Diagnosing Response Style Behavior by Means of a Latent-Class Factor Approach. Socio-Demographic Correlates of Gender Role Attitudes and Perceptions of Ethnic Discrimination Reexamined

It is generally accepted that response style behavior in survey research may seriously distort the measurement of attitudes and subsequent causal models that include attitudinal dimensions. However, there in no single accepted methodological approach in dealing with this issue. This article aims at illustrating the flexibility of a latent class factor approach in diagnosing response style behavior and in adjusting findings from causal models with latent variables. We present a substantive example from the Belgian MHSM research project on integration-related attitudes among ethnic minorities. We argue that an extreme response style can be detected in analyzing two independent sets of Likert-type questions referring to `gender roles' and `feelings of ethnic discrimination'. If the response style is taken into account the effect of covariates on attitudinal dimensions is more adequately estimated.     

Air pollution-mortality models: A demonstration of the effects of random measurement error

Errors of measurement have long been recognized as a chronic problem in statistical analysis. Although there is a vast statistical literature of multiple regression models estimating the air pollution-mortality relationship, this problem has been largely ignored. It is well known that pollution measures contain error, but the consequences of this error for regression estimates is not known. We use Lave and Seskin's air pollution model to demonstrate the consequences of random measurement error. We assume a range of 0% to 50% of the variance of the pollution measures is due to error. We find large differences in the estimated effects on mortality of the pollution variables as well as the other explanatory variables once this measurement error is taken into account. These results cast doubt on the usual regression estimates of the mortality effects of air pollution. More generally our results demonstrate the consequences of random measurement error in the explanatory variable of a multiple regression analysis and the misleading conclusions that may result in policy research if this error is ignored.     

Treatment effect estimation with covariate measurement error

This paper investigates the effect that covariate measurement error has on a treatment effect analysis built on an unconfoundedness restriction in which there is conditioning on error free covariates. The approach uses small parameter asymptotic methods to obtain the approximate effects of measurement error for estimators of average treatment effects. The approximations can be estimated using data on observed outcomes, the treatment indicator and error contaminated covariates without employing additional information from validation data or instrumental variables. The results can be used in a sensitivity analysis to probe the potential effects of measurement error on the evaluation of treatment effects.     

A simple estimator for nonlinear error in variable models

We propose a simple estimator for nonlinear method of moment models with measurement error of the classical type when no additional data, such as validation data or double measurements, are available. We assume that the marginal distributions of the measurement errors are Laplace (double exponential) with zero means and unknown variances and the measurement errors are independent of the latent variables and are independent of each other. Under these assumptions, we derive simple revised moment conditions in terms of the observed variables. They are used to make inference about the model parameters and the variance of the measurement error. The results of this paper show that the distributional assumption on the measurement errors can be used to point identify the parameters of interest. Our estimator is a parametric method of moments estimator that uses the revised moment conditions and hence is simple to compute. Our estimation method is particularly useful in situations where no additional data are available, which is the case in many economic data sets. Simulation study demonstrates good finite sample properties of our proposed estimator. We also examine the performance of the estimator in the case where the error distribution is misspecified.     

The effects of sampling on measures of association between variables based on sample means

Many studies that involve people's perceptions or behaviors focus on aggregate rather than individual responses. For example, variables describing public perceptions for some set of events may be represented as mean scores for each event. Event mean scores then become the unit of analysis for each variable. The variance of these mean scores for a variable is not only a function of the variation among the events themselves, but is also due to the variation among respondents and their possible responses. This is also the case for the covariances between variables based on event mean scores. In many contexts the variance and covariance components attributable to the sampling of respondents and their responses may be large; these components can be described as measurement error. In this paper we show how to estimate variances and covariances of aggregate variables that are free of these sources of measurement error. We also present a measure of reliability for the event means and examine the effect of the number of respondents on these spurious components. To illustrate how these estimates are computed, forty-two respondents were asked to rate forty events on seven risk perception variables. Computing the variances and covariances for these variables based on event means resulted in relatively large components attributable to measurement error. A demonstration is given of how this error is removed and the resulting effect on our estimates.     

Alternative value estimates of owner-occupied housing: Evidence on sample selection bias and systematic errors

Numerous econometric models have used various estimates of housing value as dependent variables. The three most common measures, in order of descending popularity, have been homeowner estimates, sales price, and assessed value. Each of these measures has limitations. The use of sales price can cause sample selection bias, while owner and tax assessor estimates are subject to measurement error. This study investigates the magnitude of the selection bias associated with sales price samples, and whether the errors in owner and assessor estimates are systematically related to independent variables typically included in estimated equations. Our most important conclusion is that the use of owner estimates may cause bias in the estimated coefficients on many independent variables.     

Adjusting for measurement error in the value added model: evidence from Portugal

The multilevel value added approach to measuring school effectiveness is now widely used. We propose a method to adjust for measurement error to investigate the extent to which this changes school effect estimates. It is applied to longitudinal data collected in the region of Cova da Beira (NUT III) for 1st, 3rd, 5th, 7th and 8th grades. Three different variance component models are considered, depending on the predictor variables included. Assuming measurement error occurs in explanatory and/or response variables, corrections are made for different values of the coefficient of reliability. Moreover, models are fitted under the assumption of either independent or correlated measurement errors.     

Modelling response error in school effectiveness research

Statistical modelling of school effectiveness in educational research is considered. Variance component models are generally accepted for the analysis of such studies. A shortcoming is that outcome variables are still treated as measured without an error. Unreliable variables produce biases in the estimates of the other model parameters. The variability of the relationships across schools and the effects of schools on students' outcomes differ substantially when taking the measurement error in the dependent variables of the variance component models into account. The random effects model can be extended to handle measurement error using a response model, leading to a random effects item response theory model. This extended random effects model is in particular suitable when subjects are measured repeatedly on the same outcome at several points in time.     

Covariate Measurement Error in Quadratic Regression

We consider quadratic regression models where the explanatory variable is measured with error. The effect of classical measurement error is to flatten the curvature of the estimated function. The effect on the observed turning point depends on the location of the true turning point relative to the population mean of the true predictor. Two methods for adjusting parameter estimates for the measurement error are compared. First, two versions of regression calibration estimation are considered. This approximates the model between the observed variables using the moments of the true explanatory variable given its surrogate measurement. For certain models an expanded regression calibration approximation is exact. The second approach uses moment-based methods which require no assumptions about the distribution of the covariates measured with error. The estimates are compared in a simulation study, and used to examine the sensitivity to measurement error in models relating income inequality to the level of economic development. The simulations indicate that the expanded regression calibration estimator dominates the other estimators when its distributional assumptions are satisfied. When they fail, a small-sample modification of the method-of-moments estimator performs best. Both estimators are sensitive to misspecification of the measurement error model.     

Uitbijternegerende schatters bij duplobepalingen

Outlyer-ignoring estimators for measurement in duplo.
By hypothesis a measurement u is the sum of two independent random variables, the normal random variable with expectation μ, and standard error σ, and a random error φ:

Basically two independent measurements u₁ and u₂ over u are to give the estimate x=1/2(u₁+ u₂) over μ.
However, to reduce the effect of the error φ on a final estimate of μ, one adds, according to a common practice, a third or even a fourth measurement u₃, u₄, in the case that the basic pair differs by more than a number A. For this extended set of measurements two outlyer-ignoring estimator y and z of μ are defined, and investigated against three specifications fo the error φ. Also an outlyer-ignoring estimate of σ is considered, and its application is illustrated by an example.     

Dynamic linkages and the propagation mechanism driving major international stock markets: An analysis of the pre- and post-crash eras

The stock market crash of October 1987 earmarked fears of a deep-seated financial crisis. In recent years, while there has been a number of empirical studies devoted to examinations of the number of common trends in a system of stock price indexes, only a minority has focused on what effect the crash has had on the characteristics [namely, the amount of co-movements amongst markets, their dynamic linkages, and implications for the transmission or propagation mechanism] of major stock markets. In this paper, we demonstrate how the techniques of unit root testing, cointegration, vector error-correction modelling (VECM) and forecast error variance decomposition (VDC) analysis, may be used to shed some light on these concerns in the context of six major international stock markets. Using two non-overlapping samples, we find evidence of a single cointegrating vector (or five common trends) over each of the pre- and post crash samples. A VECM is then constructed in which the temporal causal dynamics are examined, followed by decomposing the total impact of an unanticipated shock to each of the variables beyond the sample period, into proportions attributable to shocks in the other variables including its own. Results tend to broadly indicate: (1) the crash does not appear to have affected the relative leading role played by the US market over other markets; (2) the German and, British markets seem to have become more dependent on other markets over the post-crash era relative to the pre-crash; and (3) provide confirming evidence that, in general, the crash has brought about a greater interaction amongst markets, with a greater role for fluctuations in explaining shocks across markets (including that for the U.S.).     

Recovering the Metric Structure in Ordinal Data: Linear Versus Nonlinear Principal Components Analysis

Two techniques for data reduction as part of the SPSS package are compared in a Monte Carlo study: principal components analysis (PCA) and nonlinear principal components analysis (NPCA). The relative performance of these techniques in recovering the component scores underlying subjects' scores on observed ordinal variables is studied for two-dimensional spaces. The relative performance is examined as a function of (a) the sample size, (b) the number of categories in the variables, (c) the amount of measurement error, (d) the type of nonlinearity in the data, and (e) the degree of heterogeneity of the marginal distributions of the variables. As expected, when the sample size increases the performance of NPCA improves when compared to PCA. For the range of values considered, there is no effect of the number of categories on the relative performance of PCA and NPCA. For the other factors the effects are more complicated: adding error does not affect PCA as strongly as NPCA, as expected, but not for heterogeneously distributed variables for a particular form of nonlinearity, in which case NPCA becomes more appropriate. PCA appears to outperform NPCA for linear data, but also for a substantial number of nonlinear data sets.     

Errors-in-variables in demand systems

The rejection of symmetry and other restrictions in demand systems may be due to measurement errors in the exogenous variables. It is shown that symmetry conditions can be used to identify and consistently estimate a linear model's parameters when measurement error exists. Several identification rules are derived and estimation of identified models is considered. Results are applied to estimation of the Almost Ideal Demand System for the United Kingdom.     

附表计量法在工程预算编审中的应用研究

附表计量法主要是利用预先设计好的附表参数或计算结果作为工程量计算表中计算式计算式的方法。主要是在附表计量法中参照工程项目的计量特征进行独立设置的,因此不同的项目分布工程有着不同的计量附表。作为计算表附属的计量附表,在设置上可以相对灵活,还可以图文并茂,以便于预算的编制和审核,同样可以供工程施工管理相关人员使用,实现了一表通用、一表多用。通常我们在反复进行各个使用方法后,能够对计量附表中的错误进行及时纠正,以保证计量附表能够直接应用于计量全过程。     

Assessing the importance of measurement error in capital investment models

New developments in the economics of capital investment emphasize the role of financial variables. Econometric evidence on these hypotheses is potentially compromised by measurement error due to accounting conventions. The paper reviews new capital investment models and considers ways in which accounting procedures might lead to measurement error biases. Advances in errors-in-variables econometric models are employed to gauge the impact of measurement error on estimates of financial influences on capital investment. Cash-flow models appear to be especially susceptible to measurement error but q models seem fairly insensitive to measurement problems.     

ERRORS IN VARIABLES IN ECONOMETRICS: NEW DEVELOPMENTS AND RECURRENT THEMES*

The paper reviews some old and new approaches to the analysis of linear models with errors in variables. The emphasis is on the identification problems that usually arise in errors–in–variables models and on the various types of additional information that econometricians have invoked to be able to estimate parameters consistently. The approaches discussed include instrumental variables, grouping, simultaneous equations, multiple equations and bounds on measurement error variances.     

A new measurement procedure for attitudinal research. Analysis of its psychometric and informational properties

Since measurement errors have strong effects in all relationships (statistical or otherwise) studied, there is an increasing interest in the data quality, which is the major justification for this research. This paper aims to present a new measurement procedure, the letter scale, which avoids many of the problems connected with the response modalities traditionally used in attitudinal research, especially the ordinal categorical scales. This paper analyzes the error composition of the scores obtained with this new measurement procedure. The validity of the procedure is also analyzed and the observed variance is assessed to determine which part of the observed variance is “valid”, which part is random error (attenuating relationships) and which is correlated error (magnifying relationships). Structural equation models will be used to provide estimates of the measurement quality: (i) Reliability, (ii) Construct validity, method effect and residual variance. In addition, this letter scale is evaluated under another different perspective, Information Theory measures are also used to assess the amount of information transmitted. The relative merits of this new measurement procedure as opposed to other common response modalities will be discussed in both cases.     

The presence of an error term does not preclude causal inference in regression: a comment on Krause (2012)

A recent article by Krause (Qual Quant, doi:10.1007/s11135-012-9712-5, Krause (2012)) maintains that: (1) it is untenable to characterize the error term in multiple regression as simply an extraneous random influence on the outcome variable, because any amount of error implies the possibility of one or more omitted, relevant explanatory variables; and (2) the only way to guarantee the prevention of omitted variable bias and thereby justify causal interpretations of estimated coefficients is to construct fully specified models that completely eliminate the error term. The present commentary argues that such an extreme position is impractical and unnecessary, given the availability of specialized techniques for dealing with the primary statistical consequence of omitted variables, namely endogeneity, or the existence of correlations between included explanatory variables and the error term. In particular, the current article discusses the method of instrumental variable estimation, which can resolve the endogeneity problem in causal models where one or more relevant explanatory variables are excluded, thus allowing for accurate estimation of effects. An overview of recent methodological resources and software for conducting instrumental variables estimation is provided, with the aim of helping to place this crucial technique squarely in the statistical toolkit of applied researchers.     

Millsian causation

The Directed Acyclic Graph (DAG) theory of causation is based on the assumption that randomly sampling the variables of a causal system will yield a joint probability distribution that satisfies the Markovian condition. It is shown here that this condition can be split into two parts, one of which is named the Millsian condition. It is further shown that the Millsian condition alone implies that causally unrelated sets of variables are conditionally independent given their common causes, very likely a key requirement stated by John Stuart Mill 150 years ago. In Millsian causation, unlike Markovian causation, it is possible for an indirect cause to be associated with its effect even when controlling for the intermediate direct causes. This phenomenon is explained by taking into account the existence of potential causal modulation.