Parsimony in Model Selection: Tools for Assessing Fit Propensity

TL;DR

This paper introduces a toolkit and R package for assessing the fit propensity of structural equation models, emphasizing the importance of parsimony beyond just the number of parameters, to improve model selection.

Contribution

It provides a novel toolkit and R package to evaluate model fit propensity, addressing limitations of traditional criteria and promoting better understanding of parsimony in model selection.

Findings

The toolkit reveals differences in fit propensity among models.

Application to Rosenberg Self-Esteem Scale demonstrates practical utility.

Highlights limitations of existing model selection criteria.

Abstract

Theories can be represented as statistical models for empirical testing. There is a vast literature on model selection and multimodel inference that focuses on how to assess which statistical model, and therefore which theory, best fits the available data. For example, given some data, one can compare models on various information criterion or other fit statistics. However, what these indices fail to capture is the full range of counterfactuals. That is, some models may fit the given data better not because they represent a more correct theory, but simply because these models have more fit propensity - a tendency to fit a wider range of data, even nonsensical data, better. Current approaches fall short in considering the principle of parsimony (Occam's Razor), often equating it with the number of model parameters. Here we offer a toolkit for researchers to better study and understand parsimony through the fit propensity of Structural Equation Models. We provide an R package (ockhamSEM) built on the popular lavaan package. To illustrate the importance of evaluating fit propensity, we use ockhamSEM to investigate the factor structure of the Rosenberg Self-Esteem Scale.