Small Samples, Big Insights: A Methodological Comparison of Estimation Techniques for Latent Divergent Thinking...

Area of Science:

• Psychology
• Quantitative Psychology
• Psychometrics

Background:

• Small sample sizes pose significant challenges in psychological research, particularly for expert populations or complex methodologies.
• Frequentist confirmatory factor analysis (CFA) is sensitive to sample size, leading to convergence issues, inadmissible parameters, and poor model fit.
• Bayesian methods provide a robust alternative, less affected by sample size and capable of incorporating prior knowledge.

Purpose of the Study:

• To introduce small-sample-size structural equation modeling (SEM) to creativity research.
• To investigate the relationship between creative fluency, creative cleverness, and right-wing authoritarianism (RWA) using SEM with limited sample sizes.
• To compare the stability and reliability of frequentist versus Bayesian SEM under progressively smaller sample sizes.

Main Methods:

• Structural equation modeling (SEM) was employed, comparing frequentist and Bayesian approaches.
• The study began with a sample size of N = 198 and was progressively reduced in increments of n = 25.
• Key metrics assessed included frequentist fit indices and Bayesian Rhat values, alongside standard errors and regression coefficients.

Main Results:

• Frequentist fit indices degraded significantly below a sample size of N = 100.
• Bayesian multivariate Rhat values indicated stable convergence down to N = 50.
• Standard errors for fluency loadings inflated 40-50% faster in frequentist SEM compared to Bayesian estimation, while RWA-cleverness regression coefficients remained significant across all sample reductions.

Conclusions:

• Bayesian priors play a crucial role in stabilizing SEM results with small sample sizes.
• The relationship between right-wing authoritarianism and creative cleverness demonstrates robustness even with limited sample sizes.
• The findings provide practical guidelines for determining minimum sample sizes in bifactor modeling within psychological research.