Article

Hierarchical Linear Modeling with Maximum Likelihood, Restricted Maximum Likelihood, and Fully Bayesian Estimation

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Abstract

Hierarchical linear modeling (HLM) is a useful tool when analyzing data collected from groups. There are many decisions to be made when constructing and estimating a model in HLM including which estimation technique to use. Three of the estimation techniques available when analyzing data with HLM are maximum likelihood, restricted maximum likelihood, and fully Bayesian estimation. Which estimation technique is employed determines how estimates can be interpreted and the models that may be compared. The purpose of this paper is to conceptually introduce and compare these methods of estimation in HLM and interpret the computer output that results from using them. This is done for the intraclass correlation, parameter estimates, and model fit indices using a simulated dataset that is available online. The statistical program R is utilized for all analyses and syntax is provided in Appendix 1. This paper is written to aid applied researchers who wish to better understand the differences between the estimation techniques and how to interpret their HLM results. Accessed 5,153 times on https://pareonline.net from April 12, 2017 to December 31, 2019. For downloads from January 1, 2020 forward, please click on the PlumX Metrics link to the right.

Keywords: Research Methodology, Statistical Analysis

How to Cite:

Boedeker, P., (2017) “Hierarchical Linear Modeling with Maximum Likelihood, Restricted Maximum Likelihood, and Fully Bayesian Estimation”, Practical Assessment, Research, and Evaluation 22(1): 2. doi: https://doi.org/10.7275/5vvy-8613