Impact Evaluation Using Analysis of Covariance With Error-Prone Covariates That Violate Surrogacy

2019 ◽  
Vol 43 (6) ◽  
pp. 335-369
Author(s):  
J. R. Lockwood ◽  
Daniel F. McCaffrey
Keyword(s):  
Measurement Error ◽  
Measurement Errors ◽  
Ordinary Least Squares ◽  
Analysis Of Covariance ◽  
Asymptotic Results ◽  
Teacher Effects ◽  
Intervention Effects ◽  
Ols Regression ◽  
Ancova Model

Background: Analysis of covariance (ANCOVA) is commonly used to adjust for potential confounders in observational studies of intervention effects. Measurement error in the covariates used in ANCOVA models can lead to inconsistent estimators of intervention effects. While errors-in-variables (EIV) regression can restore consistency, it requires surrogacy assumptions for the error-prone covariates that may be violated in practical settings. Objectives: The objectives of this article are (1) to derive asymptotic results for ANCOVA using EIV regression when measurement errors may not satisfy the standard surrogacy assumptions and (2) to demonstrate how these results can be used to explore the potential bias from ANCOVA models that either ignore measurement error by using ordinary least squares (OLS) regression or use EIV regression when its required assumptions do not hold. Results: The article derives asymptotic results for ANCOVA with error-prone covariates that cover a variety of cases relevant to applications. It then uses the results in a case study of choosing among ANCOVA model specifications for estimating teacher effects using longitudinal data from a large urban school system. It finds evidence that estimates of teacher effects computed using EIV regression may have smaller bias than estimates computed using OLS regression when the data available for adjusting for students’ prior achievement are limited.

Bias for Treatment Effect by Measurement Error in Pretest in ANCOVA Analysis

2022 ◽  
pp. 001316442110688
Author(s):  
Yasuo Miyazaki ◽  
Akihito Kamata ◽  
Kazuaki Uekawa ◽  
Yizhi Sun
Keyword(s):  
Measurement Error ◽  
Treatment Effect ◽  
Measurement Errors ◽  
Treatment Effects ◽  
Population Group ◽  
Analysis Of Covariance ◽  
Negative Effects ◽  
Ancova Model ◽  
Positive Treatment ◽  
True Scores

This paper investigated consequences of measurement error in the pretest on the estimate of the treatment effect in a pretest–posttest design with the analysis of covariance (ANCOVA) model, focusing on both the direction and magnitude of its bias. Some prior studies have examined the magnitude of the bias due to measurement error and suggested ways to correct it. However, none of them clarified how the direction of bias is affected by measurement error. This study analytically derived a formula for the asymptotic bias for the treatment effect. The derived formula is a function of the reliability of the pretest, the standardized population group mean difference for the pretest, and the correlation between pretest and posttest true scores. It revealed a concerning consequence of ignoring measurement errors in pretest scores: treatment effects could be overestimated or underestimated, and positive treatment effects can be estimated as negative effects in certain conditions. A simulation study was also conducted to verify the derived bias formula.

scholarly journals Evaluation of linear regression techniques for atmospheric applications: the importance of appropriate weighting

2018 ◽  
Vol 11 (2) ◽  
pp. 1233-1250 ◽  
Author(s):  
Cheng Wu ◽  
Jian Zhen Yu
Keyword(s):  
Measurement Error ◽  
Linear Regression ◽  
Measurement Uncertainty ◽  
Measurement Errors ◽  
Ordinary Least Squares ◽  
Pseudorandom Number Generator ◽  
Data Generation ◽  
Comparison Results ◽  
Deming Regression ◽  
Regression Techniques

Abstract. Linear regression techniques are widely used in atmospheric science, but they are often improperly applied due to lack of consideration or inappropriate handling of measurement uncertainty. In this work, numerical experiments are performed to evaluate the performance of five linear regression techniques, significantly extending previous works by Chu and Saylor. The five techniques are ordinary least squares (OLS), Deming regression (DR), orthogonal distance regression (ODR), weighted ODR (WODR), and York regression (YR). We first introduce a new data generation scheme that employs the Mersenne twister (MT) pseudorandom number generator. The numerical simulations are also improved by (a) refining the parameterization of nonlinear measurement uncertainties, (b) inclusion of a linear measurement uncertainty, and (c) inclusion of WODR for comparison. Results show that DR, WODR and YR produce an accurate slope, but the intercept by WODR and YR is overestimated and the degree of bias is more pronounced with a low R2 XY dataset. The importance of a properly weighting parameter λ in DR is investigated by sensitivity tests, and it is found that an improper λ in DR can lead to a bias in both the slope and intercept estimation. Because the λ calculation depends on the actual form of the measurement error, it is essential to determine the exact form of measurement error in the XY data during the measurement stage. If a priori error in one of the variables is unknown, or the measurement error described cannot be trusted, DR, WODR and YR can provide the least biases in slope and intercept among all tested regression techniques. For these reasons, DR, WODR and YR are recommended for atmospheric studies when both X and Y data have measurement errors. An Igor Pro-based program (Scatter Plot) was developed to facilitate the implementation of error-in-variables regressions.

Features of accumulation of amounts of measurement error

2017 ◽  
Vol 928 (10) ◽  
pp. 58-63 ◽  
Author(s):  
V.I. Salnikov
Keyword(s):  
Measurement Error ◽  
Confidence Interval ◽  
Normal Distribution ◽  
Confidence Level ◽  
Measurement Errors ◽  
Truncated Normal Distribution ◽  
Truncated Normal ◽  
The Law ◽  
Normal Law

The initial subject for study are consistent sums of the measurement errors. It is assumed that the latter are subject to the normal law, but with the limitation on the value of the marginal error Δpred = 2m. It is known that each amount ni corresponding to a confidence interval, which provides the value of the sum, is equal to zero. The paradox is that the probability of such an event is zero; therefore, it is impossible to determine the value ni of where the sum becomes zero. The article proposes to consider the event consisting in the fact that some amount of error will change value within 2m limits with a confidence level of 0,954. Within the group all the sums have a limit error. These tolerances are proposed to use for the discrepancies in geodesy instead of 2m*SQL(ni). The concept of “the law of the truncated normal distribution with Δpred = 2m” is suggested to be introduced.

scholarly journals Analysis of the System of Controlling Paid Parking Zones

2021 ◽  
Vol 13 (8) ◽  
pp. 4211
Author(s):  
Maciej Kozłowski ◽  
Andrzej Czerepicki ◽  
Piotr Jaskowski ◽  
Kamil Aniszewski
Keyword(s):  
Control System ◽  
Smart City ◽  
Measurement Errors ◽  
Fundamental Problem ◽  
Urban Traffic ◽  
Statistical Dependence ◽  
Actual State ◽  
Event Time ◽  
Operational Data

Urban traffic can be curbed in various ways, for instance, by introducing paid unguarded parking zones (PUPZ). The operational functionality of this system depends on whether or not the various system features used to document parking cases function properly, including those which enable positioning of vehicles parked in the PUPZ, recognition of plate numbers, event time recording, and the correct anonymisation of persons and other vehicles. The most fundamental problem of this system is its reliability, understood as the conformity of control results with the actual state of matters. This characteristic can be studied empirically, and this article addresses the methodology proposed for such an examination, discussed against a case study. The authors have analysed the statistical dependence of the e-control system’s measurement errors based on operational data. The results of this analysis confirm the rationale behind the deployment of the e-control system under the implementation of the smart city concept in Warsaw.

scholarly journals A Method for Assessing Threats to the Economic Security of a Region: A Case Study of Public Procurement in Russia

Risks ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 10
Author(s):  
Valentina Kravchenko ◽  
Tatiana Kudryavtseva ◽  
Yuriy Kuporov
Keyword(s):  
Regression Models ◽  
Public Procurement ◽  
Ordinary Least Squares ◽  
Economic Security ◽  
Government Procurement ◽  
Security Monitoring ◽  
Significant Relationships ◽  
Monitoring Tools ◽  
Russian Region

The issue of economic security is becoming an increasingly urgent one. The purpose of this article is to develop a method for assessing threats to the economic security of the Russian region. This method is based on step-by-step actions: first of all, choosing an element of the region’s economic security system and collecting its descriptive indicators; then grouping indicators by admittance-process-result categories and building hypotheses about their influence; testing hypotheses using a statistical package and choosing the most significant connections, which can pose a threat to the economic security of the region; thereafter ranking regions by the level of threats and developing further recommendations. The importance of this method is that with the help of grouping regions (territory of a country) based on proposed method, it is possible to develop individual economic security monitoring tools. As a result, the efficiency of that country’s region can be higher. In this work, the proposed method was tested in the framework of public procurement in Russia. A total of 14 indicators of procurement activity were collected for each region of the Russian Federation for the period from 2014 to 2018. Regression models were built on the basis of the grouped indicators. Ordinary Least Squares (OLS) Estimation was used. As a result of pairwise regression models analysis, we have defined four significant relationships between public procurement indicators. There are positive connections between contracts that require collateral and the percentage of tolerances, between the number of bidders and the number of regular suppliers, between the number of bidders and the average price drop, and between the number of purchases made from a single supplier and the number of contracts concluded without reduction. It was determined that the greatest risks for the system were associated with the connection between competition and budget savings. It was proposed to rank analyzed regions into four groups: ineffective government procurement, effective government procurement, and government procurement that threatens the system of economic security of the region, that is, high competition with low savings and low competition with high savings. Based on these groups, individual economic security monitoring tools can be developed for each region.

scholarly journals ON THE UNIFORM CONVERGENCE OF DECONVOLUTION ESTIMATORS FROM REPEATED MEASUREMENTS

2021 ◽  
pp. 1-22
Author(s):  
Daisuke Kurisu ◽  
Taisuke Otsu
Keyword(s):  
Multivariate Analysis ◽  
Measurement Error ◽  
Uniform Convergence ◽  
Measurement Errors ◽  
Convergence Rates ◽  
Free Variable ◽  
Error Model ◽  
Repeated Measurements ◽  
Empirical Characteristic Function ◽  
Measurement Error Model

This paper studies the uniform convergence rates of Li and Vuong’s (1998, Journal of Multivariate Analysis 65, 139–165; hereafter LV) nonparametric deconvolution estimator and its regularized version by Comte and Kappus (2015, Journal of Multivariate Analysis 140, 31–46) for the classical measurement error model, where repeated noisy measurements on the error-free variable of interest are available. In contrast to LV, our assumptions allow unbounded supports for the error-free variable and measurement errors. Compared to Bonhomme and Robin (2010, Review of Economic Studies 77, 491–533) specialized to the measurement error model, our assumptions do not require existence of the moment generating functions of the square and product of repeated measurements. Furthermore, by utilizing a maximal inequality for the multivariate normalized empirical characteristic function process, we derive uniform convergence rates that are faster than the ones derived in these papers under such weaker conditions.

Guidelines for choosing volume equations in the presence of measurement error in height

2000 ◽  
Vol 30 (2) ◽  
pp. 306-310 ◽  
Author(s):  
M S Williams ◽  
H T Schreuder
Keyword(s):  
Measurement Error ◽  
Tree Species ◽  
Measurement Errors ◽  
Tree Diameter ◽  
Total Height ◽  
Volume Equations

Assuming volume equations with multiplicative errors, we derive simple conditions for determining when measurement error in total height is large enough that only using tree diameter, rather than both diameter and height, is more reliable for predicting tree volumes. Based on data for different tree species of excurrent form, we conclude that measurement errors up to ±40% of the true height can be tolerated before inclusion of estimated height in volume prediction is no longer warranted.

scholarly journals An improved computational method to assess pituitary responsiveness to secretagogue stimuli

2002 ◽  
pp. 323-332 ◽  
Author(s):  
A Sartorio ◽  
G De Nicolao ◽  
D Liberati
Keyword(s):  
Measurement Error ◽  
Measurement Errors ◽  
Pituitary Hormones ◽  
Computational Method ◽  
Kinetics Parameters ◽  
Thyrotrophin Releasing Hormone ◽  
Deconvolution Analysis ◽  
Releasing Hormone ◽  
Sampling Protocols ◽  
Peak Value

OBJECTIVE: The quantitative assessment of gland responsiveness to exogenous stimuli is typically carried out using the peak value of the hormone concentrations in plasma, the area under its curve (AUC), or through deconvolution analysis. However, none of these methods is satisfactory, due to either sensitivity to measurement errors or various sources of bias. The objective was to introduce and validate an easy-to-compute responsiveness index, robust in the face of measurement errors and interindividual variability of kinetics parameters. DESIGN: The new method has been tested on responsiveness tests for the six pituitary hormones (using GH-releasing hormone, thyrotrophin-releasing hormone, gonadotrophin-releasing hormone and corticotrophin-releasing hormone as secretagogues), for a total of 174 tests. Hormone concentrations were assayed in six to eight samples between -30 min and 120 min from the stimulus. METHODS: An easy-to-compute direct formula has been worked out to assess the 'stimulated AUC', that is the part of the AUC of the response curve depending on the stimulus, as opposed to pre- and post-stimulus spontaneous secretion. The weights of the formula have been reported for the six pituitary hormones and some popular sampling protocols. RESULTS AND CONCLUSIONS: The new index is less sensitive to measurement error than the peak value. Moreover, it provides results that cannot be obtained from a simple scaling of either the peak value or the standard AUC. Future studies are needed to show whether the reduced sensitivity to measurement error and the proportionality to the amount of released hormone render the stimulated AUC indeed a valid alternative to the peak value for the diagnosis of the different pathophysiological states, such as, for instance, GH deficits.

Use of simulation–extrapolation estimation in catch–effort analyses

1999 ◽  
Vol 56 (7) ◽  
pp. 1234-1240
Author(s):  
W R Gould ◽  
L A Stefanski ◽  
K H Pollock
Keyword(s):  
Measurement Error ◽  
Measurement Errors ◽  
Mean Squared Error ◽  
Estimation Procedure ◽  
Bias Reduction ◽  
Estimation Methods ◽  
Effort Estimation ◽  
Stat Assoc ◽  
General Terms ◽  
Naive Estimator

All catch-effort estimation methods implicitly assume catch and effort are known quantities, whereas in many cases, they have been estimated and are subject to error. We evaluate the application of a simulation-based estimation procedure for measurement error models (J.R. Cook and L.A. Stefanski. 1994. J. Am. Stat. Assoc. 89: 1314-1328) in catch-effort studies. The technique involves a simulation component and an extrapolation step, hence the name SIMEX estimation. We describe SIMEX estimation in general terms and illustrate its use with applications to real and simulated catch and effort data. Correcting for measurement error with SIMEX estimation resulted in population size and catchability coefficient estimates that were substantially less than naive estimates, which ignored measurement errors in some cases. In a simulation of the procedure, we compared estimators from SIMEX with "naive" estimators that ignore measurement errors in catch and effort to determine the ability of SIMEX to produce bias-corrected estimates. The SIMEX estimators were less biased than the naive estimators but in some cases were also more variable. Despite the bias reduction, the SIMEX estimator had a larger mean squared error than the naive estimator for one of two artificial populations studied. However, our results suggest the SIMEX estimator may outperform the naive estimator in terms of bias and precision for larger populations.

scholarly journals The Effect of Random Error in Exposure Measurement upon the Shape of the Exposure Response

Dose-Response ◽  
2005 ◽  
Vol 3 (4) ◽  
pp. dose-response.0 ◽  
Author(s):  
Kenny S. Crump
Keyword(s):  
Measurement Error ◽  
Measurement Errors ◽  
Epidemiological Data ◽  
Epidemiological Studies ◽  
Random Errors ◽  
Exposure Measurement ◽  
Considerable Uncertainty ◽  
Exposure Response ◽  
Log Normal ◽  
Normally Distributed

Although statistical analyses of epidemiological data usually treat the exposure variable as being known without error, estimated exposures in epidemiological studies often involve considerable uncertainty. This paper investigates the theoretical effect of random errors in exposure measurement upon the observed shape of the exposure response. The model utilized assumes that true exposures are log-normally distributed, and multiplicative measurement errors are also log-normally distributed and independent of the true exposures. Under these conditions it is shown that whenever the true exposure response is proportional to exposure to a power r, the observed exposure response is proportional to exposure to a power K, where K < r. This implies that the observed exposure response exaggerates risk, and by arbitrarily large amounts, at sufficiently small exposures. It also follows that a truly linear exposure response will appear to be supra-linear—i.e., a linear function of exposure raised to the K-th power, where K is less than 1.0. These conclusions hold generally under the stated log-normal assumptions whenever there is any amount of measurement error, including, in particular, when the measurement error is unbiased either in the natural or log scales. Equations are provided that express the observed exposure response in terms of the parameters of the underlying log-normal distribution. A limited investigation suggests that these conclusions do not depend upon the log-normal assumptions, but hold more widely. Because of this problem, in addition to other problems in exposure measurement, shapes of exposure responses derived empirically from epidemiological data should be treated very cautiously. In particular, one should be cautious in concluding that the true exposure response is supra-linear on the basis of an observed supra-linear form.

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