Introduction

LMMs are statistical models for continuous outcome variables in which the residuals are normally distributed but may not be independent or have constant variance. Study designs leading to data sets that may be appropriately analyzed using LMMs include (1) studies with clustered data, such as students in classrooms, or experimental designs with random blocks, such as batches of raw material for an industrial process, and (2) longitudinal or repeatedmeasures studies, in which subjects are measured repeatedly over time or under different conditions. These designs arise in a variety of settings throughout the medical, biological, physical, and social sciences. LMMs provide researchers with powerful and flexible analytic tools for these types of data.