, Volume 49, Issue 1, pp 37-47

Using phantom and imaginary latent variables to parameterize constraints in linear structural models

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The most widely-used computer programs for structural equation models analysis are the LISREL series of Jöreskog and Sörbom. The only types of constraints which may be made directly are fixing parameters at a constant value and constraining parameters to be equal. Rindskopf (1983) showed how these simple properties could be used to represent models with more complicated constraints, namely inequality constraints on unique variances. In this paper, two new concepts are introduced which enable a much wider variety of constraints to be made. The concepts, “phantom” and “imaginary” latent variables, allow fairly general equality and inequality constraints on factor loadings and structural model coefficients.

During the preparation of this article, it was discovered that another researcher, Jack McArdle, had concurrently and independently discovered some of the techniques reported here. While he has chosen not to publish his research, I wish to acknowledge his work. I would like to thank Art Woodward for telling me about “sort-of simple” structure.