A statistical test to reject the structural interpretation of a latent factor model

TL;DR

This paper introduces a statistical test to challenge the common structural interpretation of latent factor models, demonstrating its application on life satisfaction data and revealing that the latent construct may not causally influence outcomes as assumed.

Contribution

It develops a novel test to empirically reject the structural assumptions of latent factor models, highlighting potential misinterpretations in factor analysis.

Findings

Strong evidence against the structural interpretation of the latent factor for life satisfaction.

The test can be applied to other latent constructs to assess their causal assumptions.

Implications for the development and evaluation of psychological and social measures.

Abstract

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 a single factor is adequate, research often proceeds by using a univariate summary of the indicators in subsequent research. Implicit in such practices is the assumption that it is the underlying latent, rather than the indicators, that is causally efficacious. The assumption that the indicators do not have effects on anything subsequent, and that they are themselves only affected by antecedents through the underlying latent is a strong assumption, effectively imposing a structural interpretation on the latent factor model. In this paper, we show that this structural assumption has empirically testable implications, even though the latent variable itself is unobserved. We develop a statistical test to potentially reject the structural interpretation of a latent factor model. We apply this test to 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 measures and for the use of factor analysis itself.