# ST813: Statistical Modelling

Study Board of Science

Teaching language: Danish or English depending on the teacher, but English if international students are enrolled
EKA: N370004102
Assessment: Second examiner: External
Offered in: Odense
Offered in: Autumn
Level: Master's level course approved as PhD course

ECTS value: 10

Date of Approval: 24-04-2024

Duration: 1 semester

Version: Approved - active

## Comment

The course is co-read with ST523.

## Entry requirements

The course cannot be chosen if you have passed, registered, or have followed ST523, or if ST523 is a constituent part of your Curriculum.

Students taking the course are expected to:

• Have knowledge of linear algebra, calculus, basic statistics
• Be able to use the statistical software R

## Course introduction

The aim of the course is to enable the student to work with linear and generalized linear models from a theoretical as well as applied perspective. Students will gain insight into the mathematical structure of linear and generalized linear models, including experience in recognizing such models from a given statistical problem.
The course builds on the knowledge acquired in the courses ST521: Mathematical Statistics and on knowledge of linear algebra corresponding to the course MM505 Linear Algebra or MM538: Algebra and Linear Algebra, and gives an academic basis for advanced courses in statistics and master thesis projects.

In relation to the competence profile of the degree it is the explicit focus of the course to:
• Give the competence to handle model building and/or model calculations.
• Give skills to perform statistical analyses.
• Give theoretical knowledge about and practical experience with the application of methods and models in statistics.

## Expected learning outcome

The learning objective of the course is that the student demonstrates the ability 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;
• 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;
• derive theoretical properties of new models based on the general theory and clearly distinguish between exact and asymptotic results;
• give an overview of the most important examples of linear and generalized linear models as well as identify which problems can be solved by means of such models;
• apply the theoretical results for linear and generalized linear models to concrete examples and explain the practical interpretation of the results
• 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.

## Content

The following main topics are contained in the course:
• 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;
• Iterative least- squares algorithm;
• Normal-theory linear models,
• Logistic regression,
• Analysis of count data, positive data.
• Applications of statistical modelling to different data types, amongst others examples from health sciences, biology, economy, etc.

## Literature

See itslearning for syllabus lists and additional literature references.

Autumn

N370004102

## Assessment

Second examiner: External

## Language

Normally, the same as teaching language

## Examination aids

To be announced during the course

10

## Indicative number of lessons

80 hours per semester

## Teaching Method

The teaching activities are reflected in an estimated allocation of the workload of an average student as follows:

• Intro phase (lectures) - 48 hours
• Training phase: 32 hours

In the intro phase a modified version of the classical lecture is employed, where the terms and concepts of the topic are presented, from theory as well as from examples based on actual data. In these hours there is room for questions and discussions. In the training phase the students work with data-based problems and discussion topics, related to the content of the previous lectures in the intro phase. In these hours there is a possibility of working specifically with selected difficult concepts. In the study phase the students work independently with problems and the understanding of the terms and concepts of the topic. Questions from the study phase can afterwards be presented in either the intro phase hours or the training phase hours.

Educational activities in which the students are expected to:

• Work with the new concepts and terms introduced.
• Increase their understanding of the topics covered during the lectures.
• Solve relevant exercises.
• Read the text book chapters and the scientific journal articles provided as support for the lectures

## Teacher responsible

Name E-mail Department

## Timetable

##### Odense
Show full time table

Institut for Matematik og Datalogi (matematik)

NAT

Odense

## Recommended course of study

Profile Education Semester Offer period

## Transition rules

Transitional arrangements describe how a course replaces another course when changes are made to the course of study.
If a transitional arrangement has been made for a course, it will be stated in the list.
See transitional arrangements for all courses at the Faculty of Science.