ST523: Statistical Modelling

Academic preconditions. Students taking the course are expected to:

• Have knowledge of linear algebra, calculus, basic statistics as presented in ST521 and MM538
• Be able to use the statistical software R

• 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.

• 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.

Planned lessons:

Total number of planned lessons: 80 hours

Hereof:

Common lessons in classroom/auditorium: 80 hours

During the lectures, terms and concepts of the topics are presented from theory as well as from examples based on actual data.

During the exercise sessions, students work with theoretical questions as well as with data-based  problems using statistical software.

Other planned teaching activities:

The students work independently with problems and the understanding of the terms and concepts of the topic.