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