Abstract
Any exploratory factor analysis model requires at least three indicators (observed variables) for each common factor to ensure model identifiability. If one would make exploratory factor analysis for a data set in which one of common factors would have only two indicators in its population, one would encounter difficulties such as improper solutions and nonconvergence of iterative process in calculating estimates.
In this paper, we first develop conditions for identifiability of the remaining factor loadings except for a factor loading vector which relates to a common factor with only two indicators. Two models for analyzing such data sets are then proposed with the help of confirmatory factor analysis and covariance structure analysis. The first model is an exploratory factor analysis model that permits correlation between unique factors; the second model is a kind of confirmatory factor model with equal factor loadings. Two real data sets are analyzed to illustrate usefulness of these models.
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Kano, Y. Exploratory Factor Analysis with a Common Factor with Two Indicators. Behaviormetrika 24, 129–145 (1997). https://doi.org/10.2333/bhmk.24.129
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DOI: https://doi.org/10.2333/bhmk.24.129