Regression analysis with dependent data Kerby Shedden Department of Statistics, University of Michigan November 14, 2021 1 / 53 Dependent data Ordinary least squares (OLS) is most appropriate for uncorrelated and homoscedastic data with a

Decomposing Variance Kerby Shedden Department of Statistics, University of Michigan October 10, 2021 1 / 40 Law of total variation For any regression model involving a response y ∈ R and a covariate vector x ∈ Rp , we can decompose the

Specification Errors, Measurement Errors, Confounding Kerby Shedden Department of Statistics, University of Michigan October 20, 2021 1 / 42 An unobserved covariate Suppose we have a data generating model of the form y = α + βx + γz + .

Prediction Kerby Shedden Department of Statistics, University of Michigan October 27, 2021 1 / 27 Prediction analysis In a prediction-oriented analysis, we fit a model to capture the conditional mean relationship between independent variables

Model selection Kerby Shedden Department of Statistics, University of Michigan November 8, 2021 1 / 24 Background Suppose we observe data y and are considering a family of models fθ that may approximately describe how y was generated. If we

Generalized Linear Models Kerby Shedden Department of Statistics, University of Michigan December 6, 2021 1 / 52 Motivation for nonlinear models The key properties of a linear model are that E [y |X ] = X β and var[y |X ] ∝ I . In some

Generalized Estimating Equations Kerby Shedden Department of Statistics, University of Michigan December 6, 2021 1 / 28 Score equations Suppose we have multivariate Gaussian data with mean structure E [y |X ] = X β and covariance structure

Regression diagnostics Kerby Shedden Department of Statistics, University of Michigan October 31, 2021 1 / 46 Motivation When working with a linear model with design matrix X , the conventional linear model is based on the following

Fitting and inference for linear models using least squares Kerby Shedden Department of Statistics, University of Michigan October 12, 2021 1 / 171 Goals and terminology The goal is to learn about an unknown function f that relates variables