Performances of Maximum Likelihood and Bayesian Methods Used For Estimating Three-Level Hierarchical Models: A Comparative Study
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Tarih
2020
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Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
Objective: Hierarchical data with two or more levels are common in different fields of research including medical, educational, social and sports sciences. Maximum likelihood (ML) and Bayesian Markov Chain Monte Carlo (MCMC) estimation methods are widely used in regression analyses used for modelling these hierarchical data. However, the performances of these methods are not well studied for the estimation of three-level models. This paper aims at finding the optimal estimation technique under various combinations of number of clusters at second and third levels in three-level data sets. Material and Methods: A data application example is presented using a three-level dataset on football player's performance. Then, a simulation study based on the 3-level hierarchical linear model is performed for the comparison of four different maximum likelihood and Bayesian estimation approaches under various number clusters. Results: The data analysis and simulation study illustrate how strongly different estimation approaches affect the model parameter estimates, especially variance components. It is found that, if the main interest of the analysis is in the fixed part of the model, then any maximum likelihood or Bayesian method can be used, provided that the number of clusters at both levels are more than four. However, the main difference between these meth-ods occurred in estimating the random terms. Conclusion: Results of the simulation study showed that using restricted maximum likelihood method is associated with better results for both regression coefficient and variance estimates. Obtaining valid variance estimates with Bayesian MCMC estimation requires careful consideration for defining prior distributions.
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Anahtar Kelimeler
Kaynak
Türkiye Klinikleri Biyoistatistik Dergisi
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Cilt
12
Sayı
3
