scholarly journals Structural Equation Models with Unobservable Variables and Measurement Error: Algebra and Statistics

1981 ◽  
Vol 18 (3) ◽  
pp. 382 ◽  
Author(s):  
Claes Fornell ◽  
David F. Larcker
Keyword(s):  
Measurement Error ◽  
Structural Equation ◽  
Structural Equation Models

scholarly journals Structural Equation Models with Unobservable Variables and Measurement Error: Algebra and Statistics

1981 ◽  
Vol 18 (3) ◽  
pp. 382-388 ◽  
Author(s):  
Claes Fornell ◽  
David F. Larcker
Keyword(s):  
Statistical Analysis ◽  
Measurement Error ◽  
Structural Equation ◽  
Goodness Of Fit ◽  
Structural Equation Models ◽  
Structural Equations ◽  
Testing System

Several issues relating to goodness of fit in structural equations are examined. The convergence and differentiation criteria, as applied by Bagozzi, are shown not to stand up under mathematical or statistical analysis. The authors argue that the choice of interpretative statistic must be based on the research objective. They demonstrate that when this is done the Fornell-Larcker testing system is internally consistent and that it conforms to the rules of correspondence for relating data to abstract variables.

Using structural equation models to evaluate the magnitude of measurement error in blood pressure

2001 ◽  
Vol 20 (15) ◽  
pp. 2351-2368 ◽  
Author(s):  
J. M. Batista-Foguet ◽  
G. Coenders ◽  
M. Artés Ferragud
Keyword(s):  
Blood Pressure ◽  
Measurement Error ◽  
Structural Equation ◽  
Structural Equation Models

Evaluating Structural Equation Models with Unobservable Variables and Measurement Error

1981 ◽  
Vol 18 (1) ◽  
pp. 39-50 ◽  
Author(s):  
Claes Fornell ◽  
David F. Larcker
Keyword(s):  
Measurement Error ◽  
Sample Size ◽  
Structural Equation ◽  
Structural Model ◽  
Structural Equation Models ◽  
Statistical Tests ◽  
Explanatory Power ◽  
Measurement Model ◽  
Measurement Properties ◽  
Chi Square

The statistical tests used in the analysis of structural equation models with unobservable variables and measurement error are examined. A drawback of the commonly applied chi square test, in addition to the known problems related to sample size and power, is that it may indicate an increasing correspondence between the hypothesized model and the observed data as both the measurement properties and the relationship between constructs decline. Further, and contrary to common assertion, the risk of making a Type II error can be substantial even when the sample size is large. Moreover, the present testing methods are unable to assess a model's explanatory power. To overcome these problems, the authors develop and apply a testing system based on measures of shared variance within the structural model, measurement model, and overall model.

scholarly journals Correcting measurement error bias in interaction models with small samples

2006 ◽  
Vol 3 (2) ◽  
Author(s):  
Josep Bisbe ◽  
Germà Coenders ◽  
Willem Saris ◽  
Joan Batista-Foguet
Keyword(s):  
Measurement Error ◽  
Least Squares ◽  
Structural Equation ◽  
Structural Equation Models ◽  
Ordinary Least Squares ◽  
Alternative Methods ◽  
Small Samples ◽  
Least Squares Regression ◽  
Interaction Terms ◽  
Error Bias

Several methods have been suggested to estimate non-linear models with interaction terms in the presence of measurement error. Structural equation models eliminate measurement error bias, but require large samples. Ordinary least squares regression on summated scales, regression on factor scores and partial least squares are appropriate for small samples but do not correct measurement error bias. Two stage least squares regression does correct measurement error bias but the results strongly depend on the instrumental variable choice. This article discusses the old disattenuated regression method as an alternative for correcting measurement error in small samples. The method is extended to the case of interaction terms and is illustrated on a model that examines the interaction effect of innovation and style of use of budgets on business performance. Alternative reliability estimates that can be used to disattenuate the estimates are discussed. A comparison is made with the alternative methods. Methods that do not correct for measurement error bias perform very similarly and considerably worse than disattenuated regression.

Analyzing Individual and Average Causal Effects via Structural Equation Models

Methodology ◽  
2005 ◽  
Vol 1 (1) ◽  
pp. 39-54 ◽  
Author(s):  
Rolf Steyer
Keyword(s):  
Measurement Error ◽  
Untreated Control ◽  
Structural Equation ◽  
Structural Equation Models ◽  
Causal Effect ◽  
Latent Trait ◽  
Causal Effects ◽  
Control Group ◽  
Expected Outcome ◽  
The Individual

Abstract. Although both individual and average causal effects are defined in Rubin's approach to causality, in this tradition almost all papers center around learning about the average causal effects. Almost no efforts deal with developing designs and models to learn about individual effects. This paper takes a first step in this direction. In the first and general part, Rubin's concepts of individual and average causal effects are extended replacing Rubin's deterministic potential-outcome variables by the stochastic expected-outcome variables. Based on this extension, in the second and main part specific designs, assumptions and models are introduced which allow identification of (1) the variance of the individual causal effects, (2) the regression of the individual causal effects on the true scores of the pretests, (3) the regression of the individual causal effects on other explanatory variables, and (4) the individual causal effects themselves. Although random assignment of the observational unit to one of the treatment conditions is useful and yields stronger results, much can be achieved with a nonequivalent control group. The simplest design requires two pretests measuring a pretest latent trait that can be interpreted as the expected outcome under control, and two posttests measuring a posttest latent trait: The expected outcome under treatment. The difference between these two latent trait variables is the individual-causal-effect variable, provided some assumptions can be made. These assumptions - which rule out alternative explanations in the Campbellian tradition - imply a single-trait model (a one-factor model) for the untreated control condition in which no treatment takes place, except for change due to measurement error. These assumptions define a testable model. More complex designs and models require four occasions of measurement, two pretest occasions and two posttest occasions. The no-change model for the untreated control condition is then a single-trait-multistate model allowing for measurement error and occasion-specific effects.

Evaluating Structural Equation Models with Unobservable Variables and Measurement Error: A Comment

1981 ◽  
Vol 18 (3) ◽  
pp. 375-381 ◽  
Author(s):  
Richard P. Bagozzi
Keyword(s):  
Measurement Error ◽  
Structural Equation ◽  
Structural Equation Models

The author comments on Fornell and Larcker's article in the February 1981 issue of JMR. He indicates some limitations of the analyses, pinpoints where they can be misleading, and introduces some new notions.

scholarly journals Simultaneous estimation of indirect and interaction effects using structural equation models

2004 ◽  
Vol 1 (1) ◽  
pp. 163-184
Author(s):  
Joan Manuel Batista-Foguet ◽  
Germà Coenders ◽  
Willem Saris ◽  
Josep Bisbe
Keyword(s):  
Regression Analysis ◽  
Measurement Error ◽  
Structural Equation ◽  
Structural Equation Models ◽  
Interaction Effects ◽  
Linear Constraints ◽  
Simultaneous Estimation ◽  
Equation Approach ◽  
Direct Effects ◽  
And Performance

Interaction effects are usually modeled by means of moderated regression analysis. Structural equation models with non-linear constraints make it possible to estimate interaction effects while correcting for measurement error. From the various specifications, Jöreskog and Yang's (1996, 1998), likely the most parsimonious, has been chosen and further simplified. Up to now, only direct effects have been specified, thus wasting much of the capability of the structural equation approach. This paper presents and discusses an extension of Jöreskog and Yang's specification that can handle direct, indirect and interaction effects simultaneously. The model is illustrated by a study of the effects of an interactive style of use of budgets on both company innovation and performance.

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