The Intraclass Correlation Coefficient
One of the first things that anyone typically learns in a multilevel modeling class is the Intraclass Correlation Coefficient or ICC. This is a useful statistic that is very similar to the old concept of an R² in regression analysis. It…
How to Start a Multilevel Analysis
I recently got an email from a former ICPSR student asking a question that I thought was kind of interesting. He wanted to know how to go about approaching a generic exploratory analysis with multilevel data before you have settled…
Where do random effects come from?
These notes are from a lecture I’ve given a version of a few times now (at ICPSR and UK). Basically, random effects are latent variables that can be directly estimated in a linear model and need to be approximated in…
Making Informed Choices on Fixed, Random, and Mixed Effects Models
A while back I gave a few guest lectures on multilevel and panel data modeling in an advanced econometrics class. One lecture in that I enjoyed giving was on the differences between fixed, random, and mixed effects models and the ways…
Independence across Levels in Mixed Effects Models
One issue that comes up every so often is the appropriate number of levels to have in an analysis. Any fixed or random effects model has at least two levels but you can presumably come up with more in most applications. This…
Nonlinear Multilevel Modeling is Hard
Often when people talk about multilevel modeling what they really mean is HLM (hierarchical linear modeling). This is a multilevel model for a linear(ish) and continuous(ish) dependent variable and it amounts to a relatively trivial complication for a GLS model…
Multilevel Data Structure
One of the basic assumptions of most standard statistical models is that the data are independent and identically distributed or that they do not have meaningful correlations among observations once we account for all of your independent variables of interest….
On Multilevel Modeling
If there’s one methodological area that I know better than and use more than any other it’s multilevel/mixed effects modeling. These are models that fit data with unobserved heterogeneity from some missing variables. In other words, your model isn’t perfect…