Hi everyone,
I'm posting the slides from the intro to MLM presented last week. In addition, there are three slides showing generic multilevel regression model formulas (for a random effect two-level model). To keep us on time today, I would like us to bring the discussion about these concepts to the form. Please post any questions or points for discussion below this thread. This is a concept and methodological approach that will continue to surface throughout the course and during future health disparities research discussions.
MLM are models where parameters vary at more than one level and are appropriate for nested data structures (students nested within schools or repeated measures nested within individuals).
As an [attempted] simple example of a two-level model. At Level 1, both the intercepts and slopes in the clusters can be either fixed (meaning that all clusters have the same values), non-randomly varying (meaning that the intercepts and/or slopes are predictable from an independent variable at Level 2), or randomly varying (meaning that the intercepts and/or slopes are different in the different clusters, and that each have their own overall mean and variance). The dependent variables are the intercepts and the slopes for the independent variables at Level 1 in the cluster at Level 2. These can be expressed as: (1) random intercepts (the scores on the dependent variable for each individual (level 1) are predicted by the intercept that varies across clusters). this provides intraclass coefficients (ICC) ; (2) Random slopes model ( slopes are allowed to vary across individuals, and therefore, the slopes are different across clusters); and (3) Random intercept and random slope model (the most complex but also most reflective of "real" world).
Remember these are still regression models. Meaning the same general model testing and building approaches (and tools) are often employed. One important thing to keep in mind is that the necessary statistical power is dependent on whether you're interested in estimating level 1 effects or level 2 effects. If level two effects, then the number of clusters (rather than the number of observations) is important. Also whether the model is a fixed vs. random effects model will also influence the statistical power needed.