# ST523: Statistical Modelling

## Comment

## Entry requirements

## Academic preconditions

Academic preconditions. 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

- 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

- 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

- 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

## Examination regulations

## Exam element a)

## Timing

## Tests

## 2 take-home assignments, graded overall

## EKA

## Assessment

## Grading

## Identification

## Language

## Examination aids

## ECTS value

## Indicative number of lessons

## Teaching Method

The teaching method is based on three phase model.

- Intro phase: 48 hours
- Skills training phase: 32 hours, hereof: Tutorials: 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

- 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 | Department | |
---|---|---|

Birgit Debrabant | bdebrabant@imada.sdu.dk | Institut for Matematik og Datalogi (00) |