Reconciling Latent Variables and Networks: Exploring and extending the Psychometric-Toolbox

Abstract

Since the introduction of network psychometrics, several connections to statistical models in "classical" psychometrics (i.e., IRT, SEM, GLM) as well as to approaches from other research fields have been established. In this paper, these developments have been reviewed and synthesized and, based on an exploratory literature search, further advanced and presented in an accessible visual format. This perspective opens up promising opportunities to extend the psychometric-toolbox by incorporating and learning from statistical methodologies developed in other research domains, which often address similar or even identical problems. Highlighting these methodological commonalities may also foster collaboration across research fields that have traditionally remained largely independent. Moreover, awareness of these connections may render methodological development more systematic and goal-directed and may enable a meaningful division of labor, for example between the development of statistical methodology and its practical implementation for empirical research through software tools. Finally, these methodological advances provide new opportunities for empirical research and may contribute to a reconciliation with longstanding conceptual issues concerning psychometric constructs and, more broadly, psychological phenomena.

Figures (8)

• Figure 1: Each square is a statistical model (dark colored = time-series, light colored = cross-sectional or panel data), the hexagons are more general frameworks (e.g., IRT, GLM, ARMA), and models for binary variables have a dashed border. To avoid overlapping edges, some models are included more than once (without boundary), if possible, edges are directed from less to more general model, red edges indicate special cases (from more to less general), green edges indicate formal equivalences. The green check-mark means this model has an available R/Python implementation. Each model and relation has a number, with references in the appendix.
• Figure 2: A useful heuristic for differentiating between common basic data structures in empirical research is introduced by Cattell.1952.DataCube and termed 'Data-Box/Cube' in Molenaar.2012Wardenaar.2013.DataCubeRam.2015.DataCubeRobinaugh.2020.PsychopathologyIsvoranu.2022.NetworkPsychometricsBorsboom.2024. It has three dimensions [individuals ($N$) × variables ($P$) × time-points ($T$)] which classifies the four common data structures illustrated here. Borsboom.2021.NetworkPsychometrics
• Figure 3: The square lattice graph of the IM illustrated. With $X_p$ being binary random variables, pairwise interactions between variables are parametrized with $\sigma_{i j}$, and $\mu_i$ as main effect or threshold for changes in variable state.
• Figure 4: The GGM visualized, with $X_p$ being continuous (gaussian) random variables, and $\omega_{i j}$ entries in the in the $P \times P$ weight matrix $\bm{\Omega}$.
• Figure 5: Illustration of a CFA model with four observed variables ($X_1, X_2, X_3, X_4$) and two latent variables ($\eta_1, \eta_2$).