Timing
3 hours weekly (2+1) during Winter Terms.

Lecturer
Herwig Friedl .

Teaching Aims
To give more emphasis on statistical modelling. Starting from the linear regression framework, results and techniques in the field of generalized linear models will be developed. To improve the student's ability to apply the theory in exploratory data analysis and further in statistical modelling. To introduce statistical software packages like R.

Learning Objectives
Students should be able to analyse real data problems by their own. They should be also familiar with the concepts of exploratory data analysis and should find and verify relationships in the data by applying the ideas of statistical modelling.

Contents
(0) Linear Regression Models. (1) Box-Cox Transformation Family. (2) Exponential Family: Members, Maximum-Likelihood Estimates (Score, Information), Quasi-Likelihood Technique. (3) Generalized Linear Models: Parameterization, Maximum-Likelihood Estimation, Pearsons' Chi-Square Statistic, Deviance and Quasi-Deviance, Modelling Over- (Under-) Dispersion. (4) Logistic Regression: Binomial Models, Logit-Models, Log Odds Ratio. (5) Loglinear Models: Poisson Models, Multinomial Responses, Contingency Tables. (6) Random Effect Models: EM (Expectation/Maximization) Algorithm, Mixture Models, Gauss-Hermite Quadrature (Approximation), Nonparametric Maximum-Likelihood Estimation, Standard Errors.

Pre-requisites
Probability, Mathematical Statistics, Computational Statistics.

Literature

• Aitkin, M.A. et al.: Statistical Modelling in GLIM, Oxford University Press, 1988.
• Friedl, H.: Linear Models, Script, Institute of Statistics, 1999.
• McCullagh, P. and Nelder, J.: Generalzed Linear Models, 2nd Edition, Chapman & Hall, 1989.

Download Homeworks:

• Homework 1 (due till oral exam)
• Homework 2 (due till oral exam)

Download Datasets:

• Aimu Data
• Aimu Data Definition File
• Bacteria Data
• Bacteria Data Definition File
• Black Cherry Trees Data
• Insects Data
• Titanic Data

Download R Macros and R Statements useful to analyze the data:

• Regression by Simulation
• Power Variance Family
• Analyze Black Cherry Trees Data
• Analyze Insects Data
• Analyze Budworm Data
• Analyze Cancer Remission Data
• Analyze Recurrence Data
• Analyze Micro-Organism Count Data

Download Slides on Linear Regression Analysis

• Chapter 1: Simple Linear Regression,
• Chapter 2: Inference in Regression Analysis,
• Chapter 3: Diagnostics,
• Chapter 4: Simultaneous Inference,
• Chapter 5: Matrix Algebra,
• Chapter 6: Multiple Linear Regression,
• Chapter 7: Extra Sums of Squares (ANOVA),
• Chapter 11: Qualitative Predictor Variables,