R package implementing the statistical tests from:
VanderWeele, T. J., & Vansteelandt, S. (2022). A statistical test to reject the structural interpretation of a latent factor model. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 84(5), 2032–2054. https://doi.org/10.1111/rssb.12555
Background
Factor analysis is routinely used to assess whether a single univariate latent variable explains the covariance among a set of observed indicators. When a one-factor model fits adequately, researchers often treat the latent variable as the causally relevant quantity in subsequent analyses. This practice implicitly assumes a structural interpretation of the latent factor model: that it is the latent variable, rather than the individual indicators, that is causally efficacious.
However, a measurement model fitting well does not imply the structural interpretation is correct. The individual indicators could each have separate causal effects on outcomes, even though their covariance structure is consistent with a single latent factor (see Figures 2 and 3 in the paper).
VanderWeele and Vansteelandt (2022) show that the structural interpretation has empirically testable implications. Specifically, under a structural latent factor model, the association between any external variable Z and indicator X_i, scaled by the reliability of X_i, must be the same across all indicators (Theorem 1). This package implements the two statistical tests proposed in the paper:
- T0: a statistical test dependent on reliability estimates (Section 3.2)
- T1: a statistical test independent of reliability estimates (Section 3.3)
Note on terminology: Following the paper, this package refers to the coefficients lambda_i as “reliabilities.” In mainstream psychometrics these are more commonly known as factor loadings.
Functions
| Function | Description |
|---|---|
test_t0(X, z) |
Statistical test dependent on reliability estimates (Section 3.2). Requires d >= 3 indicators and p >= 2 Z-levels. |
test_t1(X, z) |
Statistical test independent of reliability estimates (Section 3.3). Requires d >= 2 indicators and p >= 3 Z-levels. |
estimate_reliability(X) |
Estimation of reliability via quasi-Poisson GLM on pairwise covariances (Section 3.1). |
Code of Conduct
Please note that the structest project is released with a Contributor Code of Conduct. By contributing to this project, you agree to abide by its terms.
Reference
VanderWeele, T. J., & Vansteelandt, S. (2022). A statistical test to reject the structural interpretation of a latent factor model. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 84(5), 2032–2054. https://doi.org/10.1111/rssb.12555