ST813: Statistical Modelling (10 ECTS)

STADS: 25002701

Level
Master's level course

Teaching period
The course is offered in the spring semester.

Teacher responsible
Email: colchero@imada.sdu.dk

Timetable
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Comment:
Ubegrænset deltagerantal.

Prerequisites:
None

Academic preconditions:
The material from the course ST521: Mathematical Statistics assumed known. Knowledge of linear algebra corresponding to the course MM538: Algebra and Linear Algebra.

Course introduction
Statistical modelling consists of methods to develop and critically evaluate a statistical model for a given data set, in order to draw correct statistical conclusions from the given data. The course aims at familiarizing the participants with the basic principles and methods of statistical modelling. The course includes both linear models estimated using ordinary least squares and generalized linear models estimated using quasi-likelihood and maximum likelihood. Participants will learn to implement and evaluate the methods in the statistical software package R.

Qualifications
Participants will gain insight into the mathematical structure of linear and generalized linear models, including experience in recognizing such models from a given statistical problem. Participants will develop skills in handling the models' mathematical and statistical properties, in order to:

• recognize the different types of statistical models and describe their similarities and differences, and explain the role that the response variable, explanatory variables, variance function and link function play for statistical modeling;
• be able to manipulate the mathematical and statistical elements of linear and generalized linear models, such as parameters and principles of estimation, the derivation of statistical tests based on standard errors deviance and residual sum of squares;
• obtain an overview of the most important examples of linear and generalized linear models, and to derive theoretical properties of new models based on the general theory;
• recognize the importance of and the difference between regression and dispersion parameters, and use this knowledge in practical and theoretical contexts:
• carry out practical data analysis using statistical modeling, including investigation of a model’s adequacy using residual analysis;
• perform the statistical analysis using the statistical software R, including the ability to identify and interpret relevant information in the program output;
• document the results of a statistical analysis in the form of a written report.

Expected learning outcome
After completing the course the participant is expected to:

• have an overview of the various types of linear and generalized linear models and the main examples of these, as well as to identify which problems can be solved by means of such models;
• be skilled at manipulating the mathematical and statistical elements of linear and generalized linear models and to clearly distinguish between exact and asymptotic results;
• know how to securely apply the theoretical results for linear and generalized linear models to concrete examples and explain the practical interpretation of the results;
• have familiarity with the statistical package R, and routine in its use for statistical modeling.

Subject overview
Linear models, simple and multiple regression. Parameter estimation, hypothesis tests and confidence regions. Residual analysis. Transformation of variables, polynomial regression. The one-way ANOVA model. Model building and variable selection. Prediction. Natural exponential families; moment generating functions; variance functions; dispersion models; likelihood theory; chi -square, F- and t-tests; analysis of deviance; residual analysis; iterative least- squares algorithm; normal-theory linear models, logistic regression, analysis of count data, positive data.

Literature

Meddeles ved kursets start.

Website
This course uses e-learn (blackboard).

Prerequisites for participating in the exam
None

Assessment and marking:

1. Project report, is evaluated by external censorship by the Danish 7-mark scale (10 ECTS). (25002702)

Reexamination in the same exam period or immediately thereafter. The reexamination can have another form than the ordinary exam.

Expected working hours
The teaching method is based on three phase model.
Intro phase: 50 hours
Skills training phase: 50 hours, hereof:
 - Tutorials: 50 hours

Educational activities Study phase: 50 hours

Language
This course is taught in Danish or English, depending on the lecturer. However, if international students participate, the teaching language will always be English.

Course enrollment
See deadline of enrolment.

Tuition fees for single courses
See fees for single courses.