STA 3301 Statistical Models

STAFFING:

REQUISITES:

RATIONALE:

Linear Models and generalised linear models are very widely used statistical tools. Linear models allow us to model data with normally distributed errors and generalised linear models extend these methods to a wider family of distributions. Students seeking to specialise in statistics will need to understand and be competent in these techniques. While students are expected to have obtained some understanding of linear regression techniques in previous courses, this course offers a more mathematically complete introduction to linear models and then, building on this, extends into generalised linear models. The key functions of linear models are for describing the relationships between variables and predicting outcomes and so inference methods will be addressed in some detail. Finally, as models only give useful information when they provide an accurate reflection of the 'real world', various diagnostic tests on the appropriateness and goodness of fit of various models will be introduced.

SYNOPSIS:

This course introduces the student to linear models. Both the mathematical development and practical applications of these models will be considered. Appropriate mathematical and statistical computer programs will be used. The topics include developing multiple regression models, testing hypotheses for these models, selecting the 'best' model, diagnosing problems in model fit, developing generalised linear models, and a range of applications of generalised linear models including logistic, Poisson and log-linear models.

OBJECTIVES:

On successful completion of this course students will be able to:

1. specify a linear model, including the assumptions;
2. describe how least square and maximum likelihood estimators are calculated and specify the least squares and maximum likelihood estimators for the parameters of the linear model;
3. describe the characteristics (such as mean and variance) of the least square and maximum likelihood estimators of the parameters of the linear model;
4. describe an appropriate estimator of the error variance;
5. fit linear models using an appropriate software package;
6. use the resulting model for prediction;
7. calculate and interpret the coefficient of determination and multiple and partial correlations for the model;
8. test hypotheses about the significance of individual regression coefficients and combinations of regression coefficients;
9. test the goodness of fit of the model;
10. describe and apply a range of criteria for selecting the 'best' model;
11. conduct appropriate diagnostic checks on the model, such as analysis of residuals, checks for outliers and influential points and checks for multicollinearity and suggest possible solutions to any problems identified;
12. describe the exponential family of distributions and check whether specific distributions are members of this family;
13. find the mean and variance of a member of the exponential family of distributions;
14. specify the generalised linear model;
15. describe the role of the link function and how it is derived;
16. fit generalised linear models using appropriate software;
17. calculate the deviance and find the 'best' model using analysis of deviance;
18. fit logistic regression models to binary variables using appropriate software; and correctly interpret the results;
19. fit Poisson regression models using appropriate software and correctly interpret the results;
20. fit appropriate models to contingency table counts and test the significance of potential regressors.

TOPICS:

TEXT and MATERIALS required to be PURCHASED or accessed:

ALL textbooks and materials are available for purchase from USQ BOOKSHOP (unless otherwise stated). Orders may be placed via secure internet, free fax 1800642453, phone 07 46312742 (within Australia), or mail. Overseas students should fax +61 7 46311743, or phone +61 7 46312742. For costs, further details, and internet ordering, use the 'Textbook Search' facility at http://bookshop.usq.edu.au click 'Semester', then enter your 'Course Code' (no spaces).

REFERENCE MATERIALS:

STUDENT WORKLOAD REQUIREMENTS:

ASSESSMENT DETAILS:

NOTES:

1.

Examination dates will be available during the Semester. Please refer to Examination timetable when published.

IMPORTANT ASSESSMENT INFORMATION

1. Attendance requirements:
   There are no attendance requirements for this course. However, it is the students' responsibility to study all material provided to them or required to be accessed by them to maximise their chance of meeting the objectives of the course and to be informed of course-related activities and administration.
2. Requirements for students to complete each assessment item satisfactorily:
   To complete each of the assessment items satisfactorily, students must obtain at least 50% of the marks available for each assessment item. To complete the examination satisfactorily, students must obtain at least 50% of the marks available for the examination.
3. Penalties for late submission of required work:
   If students submit assignments after the due date without prior approval then a penalty of 10% of the total marks gained by the student for the assignment will apply for each working day late.
4. Requirements for student to be awarded a passing grade in the course:
   To be assured of a passing grade, students must demonstrate, via the summative assessment items, that they have achieved the required minimum standards in relation to the objectives of the course by satisfactorily completing all summative assessment items (the examination and assignments).
5. Method used to combine assessment results to attain final grade:
   The final grades for students will be assigned on the basis of the aggregate of the weighted marks obtained for each of the summative assessment items in the course.
6. Examination information:
   The only materials that candidates may use in the restricted examination for this course are: writing materials (non-electronic and free from material which could give the student an unfair advantage in the examination); calculators which cannot hold textual information (students must indicate on their examination paper the make and model of any calculator(s) they use during the examination.
7. Examination period when Deferred/Supplementary examinations will be held:
   Any Deferred or Supplementary examinations for this course will be held during the examination period at the end of the semester of the next offering of this course.
8. University Regulations:
   Students should read USQ Regulations 5.1 Definitions, 5.6. Assessment, and 5.10 Academic Misconduct for further information and to avoid actions which might contravene University Regulations. These regulations can be found at the URL http://www.usq.edu.au/corporateservices/calendar/part5.htm or in the current USQ Handbook.

ASSESSMENT NOTES