Comparing Estimation Methods for Multilevel Regression Parameters

Multilevel regression models are widely utilized in various fields, such as health, education, and agriculture, due to their ability to address dependencies between variables at different levels of aggregation. This study compares two estimation methods for parameters in multilevel regression models: the maximum likelihood method (MLE) and the variance constraints method (RCR). Utilizing simulation experiments repeated 1000 times across different sample sizes (15, 40, and 60), the study evaluates these methods using the Akaike Information Criterion (AIC) and mean square error (MSE). Results indicate that the MLE consistently outperforms the RCR in terms of lower AIC and MSE values, especially as sample size increases. Despite the closeness in efficiency between the methods at smaller sample sizes, the MLE's superiority becomes more pronounced with larger samples, suggesting its robustness and reliability for parameter estimation in multilevel regression models. This finding is crucial for researchers seeking accurate and efficient estimation techniques in hierarchical data analysis.