Generalized Linear Models
Instructor: Dr. Abdullah Al-Shiha
(I) Books about Generalized Linear Models:
- An Introduction to Generalized Linear Models, Second Edition. A. J. Dobson, Chapman and Hall/CRC, London, 2002.
- Generalized Linear Models, Second Edition, Peter McCullagh and John A Nelder, Chapman and Hall, 1989.
- Generalized, linear and mixed models, C. McCulloch, and S. Searle, Wiley, New York, 2001.
- Generalized Linear Models and Extensions, J. Hardin, and J. Hible, Stata Press, College Station, Texas, 2001.
- Generalized Linear Models: A Bayesian Perspective, D. K. Dey, S. K. Ghosh, and B. K. Mallick, Marcel Dekker, New York, 2000.
- Applying Generalized Linear Models, James Lindsey, Springer-Verlag, 1997.
- Generalized Additive Models, T.J. Hastie, R.J. Tibshirani, Chapman & Hall, 1990.
- Generalized Linear Models: With Applications in Engineering and the Sciences, Raymond H. Myers, Douglas C. Montgomery, and G. Geoffrey Vining. John Wiley, 2001.
- Generalized Linear Models by John P. Hoffmann, 2004.
(II) Books about Linear Models and Matrices:
· Graybill, F. A. Matrices with Applications in Statistics. 2nd Edition. Belmont, Calif.: Wadsworth, 1983.
· Graybill, F. A. Theory and Application of the Linear Model. Wadsworth & Brooks, Pacific Grove, California, 1976.
· Searle, S. R. Linear Models. New York: Wiley, 1971.
· Searle, S. R. Matrix Algebra Useful for Statistics. New York: Wiley, 1982.
Outline of the Course:
(I) Review of some statistical and mathematical aspects needed for studying generalized linear models (one week)
(II) Review of some matrix algebra (one week)
(III) Review of some aspects of General Linear models (two weeks)
(IV) Materials of the book “An Introduction to Generalized Linear Models,” 2nd Ed., by A. J. Dobson (2002).
We will cover as much materials as we can!
Contents of the book:
1. Introduction (Reading Assignment)
1.4 Distributions related to the Normal distribution
1.5 Quadratic forms
2. Model Fitting ((Reading)
2.3 Some principles of statistical modelling
2.4 Notation and coding for explanatory variables
3. Exponential Family and Generalized Linear Models
3.2 Exponential family of distributions
3.3 Properties of distributions in the exponential
3.4 Generalized linear models
4.2 Example: Failure times for pressure vessels
4.3 Maximum likelihood estimation
4.4 Poisson regression example
5.2 Sampling distribution for score statistics
5.3 Taylor series approximations
5.4 Sampling distribution for maximum likelihood estimators
5.5 Log-likelihood ratio statistic
5.6 Sampling distribution for the deviance
5.7 Hypothesis testing
6. Normal Linear Models (Reading)
6.2 Basic results
6.3 Multiple linear regression
6.4 Analysis of variance
6.5 Analysis of covariance
6.6 General linear models
7. Binary Variables and Logistic Regression
7.1 Probability distributions
7.2 Generalized linear models
7.3 Dose response models
7.4 General logistic regression model
7.5 Goodness of fit statistics
7.7 Other diagnostics
7.8 Example: Senility and WAIS
8. Nominal and Ordinal Logistic Regression
8.2 Multinomial distribution
8.3 Nominal logistic regression
8.4 Ordinal logistic regression
8.5 General comments
9. Count Data, Poisson Regression and Log-Linear
9.2 Poisson regression
9.3 Examples of contingency tables
9.4 Probability models for contingency tables
9.5 Log-linear models
9.6 Inference for log-linear models
9.7 Numerical examples