# How plausible is my model? Assessing model plausibility of structural equation models using Bayesian posterior probabilities (BPP)

## TL;DR

This paper introduces a new method to assess the plausibility of structural equation models using Bayesian posterior probabilities, making model comparison easier for researchers.

## Contribution

A novel method for selecting neighboring models to compute Bayesian posterior probabilities in structural equation modeling is proposed.

## Key findings

- The proposed method integrates seamlessly into standard structural equation modeling workflows.
- The R package modelbpp automates generating neighboring models, fitting them, and computing BPPs.
- The method helps reveal evidence against a model that may be hidden by traditional fit indices.

## Abstract

In structural equation modeling (SEM), one method to select the most plausible model from several candidates, or to compare one or more hypothesized models with similar alternatives on plausibility, is to compare the models using Bayesian posterior probability (BPP). BPP can be computed from the Bayesian information criterion (BIC) scores (Wu et al. Multivariate Behavioral Research, 55(1), 1–16, 2020). This approach complements conventional goodness-of-fit indices such as the Comparative Fit Index (CFI), the root mean square error of approximation (RMSEA), and the standardized root mean square residual (SRMR) in giving concise BPP for assessing uncertainties among all models considered. It can also reveal evidence against a model otherwise hidden by these indices. However, Wu et al. Multivariate Behavioral Research, 55(1), 1–16. (2020) did not provide guidelines on deciding the models that should be considered. To facilitate the use of BPP, we proposed a novel method for selecting this set of models, called neighboring models, to help researchers decide on the initial set. This novel method integrates seamlessly into the typical workflow for SEM analysis. Researchers can fit a model as usual and then use this method to assess whether it is the most plausible model compared with the neighboring models. We believe the proposed method will make it easier for researchers to make better-informed decisions when evaluating their models. We developed a user-friendly R package, modelbpp, to automate all the steps: generating the set of neighboring models, fitting them, and computing the BPPs, all in a single function.