Unit of study_

# STAT4022: Linear and Mixed Models

## Overview

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.

### Unit details and rules

Unit code STAT4022 Mathematics and Statistics Academic Operations 6 STAT3012 or STAT3912 or STAT3022 or STAT3922 or STAT3004 or STAT3904 None None 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 Yes

### Teaching staff

Coordinator Linh Nghiem, linh.nghiem@sydney.edu.au

## Assessment

Type Description Weight Due Length
Final exam (Take-home short release) Final Exam
Final examination
50% Formal exam period 2 hours
Outcomes assessed:
Answers with calculations. Submitted through Turnitin
10% Mid-semester break
Due date: 22 Apr 2022 at 23:59

Closing date: 22 Apr 2022
Variable
Outcomes assessed:
Online Quiz 1 during Thursday lecture
10% Week 04 50 minutes
Outcomes assessed:
Online Quiz 2 during Thursday lecture
10% Week 10 50 minutes
Outcomes assessed:
Project with a report and/or presentation
20% Week 13
Due date: 29 May 2022 at 23:59

Closing date: 29 May 2022
Variable
Outcomes assessed:
= group assignment
= Type D final exam

### Assessment summary

Detailed information for each assessment can be found on Canvas.

Final exam: If a second replacement exam is required, this exam may be delivered via an alternative assessment method, such as a viva voce (oral exam). The alternative assessment will meet the same learning outcomes as the original exam. The format of the alternative assessment will be determined by the unit coordinator.

### Assessment criteria

Resultname Markrange Description

High distinction

85 -100

Representing complete or close to complete mastery of the material.

Distinction

75-84

Representing excellence, but substantially less than complete mastery.

Credit

65-74

Representing a creditable performance that goes beyond routine knowledge and understanding, but less than excellence.

Pass

50-64

Representing at least routine knowledge and understanding over a spectrum of topics and important ideas and concepts in the course.

Fail

0-49

When you don’t meet the learning outcomes of the unit to a satisfactory standard.

### Late submission

In accordance with University policy, these penalties apply when written work is submitted after 11:59pm on the due date:

• Deduction of 5% of the maximum mark for each calendar day after the due date.
• After ten calendar days late, a mark of zero will be awarded.

The Current Student website  provides information on academic integrity and the resources available to all students. The University expects students and staff to act ethically and honestly and will treat all allegations of academic integrity breaches seriously.

We use similarity detection software to detect potential instances of plagiarism or other forms of academic integrity breach. If such matches indicate evidence of plagiarism or other forms of academic integrity breaches, your teacher is required to report your work for further investigation.

You may only use artificial intelligence and writing assistance tools in assessment tasks if you are permitted to by your unit coordinator, and if you do use them, you must also acknowledge this in your work, either in a footnote or an acknowledgement section.

Studiosity is permitted for postgraduate units unless otherwise indicated by the unit coordinator. The use of this service must be acknowledged in your submission.

## Learning support

### Simple extensions

If you encounter a problem submitting your work on time, you may be able to apply for an extension of five calendar days through a simple extension.  The application process will be different depending on the type of assessment and extensions cannot be granted for some assessment types like exams.

### Special consideration

If exceptional circumstances mean you can’t complete an assessment, you need consideration for a longer period of time, or if you have essential commitments which impact your performance in an assessment, you may be eligible for special consideration or special arrangements.

Special consideration applications will not be affected by a simple extension application.

### Using AI responsibly

Co-created with students, AI in Education includes lots of helpful examples of how students use generative AI tools to support their learning. It explains how generative AI works, the different tools available and how to use them responsibly and productively.

## Weekly schedule

WK Topic Learning activity Learning outcomes
Week 01 R Programming basics, simple linear regression Lecture (3 hr)
Week 02 Review of linear algebra, fitting multiple linear regression models Lecture and tutorial (3 hr)
Week 03 Inference for multiple regression model, extra sum of squares Lecture and tutorial (3 hr)
Week 04 Model diagnostics, leverage, outliers and influential analysis; multicollinearity Lecture and tutorial (3 hr)
Week 05 Model evaluation, variable selection, automated search procedure Lecture and tutorial (3 hr)
Week 06 Polynomial regression, additive and interaction models, models with qualitative variables Lecture and tutorial (3 hr)
Week 07 One-way and two-way ANOVA models, multiple comparison Lecture and tutorial (3 hr)
Week 08 Basic principles of experimental design, complete and fractional factorial designs Lecture and tutorial (3 hr)
Week 09 Block designs: complete, incomplete block designs, Latin-square designs Lecture and tutorial (3 hr)
Week 10 Analysis of covariance, nested factors, nested designs Lecture and tutorial (3 hr)
Week 11 Fixed and random effects, variance component estimation Lecture and tutorial (3 hr)
Week 12 Mixed effects models Lecture and tutorial (3 hr)
Week 13 Longitudional data, revision Lecture and tutorial (3 hr)
Weekly Computer lab on weekly topic Computer laboratory (1 hr)

### Study commitment

Typically, there is a minimum expectation of 1.5-2 hours of student effort per week per credit point for units of study offered over a full semester. For a 6 credit point unit, this equates to roughly 120-150 hours of student effort in total.

## Learning outcomes

Learning outcomes are what students know, understand and are able to do on completion of a unit of study. They are aligned with the University's graduate qualities and are assessed as part of the curriculum.

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.

The graduate qualities are the qualities and skills that all University of Sydney graduates must demonstrate on successful completion of an award course. As a future Sydney graduate, the set of qualities have been designed to equip you for the contemporary world.

 GQ1 Depth of disciplinary expertise Deep disciplinary expertise is the ability to integrate and rigorously apply knowledge, understanding and skills of a recognised discipline defined by scholarly activity, as well as familiarity with evolving practice of the discipline. GQ2 Critical thinking and problem solving Critical thinking and problem solving are the questioning of ideas, evidence and assumptions in order to propose and evaluate hypotheses or alternative arguments before formulating a conclusion or a solution to an identified problem. GQ3 Oral and written communication Effective communication, in both oral and written form, is the clear exchange of meaning in a manner that is appropriate to audience and context. GQ4 Information and digital literacy Information and digital literacy is the ability to locate, interpret, evaluate, manage, adapt, integrate, create and convey information using appropriate resources, tools and strategies. GQ5 Inventiveness Generating novel ideas and solutions. GQ6 Cultural competence Cultural Competence is the ability to actively, ethically, respectfully, and successfully engage across and between cultures. In the Australian context, this includes and celebrates Aboriginal and Torres Strait Islander cultures, knowledge systems, and a mature understanding of contemporary issues. GQ7 Interdisciplinary effectiveness Interdisciplinary effectiveness is the integration and synthesis of multiple viewpoints and practices, working effectively across disciplinary boundaries. GQ8 Integrated professional, ethical, and personal identity An integrated professional, ethical and personal identity is understanding the interaction between one’s personal and professional selves in an ethical context. GQ9 Influence Engaging others in a process, idea or vision.