Recursive Partitioning in the Presence of Multilevel Data

Abstract

Researchers in the social and behavioral sciences are increasingly working with data that are sampled at multiple levels, where individuals at the first level are nested within clusters at the second level, and in some cases these level-2 clusters are nested within clusters at a third level. Examples of this type of data structure can be found in large scale data programs such as the National Assessment of Educational Progress (NAEP), the Program for International Student Assessment (PISA), and Trends in International Mathematics and Science Study (TIMMS), among others. Such data require the use of special data analysis strategies that appropriately account for the presence of the multilevel data structure, in order to avoid parameter estimation bias. Simultaneous with this increase in research being done using multilevel models, has been the use of data mining techniques to fully explore relationships among variables in large and complex data files. Of these approaches, one of the most popular involves recursive partitioning methods such as classification and regression trees, and random forests. Until very recently, multilevel versions of these partitioning models were not available, leading to difficulties for researchers working with multilevel data structures who want to use recursive partitioning. This study showcases two such methods for recursive partitioning in the multilevel data context. Detailed analyses are conducted, results of these analyses are discussed, and implications of the models are described. The R code used to carry out these analyses is provided in the appendix to the manuscript.