Two-Level Nested Logistic Regression Model

Abstract

Studies including repeated measures are expected to give rise to correlated data. Such data are common in many disciplines including healthcare, banking, poll tracking, and education. Subjects or units are followed over time and are repeatedly observed under different experimental conditions, or are observed in clusters. Often times, such data are available in hierarchical structures consisting of a subset of a population of units at several levels. We review methods that include the clustering directly in the model (systematic component) as opposed to methods within the random component. These methods belong to the class of generalized linear mixed models. The basic idea behind generalized linear mixed models is conceptually straightforward (NSF-CBMS Regional Conference Series in Probability and Statistics. Institute of Mathematical Statistics and the American Statistical Association, Bethesda, MD, pp. 1–84, 2003) and incorporates random effects into the systematic component of a generalized linear model to account for the correlation. Such approaches are most useful when researchers wish to account for both fixed and random effects in the model. The desire to address the random effects in a logistic model makes it a subject-specific model. This is a conditional model that can also be used to model longitudinal or repeated measures data. We fit this model in SAS, SPSS, and R. Our method of modeling is based on: Lalonde, T., Nguyen, A. Q., Yin, J., Irimata, K., & Wilson, J. R. (2013). Modeling correlated binary outcomes with time-dependent covariates. Journal of Data Science, 11(4), 715–738.