other greenhouse gas emissions. The transportation sector is a major contributor to greenhouse gas emissions in developing countries. Therefore, this study projected an increase in fossil fuel demand for transportation and corresponding carbon dioxide emission in Pakistan from 2018 to 2030 by employing the Grey model and using annual data from 2010 to 2018. Furthermore, the determinant of fossil fuel demand is modeled using an environmental sustainability model such as stochastic regression IPAT that links environmental impact as a product of population, affluence, and technology on annual time series data spanning from 1990 to 2019. The projected values of oil demand and carbon emissions reveal an increasing trend, with average annual growth rates of 12.68% and 11.45%, respectively. The fully modified ordinary least squares (FM-OLS) findings confirmed the environmental Kuznets hypothesis. The increase in population growth emerged as the major driver for oil demand and carbon dioxide emissions, while technological advancement can reduce oil demand and corresponding carbon emissions. This study urges Pakistan to switch from oil to gas and other green energies by encouraging hybrid vehicles, as the number of vehicles on the road positively impacts the transport sector’s oil demand. Moreover, increasing economic growth and controlling the population growth rate by discouraging more children can be a valid policy for reducing oil demand and corresponding carbon emissions.

Detecting and correcting for heteroscedasticity in the presence of measurement error

The problem of measurement error in predictors has received a vast amount of attention for both linear and non-linear models. The major focus has generally been on inference for regression coefficients, while residual analysis, variance estimation and heteroscedasticity assessment have received limited attention. In this paper we propose and evaluate new methods, based on reconstructed predictors, to address these problems in the context of linear regression. Methods using moment reconstructed predictors are found to perform well, including a new model-based bootstrapping technique for testing heteroscedasticity. Motivated by an example where the predictor is methylation rate and the measurement error model is based on the binomial distribution, particular attention is given to being able to handle the situation where both the measurement error variances and the variance of the error in the equation may be changing as a quadratic function of the unobserved predictor.

Mediation analysis in the presence of continuous exposure measurement error.

The difference method is used in mediation analysis to quantify the extent to which a mediator explains the mechanisms underlying the pathway between an exposure and an outcome. In many health science studies, the exposures are almost never measured without error, which can result in biased effect estimates. This article investigates methods for mediation analysis when a continuous exposure is mismeasured. Under a linear exposure measurement error model, we prove that the bias of indirect effect and mediation proportion can go in either direction but the mediation proportion is usually be less biased when the associations between the exposure and its error-prone counterpart are similar with and without adjustment for the mediator. We further propose methods to adjust for exposure measurement error with continuous and binary outcomes. The proposed approaches require a main study/validation study design where in the validation study, data are available for characterizing the relationship between the true exposure and its error-prone counterpart. The proposed approaches are then applied to the Health Professional Follow-up Study, 1986-2016, to investigate the impact of body mass index (BMI) as a mediator for mediating the effect of physical activity on the risk of cardiovascular diseases. Our results reveal that physical activity is significantly associated with a lower risk of cardiovascular disease incidence, and approximately half of the total effect of physical activity is mediated by BMI after accounting for exposure measurement error. Extensive simulation studies are conducted to demonstrate the validity and efficiency of the proposed approaches in finite samples.

Urbanization and carbon emissions: Panel evidence from 68 low-income and lower-middle-income countries

ABSTRACT Although the developed world has almost completed the process of urbanization, developing countries are still rapidly urbanizing. Applying the extended stochastic regression on population, affluence, and technology (STIRPAT) model for the period 2000–2019, this article is an endeavor to explore the consequences of urbanization along with gross domestic product (GDP) per capita, foreign direct investment (FDI) inflow, trade openness, and mobile phone penetration on carbon dioxide emissions in 68 low-income and lower-middle-income countries across Asia, Africa, Middle East, and South America. Initially, the study used a panel unit root test to identify whether the variables are stationary or not. Subsequently, by using the co-integration test, a long-run association among the variables was seen. Finding a long-run relationship, the fully modified ordinary least squares method was applied to examine the impact of urbanization and other explanatory variables on carbon dioxide emissions. Results showed that urbanization followed by GDP per capita are the key promoters of CO2 emissions across all countries, whereas the direction and significance of inward FDI and trade openness varied across regions. Furthermore, it was observed that mobile phone penetration (as an indicator of information and communication technology [ICT]) has a significant and negative relationship with CO2 emissions, showing that ICT-based technologies might be the answer to decoupling economic growth from emissions growth.

A Hybrid Model for Orthogonal Regression

AbstractLinear functional relationships are intended to be symmetric and therefore cannot generally be accurately estimated using ordinary least squares regression equations. Orthogonal regression (OR) models allow for errors in both Y and X and therefore can provide symmetric estimates of these relationships. The most well‐established OR model, the errors‐in‐variables (EIV) model, assumes that the observed scatter around the line is due entirely to errors of measurement in Y and X and that the ratio of the error variances is known. If most of the variance around the line is known to be due to the errors of measurement in Y and X, the EIV model can provide an unbiased maximum likelihood estimate for a functional relationship. However, if a substantial part of the variability around the line is due to natural variability, which is not attributable to errors of measurement in Y or X, the ratio of the measurement error variances is not well defined and the EIV model is not directly applicable. The main contribution of this report is the development of a hybrid model that provides plausible estimates for linear functional relationships in cases with substantial natural variability and substantial errors of measurement. An analysis of female and male differential test functioning between an essay test and an objective test used as parts of a licensure examination provides an illustration of the use of the hybrid model.

A two-part measurement error model to estimate participation in undeclared work and related earnings

In undeclared work research, the estimation of the magnitude of the phenomenon (i.e., the amount of income and/or the percentage of workers involved) is of major interest. This has been done either using indirect methods or by means of ad hoc surveys such as the Eurobarometer special survey on undeclared work, our motivating study. The extent of undeclared work can be measured by means of two different outcomes: the event of working off-the-book (binary variable) and, when the event occurs, the amount of earnings deriving from the undeclared activity (continuous variable). This setup has been typically modeled via the so called two-part model: a binary choice model for the probability of observing a positive-versus-zero outcome and then, conditional on a positive outcome, a regression model for the positive outcome. We propose an extension of the two-part model that goes in two directions. The first regards the measurement error that, given the very nature of undeclared activities, is most likely to affect both the outcomes of interest. The second is that we generalize the linear regression part of the model to allow individual-level means. We also conduct an extensive simulation study to investigate the performance of the proposed model and compare it with traditional approaches.