A statistical test to reject the structural interpretation of a latent factor model
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Factor analysis is often used to assess whether a single univariate latent variable is sufficient to explain most of the covariance among a set of indicators for some underlying construct. When evidence suggests that such a single factor is adequate, research often proceeds by using a univariate summary of the indicators in subsequent research to assess causal relations pertaining to the underlying construct of interest. Implicit in such practices is the assumption that it is the underlying latent, rather than the indicators, that are causally efficacious. The assumption that the indicators do not have causal effects on anything subsequent, and that they are themselves only affected by antecedents through the underlying latent variable is a strong assumption, one that we might refer to as imposing a structural interpretation on the latent factor model. In this paper, we show that this structural assumption in fact has empirically testable implications. We develop a statistical test to potentially reject the structural interpretation of a latent factor model. We apply this test to empirical data concerning associations between the Satisfaction with Life Scale and subsequent all-cause mortality, which provides strong evidence against a structural interpretation for a univariate latent underlying the scale. Discussion is given to the implications of this result for the development, evaluation, and use of empirical measures and of the latent factor model.
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