Exploring number of response categories in factor analysis: Implications for sample size

Factor analysis is a statistical method to explore the relationships among observed variables and identify latent structures. It is crucial in scale development and validity analysis. Key factors affecting the accuracy of factor analysis results include the type of data, sample size, and the number of response categories. While some studies suggest that reliability improves with more response categories, others find no significant relationship between the number of response categories and reliability. A key consideration is that increasing the number of response categories can introduce measurement errors, especially when there are too many categories for participants to respond accurately. The study examines how different numbers of response categories affect sample size requirements in factor analysis, particularly under misspecified and correctly specified models. MonteCarloSEM package in R was used to simulate data sets based on sample size, number of response categories, model specification, and test length. Results show that a higher number of categories helps reduce bias and improve model fit, especially in smaller samples. However, when sample sizes are small or when fewer categories are used, increasing the number of items or the number of categories can improve parameter estimation. The findings suggest that for optimal results, researchers should carefully balance sample size, number of items, and response categories, particularly in studies with categorical data.