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Tentative Syllabus

PART I: Linear models
Week 1: Overview
Sept 4. Course overview
Week 2: Review of matrix algebra
Sept 9. Definitions; orthogonal projection
Sept 11. Random vector; covariance matrix; multivariate normal (MVN) distribution
Readings: Seber Ch 1, Appendix A and B
Week 3: Linear models
Sept 16. Model specification; interpretation; dummy variables
Sept 18. Matrix formulation; least squares estimation; OLS estimator; BLUE
Readings: Seber Ch 3
Week 4: Linear models (cont’)
Sept 23. Generalized inverse; estimable parameters/functions
Sept 25. General linear model; general least squares
Readings: Seber Ch 4
Week 5: Review of distributions; normal theory inference for linear model
Sept 30. Revisit of MVN distribution; Chi-squared distribution; F distribution
Oct 2. Sum of squares decomposition of linear models; geometric interpretation
Readings: Seber  Ch 1.6, Ch 2, Ch 4
Week 6: Normal theory inference for linear model (cont’)
Oct 7. Quadratic form; ANOVA
Oct 9. Testable hypotheses; confidence intervals; prediction intervals
Readings: Seber Ch 4, Ch 5
Exam I
Oct 14. In-class exam I

PART II: Generalized linear models
Week 7: Review of likelihood theory
Oct 16. Score function; information matrix; likelihood ratio test
Readings: MN Ch 1, Appendix A and C; (optional – wikipedia) Newton-Raphson Method; Gauss-Newton; Fisher-scoring
Week 8: The exponential family; model binary outcome
Oct 21. Review of the exponential family
Oct 23. Binary outcome; Bernoulli/binomial distributions
Readings: MN Ch 1, Ch2; (Agresti Ch 1)
Week 9: Logistic model for binary outcomes
Oct 28. Model parameterization; interpretation; hypothesis testing
Oct 30. Connection to 2 by 2 and k by 2 tables; Programming with SAS; R
Readings: MN Ch 4
Week 10: Logistic model (cont’)
Nov 4. Hosmer-Lemeshow goodness of fit test
Nov 6. Over-dispersion
Week 11: Model polytomous outcome
Nov 11. Nominal and ordinal outcomes; multinomial distribution
Nov 13. Polytomous logistic model; continuation ratio model (ordinal); parameter interpretation
Readings: MN Ch 5
Week 12: Model counts outcome
Nov 18. Poisson distribution; canonical link
Nov 20. Log linear model; model interpretation
Readings: MN Ch 6
Exam II
Nov 25. In-class exam II
Nov 27. No class (Thanksgiving)
Week 14: Model counts outcome (cont’)
Dec 2. Log linear model for Contingency tables
Dec 4. Over-dispersion
Week 15: Conditional likelihood
Dec 9. Matched pairs; case-control studies; nuisance parameters; complication in likelihood estimation
Dec 11. Sufficient statistic; conditional likelihood; Fisher’s exact tests;
Cochran-Mantel-Haenszel
Readings: MN Ch 7; (Agresti 6.7, 10.2)
Week 16: Quasi-likelihood
Dec 16. Examples and motivation; quasi score estimating function; properties
Readings: MN Ch 9; (Agresti 11.3-11.4)
Exam III
Dec 18. In-class Exam III (comprehensive)