An introduction to hierarchical linear modeling

Abstract

This tutorial aims to introduce Hierarchical Linear Modeling (HLM). A simple explanation of HLM is provided that describes when to use this statistical technique and identifies key factors to consider before conducting this analysis. The first section of the tutorial defines HLM, clarifies its purpose, and states its advantages. The second section explains the mathematical theory, equations, and conditions underlying HLM. HLM hypothesis testing is performed in the third section. Finally, the fourth section provides a practical example of running HLM, with which readers can follow along. Throughout this tutorial, emphasis is placed on providing a straightforward overview of the basic principles of HLM.

School Effects, Gender and Socioeconomic Differences in Reading Performance: A Multilevel Analysis

“…Following Raudenbush and Willms (1995), for the purpose of this research, a school effect is defined as, "the extent to which attending a particular school modifies a student's outcome" (p. 308). This study employs hierarchical linear modeling (HLM) as a more appropriate method for analyzing data on students nested within schools (see Arnold, 1992;Raudenbush & Bryk, 2002;Raudenbush & Willms, 1995;Woltman, Feldstain, MacKay, & Rocchi, 2012 …”

The Effects of Student and Teacher Level Variables on TIMSS 2007 and 2011 Mathematics Achievement of Turkish Students

“…Çok düzeyli yapıda olan veri setlerindeki ilişkiler, HLM ile her bir düzey ve değişken için standart hatalar kestirilerek hesaplanabilmektedir. Ayrıca, tek düzeyli analizler paylaşılan varyansı dikkate almamaktadır, HLM ise her bir düzeyde paylaşılan varyansları model içine alarak kestirim yapmaktadır (Woltman, Feldstain, MacKay ve Rocchi, 2012 Tablo 2'ye göre TIMSS 2007 ve 2011 uygulamalarında okul düzeyi değişkenler içinden sadece öğretmenin akademik başarıya vurgusu öğrencilerin matematik başarısı üzerinde istatistiksel olarak manidar etkiye sahiptir. Bu etki pozitif yönde olup orta düzeydedir.…”

Challenges in Evaluating All-Cause Hospital Readmission Measures for Use as National Consensus Standards

“…Hierarchical linear modeling using a Bayesian estimator results in two coefficient estimates of the regression model for each level (patient and hospital). 12 Generalized Bayesian estimators 13 can be used to account for the simultaneous relationships and shared variance among hierarchical levels by computing a weighted combination of the two levels. 12 Furthermore, classic estimation theories do not assume prior knowledge of a distribution for variables in the regression model.…”

“…12 Generalized Bayesian estimators 13 can be used to account for the simultaneous relationships and shared variance among hierarchical levels by computing a weighted combination of the two levels. 12 Furthermore, classic estimation theories do not assume prior knowledge of a distribution for variables in the regression model. In contrast, Bayesian estimation may be used to predict hospital performance from a common prior distribution, such as performance from a previous year, or from the grand mean of the population of all hospitals.…”