37357 Advanced Statistical Modelling PDF

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SUBJECT OUTLINE 37357 Advanced Statistical Modelling Course area

UTS: Science

Delivery

Spring 2020; standard mode; City

Credit points 6cp Requisite(s)

(35101 Introduction to Linear Dynamical Systems OR 37131 Introduction to Linear Dynamical Systems OR 33230 Mathematical Modelling 2 OR 33290 Statistics and Mathematics for Science) AND (35353 Regression Analysis OR 37252 Regression Analysis OR 36103 Statistical Thinking for Data Science) These requisites may not apply to students in certain courses. See access conditions.

Result type

Grade and marks

Attendance: 2hpw (lecture style workshop, with lab review), 2hpw (computer lab)

Subject coordinator Name: James Brown Email: [email protected]

Teaching staff Lecturer: James Brown Phone: 9514 2247 Room: CB07.05.052 Email: [email protected] xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx Tutor: Torrington Callan Email: [email protected]

Subject description Statistical modelling provides a way to understand relations among a set of quantitative and/or qualitative variables. This subject focuses on developing the generalised linear modelling framework that allows us to model a wide range of response variables as a function of a set of explanatory variables. By extending standard regression models to include a range of categorical (and continuous) response variables the subject is applicable in many areas in science, engineering, health and business. The subject also covers an introduction to the estimation theory behind the model fitting, including least squares and maximum likelihood approaches.

Subject learning objectives (SLOs) Upon successful completion of this subject students should be able to: 1. Fit a model to obtain estimates together with their standard errors for a wide variety of regression problems; and analyse the adequacy and reasonableness of a particular regression model. 2. Define relevant terminology and apply the main concepts of regression analysis, and formulate simple estimation problems using maximum likelihood estimation. 3. Understand the theory of maximum likelihood estimation and apply the approach to simplified problems. 4. Formulate applied problems in regression analysis and solve them using a variety of approaches. 5. Contribute effectively and professionally in a team context. 25/07/2020 (Spring 2020)

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6. Implement advanced regression techniques to solve authentic problems using the industry standard software SAS. 7. Interpret the appropriate output from SAS and communicate clearly the results of a statistical analysis in relation to a stated problem.

Course intended learning outcomes (CILOs) This subject also contributes specifically to the development of following course intended learning outcomes: Analyse: Examine the principles and concepts of a range of fundamental areas in the mathematical sciences (calculus, discrete mathematics, linear algebra, probability, statistics and quantitative management). (1.2) Analyse: Make arguments based on proof and conduct simulations based on selection of approaches (e.g. analytic vs numerical/experimental, different statistical tests, different heuristic algorithms) and various sources of data and knowledge. (2.2) Synthesise: Apply existing strategies to new problems, and evaluate and transform information to complete a range of activities. (2.3) Analyse: Demonstrate professional and responsible analysis of real-life problems that require application of mathematics and statistics and analysis of data. (3.2) Analyse: Information retrieval and consolidation skills applied to the critical evaluation of the mathematical/statistical aspects of information to think creatively and try different approaches to solving problems. (4.2) Apply: Succinct and accurate presentation of information, reasoning and conclusions in a variety of modes, to diverse audiences (expert and non-expert). (5.1) Analyse: Demonstrate research approaches to clarify a problem or to obtain the information required to develop mathematical solutions. (5.2)

Contribution to the development of graduate attributes The Faculty of Science has determined that our courses will aim to develop the following attributes in students at the completion of their course of study. Each subject will contribute to the development of these attributes in ways appropriate to the subject and the stage of progression, thus not all attributes are expected to be addressed in all subjects. This subject contributes to the development of the following graduate attributes: 1. Disciplinary Knowledge The lectures, weekly laboratories, and SAS assignments give students the opportunity to develop skills that are necessary in a number of mathematical disciplines and demonstrate how to apply these skills to a variety of problems. 2. An Inquiry-oriented approach A major component of the weekly laboratories is the consideration of how best to apply statistical modeling techniques to a particular data set. Statisticians who work in industry are often required to use their own judgement in model building using regression analysis and this subject gives students the opportunity to develop the necessary skills. This is reinforced by the SAS assignments, which include the requirement for students to understand and interpret model outputs. 3. Professional, ethical and social responsibility The weekly laboratories help students learn to manage their own work and to accept responsibility for their own learning and, together with the assignments, they give practice in computing skills, data handling and quantitative and graphical literacy skills. The group element of one of the SAS assignments allows students to work collaboratively. 4. Reflection, Innovation, Creativity The main assignments require students to apply a suitable modeling approach to the data provided in order to answer questions similar to those that would be posed to a modeling statistician in an industry context. 5. Communication The weekly laboratories and SAS assignments allow students to present written solutions to statistical problems using appropriate professional language.

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Teaching and learning strategies During week one materials are available on UTSOnline to help you prepare for the subject, as well as an introductory lecture-style workshop. It is particularly important that you set-up an account to use SAS online - information is provided on how to do this. During semester, the subject is four hours of classes each week, consisting of lecture-style workshops, laboratory work, tutorials and discussions, supported by at least four hours per week of individual or group study. Each week there will be a two hour face-to-face session that will involve review of the previous (computer) labs and the presentation of new material. Students should then review the lecture materials, which are available on UTSOnline, in preparation for the lab following the lecture. The practical application of this material will then occur in the weekly (computer) labs that follow. During the labs, students are encouraged to discuss approaches to solving the questions with each other, as well as discussion with the tutor, but they should then complete their own independent answers. After completing the seven assessed computer labs, full solutions will be available and students are encouraged to review the lab output prior to attending the sessions the following week. General feedback will also be given following the completion of each of the first three assignments that occur during the semester. The subject makes extensive use of UTSOnline. Lecture materials are posted prior to the lectures and students are encouraged to review prior to the lecture as interaction during the lectures is encouraged. All lab solutions and discussion of the four assignments will also be available as the session progresses. Links to the extensive online materials related to SAS are embedded within the lab materials. Assignment 2 (using SAS to model categorical and count outcomes) MUST be undertaken as a group assignment. To support this, students will complete a SPARKPlus review of the contribution by each group member to ensure equity with respect to student engagement in the assignment.

Content (topics) This subject will start with revision of linear models and least squares estimation, introduce maximum likelihood estimation, and then the generalized linear modeling framework. A variety of models within the framework will then be covered including logistic regression, poisson regression and multinomial regression.

Program Week/Session

Dates

Description

1

27 Jul

Background on distribution theory covering key continuous and discrete distributions along with the idea of 'method of moments' for estimation Notes: Please ensure you have undertaken the activities published on UTSOnline, in particular those relating to SAS.

2

3 Aug

Review of the linear regression model and least squares estimation Notes: Lab 1 - using SAS to fit simple regression linear models

3

10 Aug

Review of multiple linear regression including categorical variables, interactions, and transformations Notes: Lab 2 - building multiple linear regression models in SAS

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4

17 Aug

Introduction to maximum likelihood estimation with simple one parameter (and two parameter) examples Notes: Lab 3 - Start Assignment 1 (linear regression in SAS)

5

24 Aug

The generalized linear modeling framework for the exponential family of distributions and the role of link functions Notes: Lab 4 - basic distribution theory, maximum likelihood estimation, and linking linear models to GLMs in SAS.

6

31 Aug

Special Case 1: Logistic Regression for binary (binomial) data. Notes: Lab 5 - Introduction to logistic regression in SAS.

7

7 Sep

Logistic Regression continued... Notes: Lab 6 - More logistic regression in SAS.

StuVac

14 Sep

No lecture or labs in StuVac Week

8

21 Sep

Special Case 2: Ordered Category extensions to Logistic Regression Notes: Lab 7 - Finish Assignment 1 (logistic regression in SAS)

9

28 Sep

Special Case 3: Unordered Category extensions to Logistic Regression Notes: Hand-in Assignment 1 - linear regression and logistic regression task Lab 8 - workshop on ordinal logistic regression in SAS

10

5 Oct

No Lecture - Public Holiday Notes: Lab 9 - workshop on multinomial regression in SAS

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11

12 Oct

Special Case 4: Poisson Regression for count data Notes: Lab 10 - workshop on poisson regression in SAS

12

19 Oct

Introduction to linear mixed models Notes: Lab 11 - Start Group Assignment 2 covering multiple category and count data models

StuVac

26 Oct

No lecture or labs in StuVac Week

Assessment Assessment task 1: Weekly labs Intent:

This assessment item addresses the following graduate attributes: 1. Disciplinary Knowledge 2. Research, inquiry and critical thinking 3. Professional, ethical and social responsibility 5. Communication

Objective(s): This assessment task addresses subject learning objective(s): 1, 2, 3, 6 and 7 This assessment task contributes to the development of course intended learning outcome(s): 1.2, 2.2, 3.2 and 5.1 Type:

Laboratory/practical

Groupwork: Individual Weight:

30%

Task:

The weekly lab-sheets allow students to engage in learning throughout the subject with low stakes assessments that also give regular feedback. Each week you will be given a lab sheet to complete during the computer lab. This will guide you through using SAS in relation to the topics covered in the lectures that week. You will interpret the output you generate in SAS to answer the analysis questions on the sheet.

Due:

Each lab should be submitted (hard-copy or electronic) at the end of the designated lab session. Your mark will be based on your best 6 out of 8 labs.

Criteria:

Accuracy of analysis, clarity of communication.

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Assessment task 2: SAS assignment 1 Intent:

This assessment task contributes to the development of the following graduate attributes: 1. Disciplinary Knowledge 2. Research, enquiry and critical thinking 3. Professional, ethical and social responsibility 4. Reflection, Innovation, Creativity 5. Communication

Objective(s): This assessment task addresses subject learning objective(s): 1, 2, 4, 6 and 7 This assessment task contributes to the development of course intended learning outcome(s): 1.2, 2.3, 3.2, 4.2 and 5.2 Type:

Exercises

Groupwork:

Individual

Weight:

40%

Task:

Each SAS assignment allows students to demonstrate their ability to apply SAS to real world data to both generate and interpret the modelling output. The task is to answer all the assignment questions, including performing the necessary statistical analysis and writing up the conclusions in a clear, concise manner. Questions in this assignment will relate to material covered in lectures 1 to 7 (computer labs 1, 2, 5, and 6).

Due:

Week 9 The assignment should be submitted in hard-copy or electronically at the start of your computer lab for week commencing 28/09/2020.

Criteria:

Evidence of correct use of SAS, accuracy of interpretation, appropriate choice model, clarity of communication.

Further Ensure that you submit your answer to both the linear regression and logistic regression parts. information:

Assessment task 3: SAS assignment 2 (Group Work) Intent:

This assessment task contributes to the development of the following graduate attributes: 1. Disciplinary Knowledge 2. Research, enquiry and critical thinking 3. Professional, ethical and social responsibility 4. Reflection, Innovation, Creativity 5. Communication

Objective(s): This assessment task addresses subject learning objective(s): 1, 2, 4, 5, 6 and 7 This assessment task contributes to the development of course intended learning outcome(s): 1.2, 2.3, 3.2, 4.2 and 5.2

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Type:

Exercises

Groupwork: Group, group assessed Weight:

30%

Task:

Each SAS assignment allows students to demonstrate their ability to apply SAS to real world data to both generate and interpret the modelling output. The task is to answer all the assignment questions, including performing the necessary statistical analysis and writing up the conclusions in a clear, concise manner. Questions in this assignment will relate to material covered in lectures 8 to 10 (computer labs 8 to 10).

Due:

Monday 9 November 2020 Information on handing-in will be provided nearer the time.

Criteria:

Evidence of correct use of SAS, accuracy of interpretation, appropriate choice model, clarity of communication appropriate group contribution.

Further Students are required to do this assignment in groups. It is the responsibility of the students to form information: the groups, and there is a SPARKPlus component at the end of the assignment to allow students to evaluate the contribution of each member of their group. This can lead to adjustment of the mark received by an individual student.

Assessment feedback The assessment occurs every week throughout the subject. Therefore, students will receive feedback on their progress on a regular basis.

Supplementary assessments A supplementary assignment will be offered to all students that receive an X grade.

Minimum requirements To pass, a student must obtain an overall mark greater than 50%. In addition, students must obtain at least 40% of the marks in Assessment task 2. If 40% is not reached, an X grade fail may be awarded for the subject, irrespective of an overall mark greater than 50.

Recommended texts Draper, N.R., Smith, H. (1998) Applied Regression Analysis, 3rd edition, Wiley. This book covers the initial part of the subject. Dobson, A.J. (2002) An Introduction to Generalized Linear Models, 2nd Edition, CRC. This book covers the entire content of the subject and is available electronically from the library. There is also a 3rd Edition if you are thinking of actually purchasing, which is not necessary

Other resources Field, Andy (2010) Discovering Statistics Using SAS, Sage. A basic stats text focused on using SAS Hosmer, D.W. & Lemeshow, S. (2000) Applied Logistic Regression, 2nd Edition, Wiley http://support.sas.com/training/tutorial/ - SAS provides a lot of online help to accompany the package

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Keep in mind that we will be using the programming approach - rather than the interface... Stokes, Davis, and Koch (2012) Categorical Data Analysis Using the SAS System, 3rd Edition, SAS

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