Upon successful completion of this course, the student will be able to:
Gaussian Linear Models
Demonstrate the application of Gaussian Linear Models for observational studies and designed experiments.
Solve problems using random vectors.
Understand derivation and distribution of linear and quadratic forms.
Understand definitions and properties of multivariate normal, non-central chi-square, t, and F distributions.
Derive maximum likelihood
Derive maximum likelihood estimates of parameters in a linear model with normal, independent errors.
Linear models estimates
Derive the properties of linear models estimates (Gauss-Markov Theorem, Wald tests).
Unconstrained and con-strained models
Derive tests on linear hypotheses by estimation of both the unconstrained and con-strained model (full and reduced LRT/ANOVA).
Cell means model
Apply the cell means model in one-way and multiway fixed designs, interpret parame- ters from alternative model reparameterizations, estimability.
Explore consequences of model assumption violations and use regression diagnostics to identify possible model violations.
Derive theoretical consequences of overfitting and underfitting in model selection.