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Unit of study_

# STAT4027: Advanced Statistical Modelling

## Overview

Applied Statistics fundamentally brings statistical learning to the wider world. Some data sets are complex due to the nature of their responses or predictors or have high dimensionality. These types of data pose theoretical, methodological and computational challenges that require knowledge of advanced modelling techniques, estimation methodologies and model selection skills. In this unit you will investigate contemporary model building, estimation and selection approaches for linear and generalised linear regression models. You will learn about two scenarios in model building: when an extensive search of the model space is possible; and when the dimension is large and either stepwise algorithms or regularisation techniques have to be employed to identify good models. These particular data analysis skills have been foundational in developing modern ideas about science, medicine, economics and society and in the development of new technology and should be in the toolkit of all applied statisticians. This unit will provide you with a strong foundation of critical thinking about statistical modelling and technology and give you the opportunity to engage with applications of these methods across a wide scope of applications and for research or further study.

### Unit details and rules

Unit code STAT4027 Mathematics and Statistics Academic Operations 6 None (STAT3X12 or STAT3X22 or STAT4022) and (STAT3X13 or STAT3X23 or STAT4023) None A three year major in statistics or equivalent including familiarity with material in DATA2X02 and STAT3X22 (applied statistics and linear models) or equivalent Yes

### Teaching staff

Coordinator Jennifer Chan, jennifer.chan@sydney.edu.au

## Assessment

Type Description Weight Due Length
Tutorial quiz Final exam
Final exam
40% Formal exam period
Due date: 29 Nov 2021 at 14:00

Closing date: 29 Nov 2021
2 hours
Outcomes assessed:
Skills-based evaluation Project
Report and presentation
10% STUVAC
Due date: 21 Nov 2021 at 14:00

Closing date: 21 Nov 2021
1 week
Outcomes assessed:
Assignment Assignment 1
written answers to questions
10% Week 04
Due date: 05 Sep 2021 at 11:59

Closing date: 19 Sep 2021
1 week
Outcomes assessed:
Assignment Assignment 2
Written answers to questions
10% Week 06
Due date: 19 Sep 2021 at 11:59

Closing date: 19 Sep 2021
1 week
Outcomes assessed:
Assignment Assignment 3
Written answers to questions
10% Week 09
Due date: 17 Oct 2021 at 11:59

Closing date: 17 Oct 2021
1 week
Outcomes assessed:
Assignment Assignment 4
Written answers to questions
10% Week 11
Due date: 31 Oct 2021 at 11:59

Closing date: 31 Oct 2021
1 week
Outcomes assessed:
Creative assessment / demonstration Tutorial presentation
Tutorial presentation
10% Weekly 2 weeks
Outcomes assessed:
= group assignment

### Assessment summary

Assignment 1-4: test learning outcomes 1-2, 3-4, 5-6, and 7-9 respectively. Online submission and marking by hand.

Project and presentation: test learning outcomes 1-9 and applications. Online submission and marking by hand.

### Assessment criteria

The University awards common result grades, set out in the Coursework Policy 2014 (Schedule 1).

As a general guide, a high distinction indicates work of an exceptional standard, a distinction a very high standard, a credit a good standard, and a pass an acceptable standard.

For more information see sydney.edu.au/students/guide-to-grades.

For more information see guide to grades.

### 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.

This unit has an exception to the standard University policy or supplementary information has been provided by the unit coordinator. This information is displayed below:

No late penalty

### Academic integrity

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
Weekly Estimation methods, GLM, model strategies, survivial analysis, regression for count data, regression for binary data, regression for nominal and ordinal data, regression for rate data Lecture (24 hr)
Topic presentation Tutorial (11 hr)

### Attendance and class requirements

No compulsory attendance of lectures.

Compulsory attendance of tutorials and presentations.

### 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. Apply inference methods to estimate the model parameters. These methods include maximum likelihood, expectation maximumisation, iterative re-weighted least square, M-estimation, quasi-likelihood method and generalised estimating equation.
• LO2. Understand the idea of generalised linear models and exponential family to model counts, binary data, and data with a positive domain.
• LO3. Apply the different modeling strategies to describe the location of a data distribution including generalised additive model, regime switching, quantile, mixture and state space model.
• LO4. Analyse survival data with censoring using Kaplan Meier model and perform regression using proportional hazard with Weibull, piece-wise exponential hazard and Cox's proportional hazard models.
• LO5. Perform regression for count data allowing for different levels of dispersion using mixture model and Poisson, negative binomial and generalised Poisson distributions as well as allowing for zero inflation using zero-inflated and hurdle models.
• LO6. Perform regression for binary data using logit, probit and complementary log-log link functions. Understand the properties of these models and goodness-of-fit. Apply Fisher exact test to 2x2 contingency table and measure association between two binary variables.
• LO7. Perform regression for multinominal data in contingency table with different experimental designs using log-linear model and two logit structures: multinominal and hierarchical. Explore the relationship with Poisson and binominal regressions. Interpret the types of assoication for different log-linear models. Study special cases of collapsing table, decomposable table, incomplete table, symmetric (and quasi-symmetric) table and marginal homogenous table.
• LO8. Perform regression for ordinal data using order logit link.
• LO9. Perform beta regression for rate data.

### Graduate qualities

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.

### Outcome map

Learning outcomes Graduate qualities
GQ1 GQ2 GQ3 GQ4 GQ5 GQ6 GQ7 GQ8 GQ9

## Responding to student feedback

This section outlines changes made to this unit following staff and student reviews.

No changes have been made since this unit was last offered.

## Additional information

### Disclaimer

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