| dc.description.abstract | Parameter estimation in multinomial logistic regression models often faces
challenges when sample sizes are limited or when predictor variables exhibit high
multicollinearity, which can reduce estimation accuracy and stability. These conditions
highlight the need for a Bayesian analysis approach capable of producing reliable
and stable parameter estimates while maintaining prediction quality even under nonideal
data conditions. This study aims to compare the performance of two Markov
Chain Monte Carlo (MCMC) methods, namely Metropolis-Hastings (MH) and Gibbs
Sampling with Polya-Gamma augmentation (Gibbs-PG). MH utilizes a symmetric
Gaussian proposal distribution to efficiently explore the parameter space, whereas
Gibbs-PG employs Polya-Gamma augmentation to reduce autocorrelation and improve
mixing. The data include the Iris Dataset (three classes, four predictors) and four
simulated datasets with varying sample sizes (n = 50 and n = 500) and multicollinearity
levels (ρ = 0.2 and 0.95). Performance evaluation considers estimation
stability (standard error and confidence interval width), sampling efficiency (Effective
Sample Size, ESS), and classification accuracy for category prediction. The results
indicate that Gibbs-PG produces more stable estimates, with standard errors 30–50%
lower than MH under high multicollinearity conditions. In terms of sampling efficiency,
Gibbs-PG achieves ESS values between 15,000 and 16,000, substantially higher than
MH (27–88), indicating lower autocorrelation and more efficient mixing. Classification
accuracy reaches 96.67% for the Bayesian methods using Gibbs-PG, outperforming
Maximum Likelihood Estimation (MLE), which achieves 93.33%. Overall, Gibbs-PG
proves to be the most reliable method for precise and stable parameter estimation,
especially for datasets with high multicollinearity or limited sample sizes, while MH
remains a computationally lighter alternative. | en_US |
