The impact of item response category number on classification precision (R²ₑₙₜᵣₒₚᵧ) in latent class analysis

Abstract

The present study aims to investigate the impact of the number of response categories in polytomously scored measurement instruments on latent class analysis (LCA) outcomes under varying conditions of sample size and latent class proportion distributions. Accordingly, a comprehensive Monte Carlo simulation study was conducted in which the number of item response categories, sample size, and latent class proportions were systematically manipulated. The simulation design was based on a two–latent-class model, and 100 replications were generated for each experimental condition to ensure the stability of parameter estimates. In line with scoring formats commonly employed in educational and psychological measurement contexts, the number of response categories was specified as three, four, and five. Sample size was operationalized at three levels: small (N = 100), medium (N = 500), and large (N = 1000). Latent class proportions were examined under both equal (0.50–0.50) and unequal (0.70–0.30) distribution conditions to reflect realistic population heterogeneity. All simulation data were analyzed using the poLCA package within the R statistical computing environment. Model fit and classification performance were evaluated using multiple indices, including the log-likelihood, Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and entropy. The results revealed a systematic decrease in entropy values—indicative of reduced classification accuracy—as the number of item response categories increased. Specifically, the highest entropy values were consistently observed in measurement structures comprising three response categories. These findings suggest that a reduced number of response categories facilitates more accurate class assignment in latent class analysis. Furthermore, increases in sample size were associated with improved classification performance across all experimental conditions, underscoring the importance of adequate sample sizes in LCA applications.