Imaginary latent variables: Empirical testing for detecting deficiency in reflective measures

Abstract

Imaginary latent variables are variables with negative variances and have been used to implement constraints in measurement models. This article aimed to advance this practice and rationalize the imaginary latent variables as a method to detect possible latent deficiencies in measurement models. This rationale is based on the theory of complex numbers used in the measurement process of common factor model–based structural equation modeling. Modeling an imaginary latent variable produces a potential deficiency within its relative reflective measures through a considerable reduction in common variance indicating the most affected indicator(s).

Keywords

• Latent variable models
• Structural Equation Modeling
• Imaginary and complex numbers
• Path analysis
• Psychometrics

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