Essex University Summer School Jeff Gill Voice: 314-935-9012 Fax: 314-935-5856 Multilevel Modeling Workshop Course Description: This course covers statistical model development with explicitly defined hierarchies. Such multilevel specifications allow researchers to account for different structures in the data and provide for the modeling of variation between defined groups. The course begins with simple nested linear models and proceeds on to non-nested models, multilevel models with dichotomous outcomes, and multilevel generalized linear models. In each case, a Bayesian perspective on inference and computation is featured. The focus on the course will be practical steps for specifying, fitting, and checking multilevel models with much time spent on the details of computation in the R and bugs environments. Prerequisite Details: This course assumes only a knowledge of basic statistics as taught in a first year graduate sequence. Topices should include: probability, cross-tabulation, basic statistical summaries, and linear regression in either scalar or matrix form. Knowledge of matrix algebra is convenient but not required. Course Grade: The final grade will be based on three components: daily attendance and participation (20%), homework (60%), and a review paper (20%). Details provided. Readings should be completed before class. Office Hours: TBD. Required Reading: Gelman and Hill, "Data Analysis Using Regression and Multilevel/Hierarchical Models (Cambridge University Press 2007). Some papers will be available at jstor.org or distributed by the instructor. Topics (subject to change): Review of Single-level Regression linear regression basics specification of covariates interactions and lags standard inference assumptions and diagnostics prediction and validation transformations Logistic Regression Models specification interpreting the logistic regression coeffcients interpreting interactions evaluating, checking, and comparing fitted models Identifiability and separation Generalized Linear Models Poisson link function logistic-binomial model probit regression multinomial regression robust regression using the student's-t model Simulation of Probability Models and Statistical Inferences basics of simulation of probability models summarizing linear regressions using simulation simulation for nonlinear predictions predictive simulation for GLMs Simulation for checking statistical procedures and models fake-data simulation simulating from the fitted model and comparing to actual data using predictive simulation to check the assumptions of time-series models Causal Inference Using Regression on the Treatment Variable predictive comparisons problems with causal inference the role of randomization observational studies intermediate outcomes and causal paths Multilevel structures varying-intercept and varying-slope models clustered data repeated measurements, time-series cross sections, non-nested structures indicator variables and fixed or random effects Multilevel linear models: the basics defining convenient notation partial pooling with and without predictors fitting multilevel models in R different ways to write the same model group-level predictors model building and problems with traditional statistical significance predictions for new observations Multilevel Linear Models: Varying Slopes and Non-Nested Models varying intercepts and slopes varying slopes without varying intercepts modeling multiple varying coeffcients using the scaled inverse-Wishart distribution understanding correlations between group-level intercepts and slopes specifying non-nested models selecting, transforming, and combining regression inputs Multilevel Generalized Linear Models logistic model for state-level opinions from national polls item-response and ideal-point models non-nested overdispersed model overdispersed Poisson regression ordered categorical regression non-nested negative-binomial model Review of Model Fitting in R and Bugs R's model syntax writing likelihood functions and finding their mode using R the principles of modeling in Bugs Specifying and Fitting Multilevel Modeling in Bugs and R Bayesian inference and prior distributions fitting and understanding a varying-intercept multilevel model using R and Bugs adding individual- and group-level predictors predictions for new observations open-ended modeling in Bugs varying-intercept, varying-slope models varying intercepts and slopes with group-level predictors non-nested models multilevel logistic regression multilevel Poisson regression multilevel ordered categorical regression latent-data parameterizations of generalized linear models Likelihood and Bayesian Inference and Computation Bayesian and non-Bayesian inference for classical and multilevel regression Gibbs sampler for multilevel linear models likelihood inference, Bayesian inference, and the Gibbs sampler: the case of censored data metropolis algorithm for more general Bayesian computation specifying a log posterior density, Gibbs sampler, and Metropolis algorithm in R Sample Size and Power Calculations choices in the design of data collection classical power calculations: general principles classical power calculations for continuous outcomes multilevel power calculation for cluster sampling multilevel power calculation using fake-data simulation Understanding and summarizing the fitted models uncertainty and variability superpopulation and finite-population variances contrasts and comparisons of multilevel coefficients average predictive comparisons R-square and explained variance summarizing the amount of partial pooling multiple comparisons and statistical significance Analysis of variance classical analysis of variance ANOVA and multilevel linear and generalized linear models summarizing multilevel models using ANOVA ANOVA using multilevel models adding predictors: analysis of covariance and contrast analysis Causal inference using multilevel models multilevel aspects of data collection estimating treatment effects in a multilevel observational study treatments applied at different levels instrumental variables and multilevel modeling Model checking and comparison principles of predictive checking example: a behavioral learning experiment model comparison and deviance