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Notifications

The next live zoom session will take place on Thursday May 20 at 9:00.

We will meet at regular live zoom sessions on Thursdays at 9:00. The contents of two consecutive lectures will be covered at each of them.

The link for zoom sessions has been provided to the enrolled students by mail. It will remain valid for all zoom sessions during the semester.

Recordings are published on an external separate site, the link is provided below.

Schedule 

Schedule is not much relevant in times of distant teaching...

Lectures
Monday   9:00 - 10:30 K4  
Thursday   9:00 - 10:30 K3  
Exercise Class
Thursday 14:00 - 15:30 K11 Instructor: Arnošt Komárek

Course Materials

Progress of lectures

  1. Monday March 1. Review of linear regression.

    Extended course notes, Chap. 1, pp. 4-9.

    Video recording:

    • lecture_01_210301.mp4: Review of linear regression (43 min.)
  2. Thursday March 4. Exponential family of distributions.

    Extended course notes, Sec. 2.1, pp. 10-16.

    Video recording:

    • lecture_02_210304.mp4: Exponential family of distributions (49 min.)
  3. Thursday March 4. Generalized linear model: definition.

    Extended course notes, Sec. 2.2, pp. 16-20.

    Video recording:

    • lecture_03_210304.mp4: Generalized linear model: definition (30 min.)
  4. Thursday March 11. MLE in the GLM: likelihood, score statistic

    Extended course notes, Sec. 2.2-2.3, pp. 20-24.

    Video recording:

    • lecture_04_210311.mp4: MLE in the GLM: likelihood, score statistic (33 min.)
  5. Thursday March 11. MLE in the GLM: information matrix. Iterative weighted least squares.

    Extended course notes, Sec. 2.3-2.4, pp. 24-27.

    Video recording:

    • lecture_05_210311.mp4: MLE in the GLM: information matrix, iterative weighted least squares (36 min.)
  6. Thursday March 18. Estimation of the Dispersion Parameter. Deviance.

    Extended course notes, Sec. 2.5-2.6, pp. 27-30.

    Video recording:

    • lecture_06_210318.mp4: Estimation of the dispersion parameter. Deviance (25 min.)
  7. Monday March 22. Asymptotics for the GLM.

    Extended course notes, Sec. 2.7, pp. 30-35.

    Video recording:

    • lecture_07_210322.mp4: Asymptotics for the GLM (40 min.)
  8. Monday March 22. Diagnostic methods for the GLM. Model-building principles.

    Extended course notes, Sec. 2.8, 2.9, pp. 35-39.

    Video recording:

    • lecture_08_210322.mp4: Diagnostic methods for the GLM, model-building principles (42 min.)
  9. Thursday April 1. Binary data, alternative vs. binomial distribution of the response. Link functions for binary data.

    Extended course notes, Sec. 3.1.1 - 3.1.4, pp. 40-44.

    Video recording:

    • lecture_09_210401.mp4: Binary data (30 min.)
  10. Thursday April 1. Logistic regression.

    Extended course notes, Sec. 3.1.5, pp. 45-50.

    Video recording:

    • lecture_10_210401.mp4: Logistic regression (48 min.)
  11. Thursday April 8. Loglinear models for Poisson count data. Modelling Poisson process intensity

    Extended course notes, Sec. 3.2, pp. 51-56.

    Video recording:

    • lecture_11_210408.mp4: Poisson regression models (43 min.)
  12. Thursday April 8. Loglinear models for contingency tables - introduction.

    Extended course notes, Sec. 3.3.1, 3.3.2, pp. 56-62.

    Video recording:

    • lecture_12_210408.mp4: Loglinear models for contingency tables (48 min.)
  13. Thursday April 15. Loglinear models for two-way tables

    Extended course notes, Sec. 3.3.3, 3.3.4, pp. 61-66.

    Video recording:

    • lecture_13_210415.mp4: Loglinear models for two-way tables (37 min.)
  14. Thursday April 15. Loglinear models for three-way tables - first part.

    Extended course notes, Sec. 3.3.5, pp. 66-74.

    Video recording:

    • lecture_14_210415.mp4: Marginal and conditional associations. Simpson's paradox. Confounding and causality (53 min.)
  15. Thursday April 22. Interpretation of loglinear models for three-way tables.

    Extended course notes, Sec. 3.3.5, pp. 74-82.

    Video recording:

    • lecture_15_210422.mp4: Interpretation of loglinear models for three-way tables (44 min.)
  16. Thursday April 22. Loglinear models for multi-way tables. Equivalence between loglinear and logistic models. Overdispersion in binary data - beta binomial distribution.

    Extended course notes, Sec. 3.3.6, 3.3.7, 4.1.1 pp. 82-88.

    Video recording:

    • lecture_16_210422.mp4: Loglinear models for multi-way tables. Equivalence between loglinear and logistic models. Overdispersion in binary data - beta binomial distribution (47 min.)
  17. Thursday April 29. Overdispersion in count data - Poisson gamma distribution. Quasilikelihood metods.

    Extended course notes, Sec. 4.1.2-4.1.4, pp. 89-94.

    Video recording:

    • lecture_17_210429.mp4: Overdispersion in count data - Poisson gamma distribution. Quasilikelihood metods (45 min.)
  18. Thursday April 29. Maximum likelihood estimation under invalid models. Sandwich estimation in the GLM.

    Extended course notes, Sec. 4.2 pp. 94-99.

    Video recording:

    • lecture_18_210429.mp4: Maximum likelihood estimation under invalid models. Sandwich estimation in the GLM (30 min.)
  19. Thursday May 6. Group-dependent data. Generalized Estimating Equations (GEE).

    Extended course notes, Sec. 5.1-5.3, pp. 101-106.

    Video recording:

    • lecture_19_210506.mp4: Group-dependent data. Generalized Estimating Equations - GEE (47 min.)
  20. Thursday May 6. Linear mixed effects models - introduction. One-way ANOVA with fixed and random effects.

    Extended course notes, Sec. 6.1.1-6.1.2 pp. 107-114.

    Video recording:

    • lecture_20_210506.mp4: One-way ANOVA with fixed and random effects (35 min.)
  21. Thursday May 13. Two-way ANOVA with random effects. Random intercept and slope. Definition of Linear Mixed Effects Model.

    Extended course notes, Sec. 6.1.3, 6.1.4, 6.2.1, 6.2.2, pp. 112-118.

    Video recording:

    • lecture_21_210513.mp4: Two-way ANOVA with random effects. Random intercept and slope. Definition of Linear Mixed Effects Model (50 min.)
  22. Thursday May 13.  Marginal likelihood. Henderson's equations.

    Extended course notes, Sec. 6.3.1, 6.3.2 pp. 119-123.

    Video recording:

    • lecture_22_210513.mp4: Marginal likelihood. Henderson's equations. (36 min.)

Supplementary Course Materials

Course Plan

The course covers methods for regression analysis of data that belong to one or more of the following categories

We will learn some of the common statistical methods that allow fitting regression models to such data.

The lecture focuses on the development, theoretical justification, and interpretation of these methods.

The exercise classes will teach how to apply these methods to real problems but may include some theoretical tasks as well. A new assignment will be given about every 2 weeks.

The course will be concluded by a written data analysis project.

Prerequisites

This course assumes mid-level knowledge of linear regression theory and applications. Master students of "Probability, statistics and econometrics" must have completed the course on Linear Regression (NMSA407) before enrolling here.

Requirements for Credit/Exam 

Credit:

The credit for the exercise class will be awarded to the student who hands in a satisfactory solution to each assignment by the prescribed deadline.

Exam:

The exam has two parts:

  1. Evaluation of project report (has the assignment been completed in all aspects without major errors?)
  2. Oral part focuses on the ability to propose an acceptable model for a particular practical problem and to demonstrate understanding of the theory underlying the chosen model (incl. derivations and proofs).

To pass the exam, both parts need to be passed.