STATS 7054 - Statistical Modelling

North Terrace Campus - Semester 1 - 2014

One of the key requirements of an applied statistician is the ability to formulate appropriate statistical models and then apply them to data in order to answer the questions of interest. Most often, such models can be seen as relating a response variable to one or more explanatory variables. For example, in a medical experiment we may seek to evaluate a new treatment by relating patient outcome to treatment received while allowing for background variables such as age, sex and disease severity. In this course, a rigorous discussion of the linear model is given and various extensions are developed. There is a strong practical emphasis and the statistical package R is used extensively. Topics covered are: the linear model, least squares estimation, generalised least squares estimation, properties of estimators, the Gauss-Markov theorem; geometry of least squares, subspace formulation of linear models, orthogonal projections; regression models, factorial experiments, analysis of covariance and model formulae; regression diagnostics, residuals, influence diagnostics, transformations, Box-Cox models, model selection and model building strategies; ; logistic regression models; Poisson regression models.

  • General Course Information
    Course Details
    Course Code STATS 7054
    Course Statistical Modelling
    Coordinating Unit Statistics
    Term Semester 1
    Level Postgraduate Coursework
    Location/s North Terrace Campus
    Units 3
    Contact Up to 3 hours per week
    Prerequisites MATHS 1012
    Assumed Knowledge STATS 2107
    Assessment ongoing assessment 30%, exam 70%
    Course Staff

    Course Coordinator: Andrew Metcalfe

    Course Timetable

    The full timetable of all activities for this course can be accessed from Course Planner.

  • Learning Outcomes
    Course Learning Outcomes
    1. Explain the mathematical basis of the linear model and its extensions to the generalised linear model and non-linear models.

    2. Use the open sources programming language R for the analysis of data arising from surveys and designed experiments, and for the analysis of time series.

    3. Write a report of a statistical analysis that explains the purpose of the investigation; summarises the findings of the investigation; and documents evidence for the conclusions.

    4. Explain the role of statistical modelling in discovering information; making predictions and decision making in a range of applications including engineering, science, business, and social science.
    University Graduate Attributes

    This course will provide students with an opportunity to develop the Graduate Attribute(s) specified below:

    University Graduate Attribute Course Learning Outcome(s)
    Knowledge and understanding of the content and techniques of a chosen discipline at advanced levels that are internationally recognised. 1
    The ability to locate, analyse, evaluate and synthesise information from a wide variety of sources in a planned and timely manner. 2
    An ability to apply effective, creative and innovative solutions, both independently and cooperatively, to current and future problems. 4
    Skills of a high order in interpersonal understanding, teamwork and communication. 3
    A proficiency in the appropriate use of contemporary technologies. 2
    A commitment to continuous learning and the capacity to maintain intellectual curiosity throughout life. 4
    A commitment to the highest standards of professional endeavour and the ability to take a leadership role in the community. 4
    An awareness of ethical, social and cultural issues within a global context and their importance in the exercise of professional skills and responsibilities. 4
  • Learning Resources
    Required Resources
    Recommended Resources
    Recommended resources include the following texts, which are available in the Barr Smith Library.

    The R Book (1e), Crawley MJ, 2007.
    Nonlinear Regression with R, Hornik K & Parmigiani G, 2009.
    Applied Regression Analysis (3e), Draper NR & Smith H, 1998.
    An introduction to generalised linear models (2e), Dobson AJ, 2002.
    Generalised linear models, McCullagh P & Nelder JA, 1983.
    Statistics a guide to the unknown, Tanur J (ed), 1972
    The Pleasures of Statistics, Mosteller F, Fienberg SE, Hoaglin DC & Tanur JM, 2010.
    Bayesian ideas and data analysis, Christensen R, Johnson WO, Branscum AJ & Hanson TE, 2011.

    The journal Significance, American Statistical Association & Royal Statistical Society, is particularly relevant and is available through the Barr Smith Library.

    The journal The American Statistician, American Statistical Association, has useful expository articles on statistical modelling.

    The internet is also an excellent resource, but you need to be selective.
  • Learning & Teaching Activities
    Learning & Teaching Modes
    Two 1-hour lectures per week.

    Practical class, analysing data with R, 1 hour in Weeks 1, 3, 5, 7, 9, 11.

    Tutorials, 1 hour in Weeks 2, 4, 6, 8, 10, 12.

    The information below is provided as a guide to assist students in engaging appropriately with the course requirements.

    Activity Number  Workload hours
    Lectures 24 82
    Practicals 6 12
    Tutorials 6 12
    Group presentations 2 20
    Assignments 5 30
    TOTAL 156
    Learning Activities Summary
    Week Topic
    1 Mathematical models, statistical modelling, random number generation, Gibbs sampler, Metropolis-Hastins sampler.
    2 Bivaraite distributions. Correlation and regression in a bivariate normal distribution. Measurement error model.
    3 Multiple regression - linear model and geometry of least squares.
    4 Multiple regression - model building.
    5 Multiple regression - diagnostics and prediction.
    6 Multiple regression - application to designed experiments.
    7 Multiple regression - application to time series models.
    8 Non-linear regression.
    9 Generalised linear model - logistic regression.
    10 Generalised linear model - count data.
    11 Linear mixed effects model.
    12 Bayesian models and copulas.
    Specific Course Requirements
    A background in probability and statistics as provided by a typical introductory course. Some experience of using R will be helpful, but not essential. If you have not used R before, it would be a good idea to try doing so before the course starts. You might find either of Introductory Statistics with R, Dalgaard P, 2002, or A Beginner's Guide to R, Zuur AF, 2009, which are available from the Barr Smith Library, useful.
    Small Group Discovery Experience
    You will be asked to work as part of a small group on two short presentations of applications of statistical modelling.
  • Assessment

    The University's policy on Assessment for Coursework Programs is based on the following four principles:

    1. Assessment must encourage and reinforce learning.
    2. Assessment must enable robust and fair judgements about student performance.
    3. Assessment practices must be fair and equitable to students and give them the opportunity to demonstrate what they have learned.
    4. Assessment must maintain academic standards.

    Assessment Summary
    Task Task type Week Set Week Due Weight Learning
    Tutorials (6) Formative 2,4,6,8,10,12 5% All
    Practicals (6) Formative & summative 1,3,5,7,9,11 5% All
    Group presentations (2) Summative & formative 6,12 10% All
    Assignments (5) Formative & summative 2,4,6,8,10 3,5,7,9,11 20% All
    Examination Summative 60% All
    Assessment Detail
    Task Week Set Week Due Weight
    Assignment 1 2 3 4%
    Assignment 2 4 5 4%
    Assignment 3 6 7 4%
    Assignment 4 8 9 4%
    Assignment 5 10 11 4%
    Presentation 1 2 6 5%
    Presentation 2 6 12 5%
    Tutorials 2,4,6,8,10,12 5%
    Practicals 1,3,5,7,9,11 5%

    Attendance and active participation at five out of six tutorials contributes 5% to the assessment for this course.

    The practicals are based on the use of the programming language R in a computer suite. Attendance and evidence of making substantial progress through the practical exercise contributes 5% to the assessment for this course.

    The presentation talks are group exercises, and each member of the group is expected to present part of the talk to the class and any guests. Each presentation contribues 5% to the assessment for this course.

    The first presentation will be of an application of statistical modelling from the media: news websites or newspapers; magazines including for example the Scientific American and the New Scientist.

    The second presentation will be of an application of statistical modelling from an archived journal in any discipline.

    Presentations should not be based on articles from Significance or cases from text books.

    Five assignments contribute 20%.

    The written examination contributes 60%.
    All written assignments are to be submitted to the designated hand-in boxes in the School of Mathematical Sciences with a signed cover sheet attached.
    Course Grading

    Grades for your performance in this course will be awarded in accordance with the following scheme:

    M10 (Coursework Mark Scheme)
    Grade Mark Description
    FNS   Fail No Submission
    F 1-49 Fail
    P 50-64 Pass
    C 65-74 Credit
    D 75-84 Distinction
    HD 85-100 High Distinction
    CN   Continuing
    NFE   No Formal Examination
    RP   Result Pending

    Further details of the grades/results can be obtained from Examinations.

    Grade Descriptors are available which provide a general guide to the standard of work that is expected at each grade level. More information at Assessment for Coursework Programs.

    Final results for this course will be made available through Access Adelaide.

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