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.

Keywords

• Latent class analysis
• Polytomous response categories
• Simulation study
• Classification precision
• Entropy

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

Abstract

Latent class analysis (LCA) is widely used in educational and psychological research to identify unobserved subgroups based on categorical response patterns. Although simulation studies have primarily focused on class enumeration and model selection criteria, relatively limited attention has been given to how response-category structures influence entropy-based classification quality. The present study investigated the impact of item response-category number on entropy values under varying sample-size and latent class proportion conditions. A Monte Carlo simulation design based on a fixed two-class latent structure was implemented using the poLCA package in the R statistical environment. Response-category structures were manipulated across 3-, 4-, and 5-category conditions, while sample size was specified as 100, 500, and 1000. Latent class proportions were defined as equal (.50/.50) and unequal (.70/.30). Six indicator variables were generated under class-separation conditions, and 100 replications were conducted for each simulation condition. Model performance was evaluated using entropy (R²ₑₙₜᵣₒₚᵧ), log-likelihood, Akaike Information Criterion (AIC), and Bayesian Information Criterion (BIC). Results indicated that entropy values systematically decreased as the number of response categories increased. The 3-category conditions consistently produced the highest and most stable entropy values across sample-size conditions, whereas the 5-category structures yielded lower entropy values and greater variability. Although larger sample sizes were generally associated with more stable entropy patterns, the effect of response-category number remained evident across all sample-size conditions. The findings suggest that response-category structures may substantially influence entropy-based classification precision in LCA and highlight the importance of considering response-category design when evaluating classification quality in latent class models.

Keywords

• Latent class analysis
• Polytomous response categories
• Simulation study
• Classification precision
• Entropy

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