Measurement Error Variance Research Articles

How robust is the relationship between neural processing speed and cognitive abilities?

Individual differences in processing speed are consistently related to individual differences in cognitive abilities, but the mechanisms through which a higher processing speed facilitates reasoning remain largely unknown. To identify these mechanisms, researchers have been using latencies of the event-related potential (ERP) to study how the speed of cognitive processes associated with specific ERP components is related to cognitive abilities. Although there is some evidence that latencies of ERP components associated with higher-order cognitive processes are related to intelligence, results are overall quite inconsistent. These inconsistencies likely result from variations in analytic procedures and little consideration of the psychometric properties of ERP latencies in relatively small sample studies. Here we used a multiverse approach to evaluate how different analytical choices regarding references, low-pass filter cutoffs, and latency measures affect the psychometric properties of P2, N2, and P3 latencies and their relations with cognitive abilities in a sample of 148 participants. Latent correlations between neural processing speed and cognitive abilities ranged from -.49 to -.78. ERP latency measures contained about equal parts of measurement error variance and systematic variance, and only about half of the systematic variance was related to cognitive abilities, whereas the other half reflected nuisance factors. We recommend addressing these problematic psychometric properties by recording EEG data from multiple tasks and modeling relations between ERP latencies and covariates in latent variable models. All in all, our results indicate that there is a substantial and robust relationship between neural processing speed and cognitive abilities when those issues are addressed.

Equal Precision Measurement Structural Models

Error variance in structural models is often specified as a conditional variance associated with a manifest variable or as a regression path from a standardized error variance. This paper describes scenarios in which specification of both terms is useful: (1) Corrections for attenuation in single indicator factor models; (2) Tests of the equality in the proportion of explained variance across multiple dependent variables in regression models; (3) Factor models with two indicators; and (4) Tests of invariance in the proportion of measurement error variance across occasions in growth curve models. Examples of such models using both simulated and real-world data are presented.

Digital Tri-Axis Accelerometer with X/Y-Axial Resonators and Z-Axial Capacitive Seesaw.

A tri-axis accelerometer with a digital readout circuit and communication system is introduced. It is composed of two resonant accelerometers in the x and y-axis, and a seesaw capacitive one in the z-axis. The device is encapsulated in air to ensure that the z-axis works in an over-damped state. Moreover, the closed-loop drive circuit establishes the x-axis and y-axis in resonant mode, and the z-axis in force balance mode. A miniaturized measurement based on FPGA is designed to collect these output signals. The phase noise of the resonance part and the amplitude noise of the seesaw part are studied by simulation. The model can predict the contribution of each part to the measurement error and Allan variance. Multiplied clock and Kalman filter in sliding window are used to reduce the frequency error. The test results show that the accelerometer has low bias instability (<30 μg), low cross-coupling error (<0.5%), and low nonlinearity (<0.1%). The tri-axis digital accelerometer with serial ports is more valuable than the previous works with large commercial instruments.

Effects of fast x-ray cone-beam tomographic measurement on dimensional metrology

X-ray computed tomography (XCT) is increasingly used for dimensional metrology, where it can offer accurate measurements of internal features that are not accessible with other techniques. However, XCT scanning can be relatively slow, which often prevents routine uptake for many applications. This paper explores the feasibility of improving the speed of XCT measurements while maintaining the quality of the dimensional measurements derived from reconstructed volumes. In particular, we compare two approaches to fast XCT acquisition, the use of fewer XCT projections as well as the use of shortened x-ray exposure times for each projection. The study shows that the additional Poisson noise produced by reducing the exposure for each projection has significantly less impact on dimensional measurements compared to the artefacts associated with strategies that take fewer projection images, leading to about half the measurement error variability. Advanced reconstruction algorithms such as the conjugate gradient least squares method or total variation constrained approaches, are shown to allow further improvements in measurement speed, though this can come at the cost of increased measurement bias (e.g. 2.8% increase in relative error in one example) and variance (e.g. 25% in the same example).

Integrating Bifactor Models into a Generalizability Theory Based Structural Equation Modeling Framework

Although generalizability theory (GT) designs have traditionally been analyzed within an ANOVA framework, identical results can be obtained with structural equation models (SEMs) but extended to represent multiple sources of both systematic and measurement error variance, include estimation methods less likely to produce negative variance components, and correct for score coarseness. In research reported here, we integrated principles of bifactor modeling into a GT-SEM framework to partition systematic variance for subscale and composite scores into general and group factor effects and measurement error into multiple components. GT-bifactor modeling allowed for partitioning of variance at different levels of aggregation, clearer definitions of constructs within sampled domains, extended indices of score consistency, insights into composite and subscale score viability, and markers for best enhancing score consistency. Results for domain and facet scores from the recently updated form of the Big Five Inventory highlighted the importance of taking all sources of measurement error into account and the diagnostic benefits of GT-bifactor designs over conventional univariate and multivariate GT designs. Findings further revealed that corrections for scale coarseness noticeably enhanced overall score consistency by reducing specific-factor and random-response measurement error. We provide code in R for applying all illustrated designs in a detailed online supplement.

The reliability of students’ earnings expectations

The elicitation of subjective expectations in surveys has gained significant interest in economics. Students’ earnings expectations have been widely used to model school and occupational choices, but quantification of the reliability of this variable has not yet been done. To what extent are earnings expectations affected by random measurement error? To assess this issue, in this paper we use different waves of a survey carried out in a Spanish university eliciting the earnings expectations of economics students. A test-retest method is applied with different time spans between the first wave and subsequent repetitions of the survey: two weeks and two and a half months later. A significant number of students declared large differences in earnings expectations, even in the case where the time span between surveys was short. Apart from the reliability, we also provide an estimate of the measurement error variance. With this information we show how a sensitivity analysis can be performed in external earnings expectations data research.

Partitioning Variance for a Within-Level Predictor in Multilevel Models

Multilevel modeling (MLM) is widely used for the multilevel data structure in social science. Two MLM limitations involve partitioning variance for a within-level predictor. First, MLM does not automatically partial out the between-level variance for a within-level predictor. Second, MLM assumes a within-level predictor to be measurement-error free. Thus, the error variance cannot be separated out. The study evaluated the impact of improperly partitioning two-level variances and measurement error variances for a within-level predictor in MLM. Our findings suggested (a) whether the research interest lies in a within-level or a between-level predictor, group-mean centering or latent-mean centering must be used to partition two-level variances; (b) for the measurement error variance, the within-level factor loadings should be as high as possible (≥0.80 in our simulation settings). If these two requirements are not met, multilevel structural equation modeling (MSEM) should always be adopted for the analysis.

An R-Estimator in the Errors in Variables Linear Regression Model

This note develops an R estimator of the regression parameters in the errors in variables linear regression model, when the distributions of the vectors of covariates and measurement errors are known. The paper also contains the proof of the asymptotic uniform linearity of a sequence of a simple linear rank statistics based on the residuals of a class of nonlinear parametric regression models where covariates and regression errors are possibly dependent. This result in turn facilitates the proof of the asymptotic normality of the above mentioned R estimator in the errors in variables linear regression model. The Pitman’s asymptotic relative efficiency of this R estimator relative to the bias corrected least squares estimator is shown to increase to infinity as the measurement error variance increases to infinity at some Gaussian errors and covariate distributions.

Value added in hierarchical linear mixed models with error in variables

In this paper, we propose a methodology to evaluate the effects on the value-added estimators when there is a measurement error in variables. These errors lead to biased estimators; in most cases, these estimators have a large variance. The proposed methodology is illustrated under two scenarios: First, simulation studies for discussing the effects on value-added estimates for some values of reliability. Second, an application for real data using a Colombian database that contains the scores of two standardized tests: Saber 11 and Saber Pro. In the first test, the students are evaluated in the 11th grade of high school. In the second test, the students are evaluated in the last two years of the undergraduate program. We also implement the estimation method taking into account measurement error and adapt the Bootstrap procedure to Hierarchical Linear Mixed Model with error in variables. The results show that measurement error affects the higher-education value-added and the estimator variance. This implies universities can be incorrectly classified. Therefore, we may assert that any given university is contributing to students’ progress when, in reality, this is not so.

Residual life estimation of lithium-ion batteries based on nonlinear Wiener process with measurement error

Residual life (RL) estimation is a key issue in the prognostics and health management (PHM). This paper proposes a heuristic algorithm for RL estimation based on the nonlinear Wiener process with measurement error (ME) and also proposes an unbiased parameters estimation method. First, we use the nonlinear Wiener process with ME to model the degradation process. Then, an analytical expression of parameters estimation results with restriction of the nonlinear coefficient and variance of ME is obtained and an unbiased parameters estimation method is also derived by analyzing the natures of parameters estimation. Moreover, an empirical unbiased parameters estimation method for the degradation data with different measurement times is also proposed. After that, we extend the heuristic algorithm to the nonlinear Wiener process with ME and some relevant conclusions are proved. Finally, some simulation examples and a case study of lithium-ion batteries are used for experimental verification. The results show that the unbiased parameters estimation method is superior to the traditional maximum likelihood estimation (MLE) method and the heuristic RL estimation method can overcome the influence of imperfect prior information for lithium-ion batteries based on the nonlinear Wiener process with ME.

A quantitative genetics perspective on the body-mass scaling of metabolic rate

Widely observed allometric scaling (log-log slope<1) of metabolic rate (MR) with body mass (BM) in animals has been frequently explained using functional mechanisms, but rarely studied from the perspective of multivariate quantitative genetics. This is unfortunate, given that the additive genetic slope (bA) of the MR-BM relationship represents the orientation of the 'line of least genetic resistance' along which MR and BM may most likely evolve. Here, we calculated bA in eight species. Although most bA values were within the range of metabolic scaling exponents reported in the literature, uncertainty of each bA estimate was large (only one bA was significantly lower than 3/4 and none were significantly different from 2/3). Overall, the weighted average for bA (0.667±0.098 95% CI) is consistent with the frequent observation that metabolic scaling exponents are negatively allometric in animals (b<1). Although bA was significantly positively correlated with the phenotypic scaling exponent (bP) across the sampled species, bP was usually lower than bA, as reflected in a (non-significantly) lower weighted average for bP (0.596±0.100). This apparent discrepancy between bA and bP resulted from relatively shallow MR-BM scaling of the residuals [weighted average residual scaling exponent (be)=0.503±0.128], suggesting regression dilution (owing to measurement error and within-individual variance) causing a downward bias in bP. Our study shows how the quantification of the genetic scaling exponent informs us about potential constraints on the correlated evolution of MR and BM, and by doing so has the potential to bridge the gap between micro- and macro-evolutionary studies of scaling allometry.

Accounting for analytical and proximal soil sensing errors in digital soil mapping

AbstractDigital soil mapping (DSM) approaches provide soil information by utilising the relationship between soil properties and environmental variables. Calibration of DSM models requires measurements that may often have substantial measurement errors which propagate to the DSM outputs and need to be accounted for. This study applied a geostatistical‐based DSM approach that incorporates measurement error variances in the covariance structure of the spatial model, weights measurements in accordance with their measurement accuracies and assesses the effects of measurement errors on the accuracies of DSM outputs. The method was applied in the Western Cameroon, where soil samples from 480 locations were collected and analysed for pH, clay and soil organic carbon (SOC) using conventional and mid‐infrared spectroscopy methods. Variogram parameters and regression coefficients were estimated using residual maximum likelihood under two scenarios: with and without taking measurement errors into account. Performance of the spatial models in the two scenarios was compared using validation metrics obtained with three types of cross‐validation. Acknowledging measurement errors impacted the regression coefficients and influenced the variogram parameters by reducing the nugget and sill variance for the three soil properties. Validation metrics including mean error, root mean square error and model efficiency coefficient were quite similar in both scenarios, but the prediction uncertainties were more realistically quantified by the models that account for measurement errors, as indicated by accuracy plots. There were relatively small absolute differences in predicted values of soil properties of up to 0.1 for pH, 1.6% for clay and 2 g/kg for SOC between the two scenarios. We emphasised the need of incorporating measurement errors in DSM approaches to improve uncertainty quantification, particularly when applying spectroscopy for estimating soil properties. Further development of the approach is the extension to non‐linear machine learning regression methods.Highlights Errors in soil measurements are usually not accounted for and may affect DSM results. Measurement error variances were incorporated in the geostatistical models of three soil properties. Quantifying measurement errors in DSM allows to weigh measurements in accordance with their accuracy. Accounting for measurement errors in DSM better assesses prediction accuracy.

Efficient Identification of Multiple Parameter Errors in Power Grids by Mixed-Effects Models and Generalized Least Squares

Accurate knowledge of static parameters forms the basis for nearly all applications in the energy management system. This paper proposes an efficient method for the simultaneous identification and correction of multiple network parameter errors based on a linear mixed-effects (LME) model and the generalized least squares (GLS) method. An LME model for parameter error identification is formulated using the residual equations of multiple-snapshot state estimation with equality constraints. The parameter errors are considered as the fixed effects and the measurement errors are considered as the random effects. Then, using the measurement error variances estimated by the LME model, the GLS method is used to estimate the parameter errors along with a hypothesis testing to infer whether each parameter error is zero. The semi-supervised adversarial autoencoder is used for bad data detection in the presence of erroneous parameters and limited labels such that only measurement snapshots that are free of any bad data are used. The proposed methodology is efficient in that the LME model is only used to estimate the variances of the measurement errors using a small number of measurement snapshots, therefore the huge computation burden needed to solve a large-scale LME model is avoided. In addition, the GLS only involves inversion of low-dimension matrices, which is very efficient even a large number of measurement snapshots are used. Thorough tests of the proposed methodology on a large number of scenarios are provided to show the effectiveness of the proposed methodology with promising results.

Attribute Sentiment Scoring with Online Text Reviews: Accounting for Language Structure and Missing Attributes

The authors address two significant challenges in using online text reviews to obtain fine-grained, attribute-level sentiment ratings. First, in contrast to methods that rely on word frequency, they develop a deep learning convolutional–long short-term memory hybrid model to account for language structure. The convolutional layer accounts for spatial structure (adjacent word groups or phrases), and long short-term memory accounts for the sequential structure of language (sentiment distributed and modified across nonadjacent phrases). Second, they address the problem of missing attributes in text when constructing attribute sentiment scores, as reviewers write about only a subset of attributes and remain silent on others. They develop a model-based imputation strategy using a structural model of heterogeneous rating behavior. Using Yelp restaurant review data, they show superior attribute sentiment scoring accuracy with their model. They identify three reviewer segments with different motivations: status seeking, altruism/want voice, and need to vent/praise. Surprisingly, attribute mentions in reviews are driven by the need to inform and vent/praise rather than by attribute importance. The heterogeneous model-based imputation performs better than other common imputations and, importantly, leads to managerially significant corrections in restaurant attribute ratings. More broadly, the results suggest that social science research should pay more attention to reducing measurement error in variables constructed from text.

Measurement Invariance of Negative Affect in Ambulatory Assessments of Young-Old and Old-Old Adults

Gero-psychological research increasingly considered intense longitudinal assessments of momentary affect to address affective aging. In particular, many studies employed negative emotion item lists for ambulatory assessments of negative affect. However, frequent self-reports on emotion items within short time intervals might change alertness towards and perception of one’s emotional experiences. From an item-response-theoretic point of view, this might impair the stability of item functioning in terms of item discrimination between levels of affectivity and item severity (difficulty). Thus, we examined measurement invariance of negative emotion items commonly used for ambulatory assessments of negative affect. Ambulatory assessments from the EMIL study, obtained over seven consecutive days at six occasions per day from 123 young-old (aged 66-69) and 47 old-old (86-89) adults, were analyzed. Respondents self-reported on 13 negative emotion items, using a 0-100 slider to express the degree to which they felt the respective emotion. We ran multilevel structural equation models with Bayes estimation to analyze variability of negative affect factor loadings, item intercepts, and measurement error variances across repeated measures, thus checking for metric, scalar, and strict factorial invariance. For all sets of parameters, the findings do not strongly support measurement invariance, but point at partial invariance for item subsets. Taking on literature suggesting that criteria for invariance testing should not be too restrictive to meet pragmatic measurement equivalence requirements, further analyses and our conclusions focus on strategies that might allow for acceptable degrees of differential item functioning, enabling reliable analyses of intra-individual short-term variability in negative affect.

Measurement error-filtered machine learning in digital soil mapping

This paper presents a two-stage maximum likelihood framework to deal with measurement errors in digital soil mapping (DSM) when using a machine learning (ML) model. The framework is implemented with random forest and projection pursuit regression to illustrate two different areas of machine learning, i.e. ensemble learning with trees and feature-learning. In our proposed framework, a measurement error variance (MEV) is incorporated as a weight in the log-likelihood function so that measurements with a larger MEV receive less weight when a ML model is calibrated. We evaluate the performance of the error-filtered ML models with an error-filtered regression kriging model, in a comprehensive simulation study and in a real-world case study of Namibian data. From the results we show that prediction accuracy can be increased by using our proposed framework, especially when the MEVs are large and heterogeneous.

Sensitivity analysis for random measurement error using regression calibration and simulation-extrapolation.

Sensitivity analysis for random measurement error can be applied in the absence of validation data by means of regression calibration and simulation-extrapolation. These have not been compared for this purpose. A simulation study was conducted comparing the performance of regression calibration and simulation-extrapolation for linear and logistic regression. The performance of the two methods was evaluated in terms of bias, mean squared error (MSE) and confidence interval coverage, for various values of reliability of the error-prone measurement (0.05-0.91), sample size (125-4000), number of replicates (2-10), and R-squared (0.03-0.75). It was assumed that no validation data were available about the error-free measures, while correct information about the measurement error variance was available. Regression calibration was unbiased while simulation-extrapolation was biased: median bias was 0.8% (interquartile range (IQR): -0.6;1.7%), and -19.0% (IQR: -46.4;-12.4%), respectively. A small gain in efficiency was observed for simulation-extrapolation (median MSE: 0.005, IQR: 0.004;0.006) versus regression calibration (median MSE: 0.006, IQR: 0.005;0.009). Confidence interval coverage was at the nominal level of 95% for regression calibration, and smaller than 95% for simulation-extrapolation (median coverage: 85%, IQR: 73;93%). The application of regression calibration and simulation-extrapolation for a sensitivity analysis was illustrated using an example of blood pressure and kidney function. Our results support the use of regression calibration over simulation-extrapolation for sensitivity analysis for random measurement error.

Crown-rump length measurement error: impact on assessment of growth.

To examine the impact of first-trimester crown-rump length (CRL) measurement error on the interpretation of estimated fetal weight (EFW) and classification of fetuses as small-, large- or appropriate-for-gestational age on subsequent growth scans. We examined the effects of errors of ± 2, ± 3 and ± 4 mm in the measurement of fetal CRL on percentiles of EFW at 20, 32 and 36 weeks' gestation and classification as small-, large- or appropriate-for-gestational age. Published data on CRL measurement error were used to determine variation present in practice. A measurement error of -2 mm in first-trimester CRL shifts an EFW on the 10th percentile at the 20-week scan to around the 20th percentile, and the effect of a CRL measurement error of + 2 mm would shift an EFW on the 10th percentile to around the 5th percentile. At 32 weeks, a first-trimester CRL measurement error would shift an EFW on the 10th percentile to the 7th (+ 2 mm) or 14th (-2 mm) percentile; at 36 weeks, the EFW would shift from the 10th percentile to the 8th (+ 2 mm) or 12th (-2 mm) percentile. Published data suggest that measurement errors of 2 mm or more are common in practice. Because of the widespread and potentially severe consequences of CRL measurement errors as small as 2 mm on clinical assessment, patient management and research results, there is a need to increase awareness of the impact of CRL measurement error and to reduce measurement error variation through standardization and quality control. © 2021 International Society of Ultrasound in Obstetrics and Gynecology.

A partitioning strategy for improved state estimation performance in ill-conditioned power systems with hybrid measurement set

Considering the increase in power system size and the number of PMUs, the utilization of a computationally efficient yet accurate static state estimator is crucial. The fast-decoupled WLS estimator (FD-WLS) is the most common method employed in industrial applications, thanks to its computational efficiency and ease of implementation. However, it is known that FD-WLS fails in the presence of an ill-conditioned power system, e.g., a power system with high R/X ratio and large difference between measurement error variances. This paper proposes a partitioning strategy for ill-conditioned power systems. The proposed method forms two types of sub-systems, such that one can apply FD-WLS in the type-1 sub-systems, and conventional formulation of WLS should be applied in the type-2 sub-systems. The utilization of the proposed method enables a computational performance comparable to that of FD-WLS and an accuracy comparable to that of the centralized solution.

Beta regression model nonlinear in the parameters with additive measurement errors in variables.

We propose in this paper a general class of nonlinear beta regression models with measurement errors. The motivation for proposing this model arose from a real problem we shall discuss here. The application concerns a usual oil refinery process where the main covariate is the concentration of a typically measured in error reagent and the response is a catalyst’s percentage of crystallinity involved in the process. Such data have been modeled by nonlinear beta and simplex regression models. Here we propose a nonlinear beta model with the possibility of the chemical reagent concentration being measured with error. The model parameters are estimated by different methods. We perform Monte Carlo simulations aiming to evaluate the performance of point and interval estimators of the model parameters. Both results of simulations and the application favors the method of estimation by maximum pseudo-likelihood approximation.