On the Dimensional Indeterminacy of One-Wave Factor Analysis Under Causal Effects
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It is shown, with two sets of survey items that separately load on two distinct factors, independent of one another conditional on the past, that if it is the case that at least one of the factors causally affects the other then, in equilibrium in many settings, a factor model with a single factor will suffice to capture the structure of the associations among the items. Factor analysis with one wave of data can then not distinguish between factor models with a single factor versus those with two factors that are causally related. Therefore, unless causal relations between factors can be ruled out a priori, alleged empirical evidence from one-wave factor analysis for a single factor effectively provides no information on the actual dimensionality of the true underlying factor structure. The implications for interpreting the factor structure of self-report scales for anxiety and depression are discussed. Some further generalizations to an arbitrary number of underlying factors are noted.
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