S-043/Stat-151: Multilevel and Longitudinal Models





Data often have structure that needs to be modeled explicitly. For example, when investigating students' outcomes we need to account for the fact that students are nested inside classes that are in turn nested inside schools. If we are watching students develop over time, we need to account for the dependence of measurements across time. If we do not, our inferences will tend to be overly optimistic and wrong. The course provides an overall framework, the multilevel and generalized multilevel (hierarchical) model, for thinking about and analyzing these forms of data. We will focus on specific versions of these tools for the most common forms of longitudinal and clustered data. This course will focus on applied work, using real data sets and the statistical software R. R will be specifically taught and supported. While the primary focus will be on the linear model with continuous outcomes (i.e., the classic regression framework) we will also discuss binary, categorical, and ordinal outcomes. We will emphasize how to think about the applicability of these methods, how they might fail, and what one might do to protect oneself in such circumstances. Applications of hierarchical (multi-level) models will include the canonical specific cases of random-slope, random-intercept, mixed effect, crossed effect, marginal, and growth-curve models.