This repo contains supplemental material for the paper:
Bader, M., Jobst, L. J., & Moshagen, M. (2022). Sample size requirements for bifactor models. Structural Equation Modeling: A Multidisciplinary Journal, 29(5), 772–783. [https://doi.org/10.1080/10705511.2021.2019587]
Despite the widespread application of bifactor models, little research has considered required sample sizes for this type of model. As universal sample size recommendations are often misleading, we illustrate how to determine sample size requirements of bifactor models using Monte Carlo simulations in R. Furthermore, we present results of an extensive simulation study investigating the effects of the number of specific factors and indicators, loading magnitude, the relative general factor strength, and the validity of the proportionality condition on sample size requirements. Although a sample size of 500 was often sufficient to obtain acceptable convergence rates and parameter estimates, the exact sample size requirements depended on various model characteristics.
The folder simulation-study contains R scripts for a Monte Carlo simulation study examining various potential determinants of the sample size requirements of bifactor models. The following model characteristics are manipulated:
- number of specific factors per model
- the number of indicators per specific factor
- the average magnitude of general factor loadings
- explained common variance (ECV)
- validity of the proportionality condition.
The data generated by these population models are then analyzed by correctly specified analysis models under five different sample size conditions. Outcomes are:
- convergence rate
- relative biases in the estimated general and specific factor loadings
- standard error estimates of the factor loadings
- estimated ECV
The folder tutorial comprises sample scripts and a tutorial on how to conduct a Monte Carlo simulation to determine the required sample size for a bifactor model of interest using the R package simsem.