Multiplicative Measurement Errors Research Articles

Some Variations on Standard Income Measurement Error Models

Measurement error can have a significant impact on measures of inequality. Using a fairly flexible parametric specification of an independent multiplicative measurement error (IMME) model we explore the relationship between changes in the variance of measurement error, for a given mean of measurement error, on the Gini Coefficient. While the measured Gini is greater than the true Gini, the difference decreases as the variance of measurement error decreases. Copulas are used to relax the assumption of independence of measurement error and true income. In this case the measured Gini can be larger or smaller than the true Gini, depending on the correlation between true income and measurement error. Using the same approach with simulations the effect of a different distribution of measurement error is investigated.

Household Labor Supply and Welfare Participation in Sweden

Using a sample of Swedish households, we estimate a household labor supply model assuming that preferences for consumption and leisure can be described by a direct translog utility function. The labor supply and welfare participation decisions are treated as a discrete choice problem, and we assume that these choices follow a simple conditional logit rule. In addition, we allow unobserved individual- specific effects to be correlated across alternatives. We assume that these unobserved effects are drawn from a discrete distribution, and the correlation across alternatives is modeled using factor-loading techniques. Classification error in hours is allowed for by using a multiplicative measurement error specification. The estimates from the structural model yield inelastic labor supply among husbands and positive wage elasticity for wives. Further, the cross elasticities are close to zero.

A time-scale decomposition approach to measurement-based admission control

We propose a time-scale decomposition approach to measurement-based admission control (MBAC). We identify a critical time scale, T/spl tilde//sub h/, such that: 1) aggregate traffic fluctuations slower than T/spl tilde//sub h/ can be tracked by the admission controller and compensated for by flow admissions and departures; 2) fluctuations faster than T/spl tilde//sub h/ have to be absorbed by reserving spare bandwidth on the link. The critical time scale is shown to scale as T/sub h///spl radic/n, where T/sub h/ is the average flow duration and n is the size of the link in terms of the number of flows it can carry. An MBAC design is presented which filters aggregate measurements into low- and high-frequency components separated at the cutoff frequency, 1/T/spl tilde//sub h/, using the low-frequency component to track slow time-scale traffic fluctuations and the high-frequency component to estimate the spare bandwidth needed. Our analysis shows that the scheme achieves high utilization and is robust to traffic heterogeneity, multiple time-scale fluctuations and measurement errors. The scheme uses only measurements of aggregate bandwidth and does not need to keep track of per-flow information.

Measurement Error and the Distribution of Income

Measurement error can impact estimator precision, obscure estimated relationships between variables, and distort the estimated inter-temporal behaviour of important economic characteristics. A model for measurement error is presented, based on the common assumption that measured income is the product of true income and multiplicative measurement error which is distributed independently of the level of true income. Flexible parametric forms are utilized to model the distributions of true income (generalized gamma) and measurement error (inversed generalized gamma). The corresponding probability density of measures income is shown to be a generalized beta of the second kind (GB2) which can be estimated using MLE. An identification problem is solved with additional information as to the average function of true income reported. The procedure is applied to income data from several Latin American economies. It is found, in some cases, that true and measured income inequality move in opposite directions over time. This finding has important implications for the evaluation of policies designed to affect relative equality in the distribution of income and underscores the importance of obtaining accurate data.

On the potential of measurement error to induce differential bias on odds ratio estimates: an example from radon epidemiology.

It is well established that odds ratios estimated by logistic regression are subject to bias if exposure is measured with error. The dependence of this bias on exposure parameter values, particularly for multiplicative measurement error, and its implications in epidemiology are not, however, as fully acknowledged. We have been motivated by a German West case-control study on lung cancer and residential radon, where restriction to a subgroup exhibiting larger mean and variance of exposure than the entire group has shown higher odds ratio estimates as compared to the full analysis. By means of correction formulae and simulations, we show that bias from additive classical type error depends on the exposure variance, not on the exposure mean, and that bias from multiplicative classical type error depends on the geometric standard deviation (in other words on the coefficient of variation of exposure), but not on the geometric mean of exposure. Bias from additive or multiplicative Berkson type error is independent of exposure distribution parameters. This indicates that there is a potential of differential bias between groups where these parameters vary. Such groups are commonly compared in epidemiology: for example when the results of subgroup analyses are contrasted or meta-analyses are performed. For the German West radon study, we show that the difference of measurement error bias between the subgroup and the entire group exhibits the same direction but not the same dimension as the observed results. Regarding meta-analysis of five European radon studies, we find that a study such as this German study will necessarily result in smaller odds ratio estimates than other studies due to the smaller exposure variance and coefficient of variation of exposure. Therefore, disregard of measurement error can not only lead to biased estimates, but also to inconsistent results and wrongly concluded effect differences between groups.

Thyroid Cancer Following Scalp Irradiation: A Reanalysis Accounting for Uncertainty in Dosimetry

In the 1940s and 1950s, over 20,000 children in Israel were treated for tinea capitis (scalp ringworm) by irradiation to induce epilation. Follow-up studies showed that the radiation exposure was associated with the development of malignant thyroid neoplasms. Despite this clear evidence of an effect, the magnitude of the dose-response relationship is much less clear because of probable errors in individual estimates of dose to the thyroid gland. Such errors have the potential to bias dose-response estimation, a potential that was not widely appreciated at the time of the original analyses. We revisit this issue, describing in detail how errors in dosimetry might occur, and we develop a new dose-response model that takes the uncertainties of the dosimetry into account. Our model for the uncertainty in dosimetry is a complex and new variant of the classical multiplicative Berkson error model, having components of classical multiplicative measurement error as well as missing data. Analysis of the tinea capitis data suggests that measurement error in the dosimetry has only a negligible effect on dose-response estimation and inference as well as on the modifying effect of age at exposure.

On a repeated-measurement model with errors in dependent variable

The model in this paper is motivated by a study of the effectiveness of pulsed electromagnetic field energy on healing of wounds, in which the wound Sizes zyrat time t for subject j under treatment i were observed with error, The healed wound size Yyt, defined by" z[d], is modeled as tne dependent variable in a repeated-measurement model. Two classical measurement error models relating the observed proxy wound size z* ijtand the true wound size zijtare considered:additive and multiplicative measurement error models. In this paper, we propose estimates of variance parameters, including the variance of the measurement error, via the method of moments when the dependent variable yijtis erroneously measured due to the measurement error in zijt. The proposed estimates of variance parameters are shown to be consistent and perform well in the simulation.

Evaluating the Reliability of Predictive Control of Product Parameters

The reliability of predictive control of product parameters in the presence of additive and multiplicative measurement errors is evaluated.

Polynomial Regression and Estimating Functions in the Presence of Multiplicative Measurement Error

Summary We consider the polynomial regression model in the presence of multiplicative measurement error in the predictor. Two general methods are considered, with the methods differing in their assumptions about the distributions of the predictor and the measurement errors. Consistent parameter estimates and asymptotic standard errors are derived by using estimating equation theory. Diagnostics are presented for distinguishing additive and multiplicative measurement error. Data from a nutrition study are analysed by using the methods. The results from a simulation study are presented and the performances of the methods are compared.

A Detailed Evaluation of Adjustment Methods for Multiplicative Measurement Error in Linear Regression with Applications in Occupational Epidemiology

It is often appropriately assumed, based on both theoretical and empirical considerations, that airborne exposures in the workplace are lognormally distributed, and that a worker's mean exposure over a reference time period is a key predictor of subsequent adverse health effects for that worker. Unfortunately, it is generally impossible to accurately measure a worker's true mean exposure. We begin by introducing a familiar model for exposure that views this true mean, as well as logical surrogates for it, as lognormal random variables. In a more general context, we then consider the linear regression of a continuous health outcome on a lognormal predictor measured with multiplicative error. We discuss several candidate methods of adjusting for the measurement error to obtain consistent estimators of the true regression parameters. These methods include a simple correction of the ordinary least squares estimator based on the surrogate regression, the regression of the outcome on the covariates and on the conditional expectation of the true predictor given the observed surrogate, and a quasi-likelihood approach. By means of a simulation study, we compare the various methods for practical sample sizes and discuss important issues relevant to both estimation and inference. Finally, we illustrate promising adjustment strategies using actual lung function and dust exposure data on workers in the Dutch animal feed industry.

Effects of Multiple Determinacy and Measurement Error on Trait-Behavior and Behavior-Behavior Relations: An Integrated Conceptual Model

The relationship is demonstrated between two explanations for the attenuation of observed trait-behavior and behavior-behavior correlations: multiple determinacy, as explicated recently by Ahadi and Diener and by Strube, and measurement error, as discussed previously be Epstein, Ajzen, and others. The former pertains to multiple determinants of a behavior construct other than the trait of interest, whereas the latter pertains to multiple determinants of a behavior measure other than the behavior construct of interest. However, it is shown that in the two cases the fundamental psychometric principles involved are the same. Implications of this integrated conceptual perspective are explored with respect to the magnitude of observed trait-behavior and behavior-behavior correlations that should be expected under different circumstances, focusing particularly on the distinction between global and more narrowly defined traits.

Polynomial Regression and Estimation Function in the Presence of Multiplication Measurement Error, with Application to Nutrition

In this paper we consider the polynomial regression model in the presence of multiplicative measurement error in the predictor. Consistent parameter estimates and their associated standard errors are derived. Two general methods are considered, with the methods differing in their assumptions about the distributions of the predictor and the measurement errors. Data from a nutrition study are analyzed using the methods. Finally, the results from a simulation study are presented and the performances of the methods compared.

The role of arousal in the creation and control of the halo effect in attitude models

Within the framework of attitude theory, this study investigates the conditions under which the halo effect can be (a) created where none normally exists and (b) reduced or eliminated where it does occur. A laboratory experiment was conducted to induce physiological arousal as a mechanism for influencing halo. Using a spreading activation model of semantic memory to frame predictions, it was hypothesized and found that arousal produced a halo effect for positive beliefs, tended to reduce halo for negative beliefs, and eliminated halo (marginally) for all beliefs treated as an aggregate. The context for the study was attitudes toward blood donation. A total of 220 people participated in a fully randomized two-group posttest-only design with multiple covariates and measurement error taken into account explicitly. Theoretical and applied implications are discussed. © 1996 John Wiley & Sons, Inc.

A neural network preestimation filter for bad-data detection and identification in power system state estimation

Popular state estimation techniques in industry are mostly based on the weighted least squares (WLS) method and its derivatives. These estimators usually detect and identify multiple gross measurement errors by repeating a cycle of estimation-detection-elimination. It is rather time consuming for large systems. This paper presents a neural network preestimation filter to identify most forms of gross errors, including conforming bad data, in raw measurements before state estimation rather than afterwards. The proposed neural network model is trained to be a measurement estimator by using the correct measurements of typical system operating states. Once trained, the filter quickly identifies most forms of gross measurement errors simultaneously by comparing the square difference of the raw measurements and their corresponding estimated values with some given thresholds. System observability is maintained by replacing bad data with their reasonably accurate estimates. Using the proposed neural network preestimation filter, the efficiency of present state estimators is greatly improved. Results from several case studies are presented.

Prospective Analysis of Logistic Case-Control Studies

Abstract In a classical case-control study, Prentice and Pyke proposed to ignore the study design and instead base estimation and inference on a random sampling (i.e., prospective) formulation. We generalize this prospective formulation of case-control studies to include multiplicative models, stratification, missing data, measurement error, robustness, and other examples. The resulting estimators, which ignore the case-control study aspect and instead are based on a random-sampling formulation, are typically consistent for nonintercept parameters and are asymptotically normally distributed. We derive the resulting asymptotic covariance matrix of the parameter estimates. The covariance matrix obtained by ignoring the case-control sampling scheme and using prospective formulas instead is shown to be at worst asymptotically conservative and asymptotically correct in a variety of problems; a simple sufficient condition guaranteeing the latter is obtained.

Prospective Analysis of Logistic Case-Control Studies

Abstract In a classical case-control study, Prentice and Pyke proposed to ignore the study design and instead base estimation and inference on a random sampling (i.e., prospective) formulation. We generalize this prospective formulation of case-control studies to include multiplicative models, stratification, missing data, measurement error, robustness, and other examples. The resulting estimators, which ignore the case-control study aspect and instead are based on a random-sampling formulation, are typically consistent for nonintercept parameters and are asymptotically normally distributed. We derive the resulting asymptotic covariance matrix of the parameter estimates. The covariance matrix obtained by ignoring the case-control sampling scheme and using prospective formulas instead is shown to be at worst asymptotically conservative and asymptotically correct in a variety of problems; a simple sufficient condition guaranteeing the latter is obtained.

Optimum escapement computed using Ricker's spawner-recruit curve

The principal use of Ricker's curve is to predict the optimum number of fish allowed to escape the fishery and spawn. I suggest that the error-structure for Ricker's curve is often approximate lognormal recruitment, multiplicative normal measurement error for escapement, and additive normal measurement error for yield. Fitting Ricker's curve is an errors-in-covariates problem and I present a method which is approximately unbiased under this error-structure and can be readily adapted to other error-structures. I show that a bias arises when the usual method is used to compute optimum escapement and I present methods for reducing this bias and for computing the distribution of the estimated optimum escapement. The estimated optimum escapement is asymptotically normal but, in practice, has positive skew. The variance of the estimated optimum escapement may often be large for Pacific salmon and I show that the economic profit foregone by the fishery may be approximately proportional to this variance.

A method for determining the probability of special education eligibility

The current method for determining special education eligibility has three problems: (a) continuous variables (e.g., achievement, IQ) are artificially divided into dichotomous classes; (b) errors of measurement are not used in a meaningful way; and (c) multiple test scores are not combined to make decisions. A new method for calculating the probability that a student meets eligibility criteria is proposed. The new method avoids the distortion of dichotomous classification, uses multiple scores and measurement error in a meaningful manner, and promotes the accurate use of test data in eligibility decisions.