Measurement Error In Independent Variables Research Articles

Uncertainties in above ground tree biomass estimation

Models of above-ground tree biomass have been widely used to estimate forest biomass using national forest inventory data. However, many sources of uncertainty affect above-ground biomass estimation and are challenging to assess. In this study, the uncertainties associated with the measurement error in independent variables (diameter at breast height, tree height), residual variability, variances of the parameter estimates, and the sampling variability of national inventory data are estimated for five above-ground biomass models. The results show sampling variability is the most significant source of uncertainty. The measurement error and residual variability have negligible effects on forests above-ground biomass estimations. Thus, a reduction in the uncertainty of the sampling variability has the greatest potential to decrease the overall uncertainty. The power model containing only the diameter at breast height has the smallest uncertainty. The findings of this study provide suggestions to achieve a trade-off between accuracy and cost for above-ground biomass estimation using field work.

Exact finite-sample bias and MSE reduction in a simple linear regression model with measurement error

This paper deals with the problem of estimating a slope parameter in a simple linear regression model, where independent variables have functional measurement errors. Measurement errors in independent variables, as is well known, cause biasedness of the ordinary least squares estimator. A general procedure for the bias reduction is presented in a finite sample situation, and some exact bias-reduced estimators are proposed. Also, it is shown that certain truncation procedures improve the mean square errors of the ordinary least squares and the bias-reduced estimators.

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

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

Measurement error and outcome distributions: Methodological issues in regression analyses of behavioral coding data.

Behavioral coding is increasingly used for studying mechanisms of change in psychosocial treatments for substance use disorders (SUDs). However, behavioral coding data typically include features that can be problematic in regression analyses, including measurement error in independent variables, non normal distributions of count outcome variables, and conflation of predictor and outcome variables with third variables, such as session length. Methodological research in econometrics has shown that these issues can lead to biased parameter estimates, inaccurate standard errors, and increased Type I and Type II error rates, yet these statistical issues are not widely known within SUD treatment research, or more generally, within psychotherapy coding research. Using minimally technical language intended for a broad audience of SUD treatment researchers, the present paper illustrates the nature in which these data issues are problematic. We draw on real-world data and simulation-based examples to illustrate how these data features can bias estimation of parameters and interpretation of models. A weighted negative binomial regression is introduced as an alternative to ordinary linear regression that appropriately addresses the data characteristics common to SUD treatment behavioral coding data. We conclude by demonstrating how to use and interpret these models with data from a study of motivational interviewing. SPSS and R syntax for weighted negative binomial regression models is included in online supplemental materials.

Analyzing the Relationship between Dependent and Independent Variables in Marketing: A Comparison of Multiple Regression with Path Analysis

Multiple regression models continue to be widely used in marketing. Within the regression framework, researchers have to grapple with and resolve several contentious issues. For example, multicollinearity, non simultaneous estimation of parameters, inherent measurement error in independent variables, absence of overall goodness of fit indices, and lack of compelling guidelines for adding and deleting model variables are some common estimation problems associated with this method. In the absence of universally acceptable guidelines, researchers often use judgment calls to deal with these issues. Employing ad-hoc approaches, in turn, compromises the potential usefulness of multiple regression models. In this paper, we position path analysis as a competing technique that can address in a relatively unambiguous way, many of the above mentioned limitations of multiple regression. We illustrate the superiority of path analysis by reanalyzing data from selected marketing studies that have used multiple regression models. To enable researchers use path analysis more frequently, we provide a technical appendix depicting use of the EQS software for re-estimating multiple regression models. We discuss several implications of our results and outline avenues for future research.

Analysis of associations with change in a multivariate outcome variable when baseline is subject to measurement error.

A simple general algorithm is described for correcting for bias caused by measurement error in independent variables in multivariate linear regression. This algorithm, using standard software, is then applied to several approaches to the analysis of change from baseline as a function of baseline value of the outcome measure plus other covariates, any of which might have measurement error. The algorithm may also be used when the independent variables differ by component of the multivariate independent variable. Simulations indicate that under various conditions bias is much reduced, as is mean squared error, and coverage of 95 per cent confidence intervals is good.

PMA7: CONTROLLING FOR BIASES FROM MEASUREMENT ERRORS IN HEALTH OUTCOMES RESEARCH USING STRUCTURAL EQUATION MODELING

OBJECTIVES: Measurement errors in independent variables may lead to attenuated estimates of their effects and may contaminate estimates for other covariates in conventional linear regression models (LRM). However, the direction and magnitude of these biases are difficult to determine theoretically. Measurement error is a serious problem in health services research as health status is a latent variable that can only be measured with error using proxy variables. This study empirically evaluated the validity of LRM models in health outcomes research. METHODS: SEMs with a latent health construct are proposed and compared with LRM models to examine the bias of measurement errors in general health status using data from a study of the impact of pharmacist's consultation on both health outcomes and costs (KP/USC study). Perceived health status at a given time point was modeled as a latent variable measured by the multiple scales of the SF-36. RESULTS: The latent health construct with multiple scales of the SF-36 and its SEMs for health outcomes and costs are empirically supported by the KP/USC data. SEM estimations of the latent health construct in both the measurement model and the structural model were all statistically significant with expected signs. As predicted, LRM estimates for the SF-36 scales were attenuated. However, there is no strong evidence that LRM estimations of treatment effect were contaminated by the measurement errors in the SF-36 or that the simultaneity between health outcomes and costs. CONCLUSIONS: Measurement errors in health status variables may result in attenuated estimates of health status effects on patient outcomes. Fortunately, careful study design can eliminate the contamination of treatment effect estimates due to errors in measuring health status. Moreover, SEM methods can be used to control both attenuation and resonation biases.

Estimation methods for male labor supply functions How to take account of nonlinear taxes

Nonlinear taxes create econometric difficulties when estimating labor supply functions. One estimation method that tackles these problems accounts for the complete form of the budget constraint and uses the maximum likelihood method to estimate parameters. Another method linearizes budget constraints and uses instrumental variables techniques. Using Monte Carlo simulations I investigate the small-sample properties of these estimation methods and how they are affected by measurement errors in independent variables. No estimator is uniquely best. Hence, in actual estimation the choice of estimator should depend on the sample size and type of measurement errors in the data. Complementing actual estimates with a Monte Carlo study of the estimator used, given the type of measurement errors that characterize the data, would often help interpreting the estimates. This paper shows how such a study can be performed.

Reducing Bias in Estimates of Linear Models by Remeasurement of a Random Subsample

Measurement error in independent variables produces biased estimates of the coefficients in linear models. These biases can be reduced by obtaining repeated measurements of the variables and then estimating structural equation models with multiple indicators of latent variables. Remeasurement is usually costly, however, raising the question of whether the same benefits can be obtained by remeasuring only a fraction of the sample. Although this strategy has been tried previously, there were no appropriate statistical methods for combining the data in the remeasured subsample and the single measurement subsample. We demonstrate here how recently developed methods for incomplete data provide an attractive solution to this estimation problem. The methodology is illustrated by a reanalysis of Bielby, Hauser, and Featherman's (1977a) study of the OCG-II data.

The distance from the equator as an instrumental variable

To attack the problem of measurement errors in independent variables, the distance from the equator is used as an instrumental variable for per capita income. Application of this idea to the estimation of a demand system from the cross-country data of Kravis et al. (1982) yields promising results.

An empirical investigation of alternative approaches to estimating the equilibrium demand for housing

Two approaches to estimating the desired or equilibrium housing demand parameters have been utilized in recent literature. One approach, commonly referred to as the conventional model, assumes that households continuously consume their temporal equilibrium housing services, where a temporal equilibrium is defined with respect to the household’s current economic and demographic characteristics. Based upon this assumption, conventional demand studies have employed random samples which include a majority of households that have not recently moved. (See Lee and Kong [6] or Carliner [2].) A problem with this approach is its failure to recognize moving costs households must pay to alter their housing service consumption. The existence of moving costs suggests that households may not respond rapidly to changes in their desired consumption of housing, but instead remain in their dwelling unit until the cost incurred from consuming the non-equilibrium level of services exceeds the cost of relocating. If so, demand samples employed in conventional studies may include a significant number of disequilibrium observations. This causes two problems. First, there exist measurement errors in independent variables that have changed since the household was last in equilibrium. Second, the true equilibrium effect of an independent variable may be incorrectly estimated due to its correlation with either the occurrence of disequilibrium or the length of the housing adjustment lag. The second approach to estimating the equilibrium parameters attempts to minimize these problems by restricting the sample to households that have recently moved. (See Hanushek and Quigley [3] or Aaron [l].)