an introduction to hierarchical linear modeling

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.