## M8751 Advanced Regression Models I

Faculty of Science
Spring 2022
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Taught in person.
Teacher(s)
Mgr. David Kraus, Ph.D. (lecturer)
Guaranteed by
doc. PaedDr. RNDr. Stanislav Katina, Ph.D.
Department of Mathematics and Statistics - Departments - Faculty of Science
Supplier department: Department of Mathematics and Statistics - Departments - Faculty of Science
Prerequisites
M7222 Generalized linear models
Calculus, linear algebra, basics of probability theory and mathematical statistics, theory of estimation and hypotheses testing, linear and generalized linear models, knowledge of R software
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course offers a coverage of selected advanced regression methods and models beyond linear and generalized linear regression. The couse covers theoretical foundations, statistical models and inference, software implementation, application and interpretation.
Learning outcomes
The students will gain a deeper understanding of the methods and their relations and learn to recognize situations that can be addressed by the models discussed in the course, choose an appropriate model, implement it and interpret the results.
Syllabus
• Nonlinear parametric regression models: nonlinear least squares, Gauss--Newton method, asymptotic properties of estimators, confidence sets for parameters and response, profile likelihood, examples of parametric models.
• Regression with heteroskedastic and correlated data: linear regression with heteroskedastic errors (White estimator, weighted least squares, generalized least squares), grouped data and generalized estimating equations, serially correlated data (time series) and sandwich estimators.
• Model selection: impact of including or omitting variables on estimation and prediction, model search strategies, information criteria (AIC, BIC, their meaning and properties), cross-validation and generalized cross-validation.
• Regularization techniques: purpose and meaning of regularization, penalization methods (ridge regression, LASSO), methods based on dimension reduction (principal component regression, partial least squares), comparison, interpretation and properties, algorithms, regularization parameter selection.
• Regression models in survival analysis: censoring, censored data likelihood, parametric regression models, Cox proportional hazards model.
Literature
• VERBEKE, Geert and Geert MOLENBERGHS. Linear mixed models for longitudinal data. New York: Springer-Verlag, 2009. xxii, 568. ISBN 9781441902993. info
• KLEIN, John P. and Melvin L. MOESCHBERGER. Survival analysis : techniques for censored and truncated data. 2nd ed. New York: Springer, 2003. xv, 536. ISBN 9781441929853. info
• HASTIE, Trevor, Robert TIBSHIRANI and J. H. FRIEDMAN. The elements of statistical learning : data mining, inference, and prediction. 2nd ed. New York, N.Y.: Springer, 2009. xxii, 745. ISBN 9780387848570. info
• MOLENBERGHS, Geert and Geert VERBEKE. Models for discrete longitudinal data. New York: Springer-Verlag, 2005. ISBN 978-0-387-28980-9. info
• Survival and event history analysisa process point of view. Edited by Odd O. Aalen - Ørnulf Borgan - S. Gjessing. New York, NY: Springer, 2008. xviii, 539. ISBN 9780387202877. info
• PINHEIRO, José C. and Douglas M. BATES. Mixed-effects models in S and S-PLUS. New York: Springer, 2000. xvi, 528. ISBN 0387989579. info
Teaching methods
Lectures, exercises (all online)
Assessment methods
Oral examination, homework assignments
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught: every week.
Teacher's information
The lessons are usually in Czech or in English as needed, and the relevant terminology is always given with English equivalents.

The target skills of the study include the ability to use the English language passively and actively in their own expertise and also in potential areas of application of mathematics.

Assessment in all cases may be in Czech and English, at the student's choice.

The course is also listed under the following terms Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021.
• Enrolment Statistics (Spring 2022, recent)