Elsevier

Journal of Econometrics

Volume 89, Issues 1–2, 26 November 1998, Pages 393-421
Journal of Econometrics

Representation of measurement error in marketing variables: Review of approaches and extension to three-facet designs

https://doi.org/10.1016/S0304-4076(98)00068-2Get rights and content

Abstract

This paper explores approaches for modeling measurement error in marketing research, including random, method and measure specific sources of error. The following approaches are considered: classic confirmatory factor analysis, second-order models, panel models, additive trait-method models, correlated uniqueness models, covariance components analysis, additive trait-method-measure specific-error models, and the direct product model, where traits and methods interact. Finally, a three-facet multiplicative model is addressed wherein latent variables underlying a phenomenon under investigation are shown to interact with multiple methods and occasions of measurement. The three-facet model is illustrated on a study of consumer attitudes toward losing weight explicitly conducted for this paper.

Section snippets

Confirmatory factor analysis

Jöreskog (1969) proposed the following `measurement model' as a representation of the relationship between measures and factors (where certain restrictions must be placed on Λy and Θε below to achieve identification):
yyη+ε
where y is a p×1 vector of observed variables, η is an n×1 vector of latent (i.e., unobserved) variables or factors underlying the observed variables, ε is a p×1 vector of error variables, and it is assumed that the η's and ε's are random variables with zero means, y is

A three-facet multiplicative model

Up to this point, we have limited inquiry to two-facet designs, with traits and methods constituting the two facets. However, researchers sometimes have to deal with three facets. Given the frequency with which panel designs are conducted in marketing research, it would be useful to extend the representation of construct validity models to include a third facet, time. When one conducts a cross-national study, a third facet would take place. As an interesting case to scrutinize, we will examine

Guidelines for investigating construct validation

How should one conduct a construct validation study, given the many options? The answer to this depends on whether one has a weak or strong theory concerning how traits and measurement error function. With no or a weak basis for modeling trait and error, an exploratory procedure is recommended. The most intuitive model, the additive trait-method model, should be run first. A satisfactory fit here provides a basis for assessing convergent and discriminant validity and partitioning variance in

Conclusion

This article has explored a number of models for modeling measurement error in economics and behavioral research. From the analyses conducted herein, it is apparent that measurement error is pervasive and often large in empirical research. We reviewed procedures that permit the researcher to detect and correct for random error, measure specificity, and systematic method biases. Most of the procedures assumed linear effects for the different sources of error. However, we also considered a trait

Acknowledgements

The authors thank Dr. Robert Cudeck, Department of Psychology, University of Minnesota, for providing the MBDP routine and FORTRAN code which served as the basis for the GLS procedure used herein for the TFM model. Special thanks are expressed to the reviewers and editors for the many recommendations they made.

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