An introduction to hierarchical linear modeling

By H. Woltman, A. Feldstain, J. Mackay, Meredith Rocchi. 2012

803 citations recorded by the source corpus.

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.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/1e819bd22020c85ba6ceccdee02f46ed6289b174

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Citations in the corpus

Backward Feature Correction: How Deep Learning Performs Deep Learning (2020, background): “In machine learning, hierarchical learning is also the key to success for many models, such as hierarchical linear models [55], Bayesian networks/probabilistic directed acyclic graphical models [20], hierarchical Dirichlet allocation [52], hierarchical clustering [47], deep belief networks [39].”
Cracking but not Breaking: Joint Effects of Faultline Strength and Diversity Climate on Loyal Behavior (2015, background): “…climate significantly moderated the relationship between function faultline strength and loyal behavior (see Figure 2; g 5 2.70, p , .05; effect size 5 .08 based on Woltman et al. (2012)), but did not significantly moderate the relationship between tenure faultline strength and loyal behavior.”
A hierarchical interannual wheat yield and grain protein prediction model using spectral vegetative indices and meteorological data (2020, methodology): “It can incorporate hierarchical data, including nested data structures (Woltman et al., 2012; Garson, 2012).”
The role of students' self-beliefs, motivation and attitudes in predicting mathematics achievement: A multilevel analysis of the Programme for International Student Assessment data (2017, methodology): “…variable that is attributable to differences within or between the clusters and identify the factors at each level that are associated with this influence, while not underestimating the SE of the regression coefficients (OECD, 2009; Steele, 2008; Woltman, Feldstain, Mackay, & Rocchi, 2012).”
The beliefs that underlie autonomy-supportive and controlling teaching: A multinational investigation (2014, methodology): “We grand mean centered gender and grade level at level 1, because we entered these two variables as statistical controls rather than as independent predictors per se (following the centering recommendation of Woltman et al. 2012).”