Schedule

Introductions. Weekly schedule and topics. Fitting a basic model with lme4::lmer.

We will begin the day discussing the format lme4 expects the data to be in for fitting models. We’ll fit a few models with the data already in this format. We’ll then move to

Walking through how the basic two- and three-level models make predictions and visualizing the difference between these predictions and the observed data.

We review content from the previous course, review Homework 1, and introduce the Gelman & Hill notation for multilevel models.

We will review Gelman & Hill notation and compare and contrast different residual variance-covariance specifications. Contrasting unstructured variance-covariance matrices with alternative specifications (e.g., independent, Toeplitz)

Thinking flexibly about time and modeling non-linear trends with polynomials basis expansion. We will also discuss data transformations (e.g., log, inverse).

Basic concepts in Bayesian estimation: prior and posterior distributions, MCMC sampling, model convergence. We will fit similar models to those fit previously in the course, but using the brms package for Bayesian inference.

Extending on the models we’ve learned previously to deal with dichotomous outcomes. We will also continue our discussion of Bayesian estimation and use Bayes to estimate thse models.

We fit several multilevel binomial logistic regression models using Bayesian estimation. We walk through two full examples, including data exploration to analysis to interpretation. This includes post-hoc comparisons computed using samples from the posterior distribution.

We’ll discuss missing data and cross-classified and multiple membership models. If time allows, we will also discuss how the multilevel binomial logistic model can be used to fit a 1PL item response theory model.

Your final project is due before midnight on the 9th