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Journals / Nicel Bilimler Dergisi / 2026 / Cilt: 8 Sayı: 1

Evaluating the Performance of Bayesian Quantile Structural Equation Modeling Across Varying Sample Sizes and Error Distributions: A Simulation Study

Farklı Örneklem Büyüklükleri ve Hata Dağılımları Altında Bayesyen Kantil Yapısal Eşitlik Modellemesinin Performansının Değerlendirilmesi: Bir Simülasyon Çalışması

Zübeyde Çiçek(SÜLEYMAN DEMİREL ÜNİVERSİTESİ)0000-0003-1914-1228
Pages
18–52
Publication Date
2026-06-29
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Results show that BQSEM provides more consistent and reliable estimates than Bayesian SEM (BSEM) when error terms deviate from normality.

📌 3 Key Takeaways

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Objective & Hypothesis:Structural Equation Modeling (SEM) is commonly used to examine relationships among latent variables, but it relies on strong assumptions such as normality of error terms and focuses solely on mean effects.
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Key Findings & Data:This study evaluates the performance of BQSEM through simulation using various sample sizes (100, 500, 1000, and 3000) and error term distributions (normal, t, log-normal, and beta).
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Conclusion & Impact:Results show that BQSEM provides more consistent and reliable estimates than Bayesian SEM (BSEM) when error terms deviate from normality.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Bayesyen Yaklaşım · Kantil Regresyonu · Markov Zinciri Monte Carlo

Abstract

Structural Equation Modeling (SEM) is commonly used to examine relationships among latent variables, but it relies on strong assumptions such as normality of error terms and focuses solely on mean effects. These assumptions are not always met in practice. In contrast, Quantile Structural Equation Modeling (QSEM) does not assume normality, and allows for the interpretation of effects at different quantile levels of the outcome variable’s distribution, enabling a more detailed understanding of heterogeneous relationships. This study evaluates the performance of BQSEM through simulation using various sample sizes (100, 500, 1000, and 3000) and error term distributions (normal, t, log-normal, and beta). Quantile levels were set at 0.1, 0.5, and 0.9. Results show that BQSEM provides more consistent and reliable estimates than Bayesian SEM (BSEM) when error terms deviate from normality. All analyses were performed using Markov Chain Monte Carlo (MCMC) sampling techniques, specifically implemented through R and WinBUGS software, to estimate posterior distributions in the Bayesian framework.

Özet

Yapısal Eşitlik Modellemesi, gizil değişkenler arasındaki ilişkileri incelemede yaygın olarak kullanılan bir yöntemdir; ancak hata terimlerinin normal dağıldığı varsayımı gibi güçlü kabullere dayanmakta ve çoğunlukla yalnızca ortalama etkileri dikkate almaktadır. Bu varsayımlar uygulamada her zaman sağlanamamaktadır. Buna karşılık, Kantil Yapısal Eşitlik Modellemesi normal dağılım varsayımına ihtiyaç duymamakta ve bağımlı değişkenin dağılımının farklı kantil düzeylerinde etkilerin incelenmesine olanak tanıyarak ilişkilerin heterojen yapısını daha ayrıntılı biçimde ortaya koymaktadır. Bu çalışmada, Bayesyen Kantil Yapısal Eşitlik Modellemesinin performansı; farklı örneklem büyüklükleri (100, 500, 1000 ve 3000) ile farklı hata terimi dağılımları (normal, t, log-normal ve beta) altında simülasyon yöntemiyle değerlendirilmiştir. Analizlerde 0,1; 0,5 ve 0,9 kantil düzeyleri esas alınmıştır. Elde edilen bulgular, hata terimlerinin normal dağılımdan saptığı durumlarda Bayesyen Kantil Yapısal Eşitlik Modellemesinin, Bayesyen Yapısal Eşitlik Modellemesine kıyasla daha tutarlı ve güvenilir tahminler sunduğunu göstermektedir. Tüm analizler, Bayesyen çerçevede sonsal dağılımlarını tahmin etmek amacıyla, özellikle R ve WinBUGS yazılımları kullanılarak Markov Zinciri Monte Carlo örnekleme teknikleri ile gerçekleştirilmiştir.

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Cite This Article

Çiçek, Z. (2026). Evaluating the Performance of Bayesian Quantile Structural Equation Modeling Across Varying Sample Sizes and Error Distributions: A Simulation Study. Nicel Bilimler Dergisi, Cilt: 8 Sayı: 1, 18–52. https://doi.org/10.51541/nicel.1916264

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