After successful completion of the course, students are able to

(1) apply the appropriate generalized linear methods to build estimation and predictive models

(2) select and validate them (3) asses model fit and error and (4) use the R language for data analysis.

Introduction and overview of the course: 

• background, scope, notation, normal and related distributions, maximum likelihood estimation, least squares estimation, model fitting.

Exponential Family and Generalized Linear Models: 

• Exponential family of distributions
• Properties of distributions in the exponential family
• Generalized Linear Models
• Estimation and Inference

Normal Linear Models

Binary Variables

• Probability distributions
• The binomial distribution
• Odds and log-odds. 
• The logit link and logistic regression. 
• Maximum likelihood estimation and testing in logistic regression
• Regression Diagnostics 
• Model selection 
• Alternative links, probit regression

Nominal and Ordinal logistic regression

• Multinomial response models, multinomial logits
• Nominal logistic regression
• Ordinal logistic regresion

Count Data, Poisson regression and loglinear models

• Poisson regression
• Probability models for contingency tables
• Log-linear models and inference

• Longitudinal Data
  • Repeated measures models for normal data
  • Repeated measures models for non-normal data
• Additional topics if time allows

The class will comprise of lecture slides, board notes and handouts.  

We will use the R statistical software. You can download it and get related information from the R home page. RStudio offers a GUI R platform. A tutorial in R is posted at https://www.cyclismo.org/tutorial/R/ and another at the UCLA Institute for Digital Research and Education

The grading will be a weighted average of the final exam score (50%), 6 problem sets (exercises) (30%), and a data analysis project (20%).

FINAL EXAM

The final exam will be written and cover all topics presented in class.

EXERCISES

The exercise session will be incorporated in the class.

Students will be called to present their solutions to the problems they have ticked in TUWEL. The problems will be posted in TUWEL.

Grade: All students should do at least 20% of each assignment. The grade will be an equally weighted average of percent of ticked problems and presentation score.

DATA ANALYSIS PROJECT

Methods studied in the course will be used to analyze data. The project will consist of a summary report of the analysis and findings along with an in class presentation.

Basic concepts in probability theory, statistical estimation and testing theory, and statistical methodology as in Introduction to Statistics; Linear algebra Calculus.