Linear models are described for the situation wherein a measurement instrument is constructed for all elements of the Cartesian product of several facets when the elements of each facet are not ordered. The structure of the covariance matrix of the instrument is derived from the models. By using covariance structure analysis, the models can be tested, and estimates of the parameters can be obtained. Models for 20 tests were formulated and tested and were constructed from a design with a behavioral and a situational facet measuring social anxiety in children; for 15 tests a model proved to fit the data. It is concluded that covariance structure analysis is useful for the analysis and construction of measurement instruments.We thank David A. Kenny, Fred N. Kerlinger, Wirn J. van der Linden, Wim E. Saris, and Pieter Vijn for their comments and Ineke Wesling for typing the manuscript.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.