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

Area of Science:

• Psychometrics
• Statistical Modeling
• Psychological Measurement

Background:

• Factor analysis commonly assumes a single latent variable explains indicator covariance.
• Subsequent research often uses univariate summaries, assuming latent variables are causally efficacious.
• This implies a structural interpretation where indicators are only affected via the latent construct.

Purpose of the Study:

• To develop an empirically testable method to reject the structural interpretation of latent factor models.
• To investigate the causal assumptions underlying univariate latent variable models.
• To assess the structural interpretation of a latent factor model using real-world data.

Main Methods:

• Development of a novel statistical test for latent factor model structural assumptions.
• Application of the test to data linking the Satisfaction-with-Life Scale to all-cause mortality.
• Empirical evaluation of the test's ability to reject structural interpretations.

Main Results:

• The statistical test provides empirically testable implications for structural assumptions.
• Analysis of Satisfaction-with-Life Scale data showed strong evidence against a structural interpretation.
• The latent variable underlying the scale may not be the sole or primary causal agent.

Conclusions:

• The structural interpretation of latent factor models is a strong assumption that can be empirically challenged.
• Results question the causal efficacy of the latent variable for the Satisfaction-with-Life Scale.
• Implications for the development, evaluation, and application of psychological measures and factor analysis are discussed.