Latent Variable Models and Networks: Statistical Equivalence and Testability.

Area of Science:

• Psychology
• Network Science
• Statistical Modeling

Background:

• Psychological constructs are increasingly represented using network models as an alternative to traditional latent variable models.
• Latent variable models explain variable relations via unobserved common causes, while network models propose direct causal links between observed variables.

Purpose of the Study:

• To critically evaluate the plausibility of network and latent variable models, despite their mathematical equivalences.
• To highlight how constraints meaningful in one framework may lack clear interpretation in the equivalent model of the other.

Main Methods:

• Mathematical comparison of network and latent variable models.
• Analysis of constraint interpretability across frameworks.
• Development of a model comparison test based on diverging predictions for correlations.

Main Results:

• Mathematical equivalences do not guarantee equal plausibility or interpretability of models.
• Sparse network models and unidimensional factor models yield diverging predictions regarding zero-order and partial correlations.
• An empirical example demonstrates the application of the proposed model comparison test.

Conclusions:

• The choice between network and latent variable models depends on the interpretability of model constraints within the specific research context.
• A novel statistical procedure is proposed to discriminate between these models based on correlation patterns.
• Network models may offer a more direct representation of psychological processes compared to latent variable models.