Unit of study_

# STAT4022: Linear and Mixed Models

Classical linear models are widely used in science, business, economics and technology. This unit will introduce the fundamental concepts of analysis of data from both observational studies and experimental designs using linear methods, together with concepts of collection of data and design of experiments. You will first consider linear models and regression methods with diagnostics for checking appropriateness of models, looking briefly at robust regression methods. Then you will consider the design and analysis of experiments considering notions of replication, randomisation and ideas of factorial designs. Throughout the course you will use the R statistical package to give analyses and graphical displays. This unit includes material in STAT3022 Applied Linear Models, but has an additional component on the mathematical techniques underlying applied linear models together with proofs of distribution theory based on vector space methods.

Code STAT4022 Mathematics and Statistics Academic Operations 6
 Prerequisites: ? None None STAT3012 or STAT3912 or STAT3022 or STAT3922 or STAT3004 or STAT3904 Material in DATA2X02 or equivalent and MATH1X02 or equivalent; that is, a knowledge of applied statistics and an introductory knowledge to linear algebra, including eigenvalues and eigenvectors

At the completion of this unit, you should be able to:

• LO1. Formulate, interpret and compare multiple types of linear regression and making inferences on all parameters of the model.
• LO2. Construct, interpret, and apply multi-strata ANOVA tables
• LO3. Explain the theoretical aspects of linear models and linear mixed models.
• LO4. Design and explain appropriate schemes and analysis for treatment allocation and data collection in common experimental designs.
• LO5. Identify and explain important features of experimental designs.
• LO6. Apply, formulate and interpret linear mixed models.
• LO7. Devise an experimental design or modelling approach to solve a problem and communicate the outcomes using the statistical programming language R.
• LO8. Derive and re-create proofs of theoretical aspects of regression methods.

## Unit outlines

Unit outlines will be available 1 week before the first day of teaching for the relevant session.