Generalized Linear Models
				Spring 2013

Texts:
Cox, D.R. and Snell, E.J. (1981) Applied Statistics. Chapman & Hall.
Davison, A.C. (2003) Statistical Models. Cambridge University Press.
McCullagh, P. and Nelder, J.A. (1989) Generalized Linear Models, 2nd edn. C&H.
Cox, D.R. and Snell, E.J. (1989) Binary data 2nd Edn. Chapman & Hall.
Chambers, J. and Hastie, T. Statistical models in S.  Wadsworth.
Venables, W.N. and Ripley, B.D. Modern Applied Statistics with S.  Springer

Other relevant books:
McCulloch, C.E. and Searle, S.R. (2001) Generalized, Linear, and Mixed Models,  Wiley
Pawitan, Y. (2001) In All Likelihood.  Oxford.
Myers, Montgomery and Vining (2002) Generalized Linear Models


Syllabus:
Linear regression and weighted linear regression
	general matrix form; projection matrix.
	precision of estimates
	t- tests and F-tests: p-values; AS section 4.7
	reduction in residual sum of squares principle
	adding a new variable to a regression model
	Transformation: Tukey's 1DOFNA; Box-Cox method
	interpretation of regression coeffients: AS section 4.3, 4.11
	special case with replication in linear regression
	decomposition of sum of squares between/within
	simple variance components problems
	reading: Applied Statistics, pages 1-50.

Model Formulae
	factors and variates
	intrinsic and extrinsic aliasing
	constraints and generalized inverses
	effect of choice of constraint
	`+', `.' and `*': interactions
	constructing an analysis of variance table in GLIM
	homologous factors
	reading: GLM sections 3.1-3.6

Examples with non-Normal response variable or non-linear effects
	dilution assay GLM section 1.2.4
	2x2 table
	vitamin C decay rate: GLM p.96
	water hardness and CNS disorders: GLM p.186
	Yields of barley and sinapis in competition: GLM p.318
	survival times of leukemia patients: AS example U
	smoking and perinatal mortality: GLM p.190
	food preference data: BD p.160; GLM p.175
	mixtures of drugs: relative potency; synergy: GLM p.387
	reading: Binary Data, Chapter 1

Definition of a generalized linear model
	natural exponential families
	cumulants and cumulant function
	link function
	model formula
	problems connected with aggregation
	fitting generalized linear models
	deviance function
	reading: GLM Chapter 2.

Some results concerning maximum likelihood estimation
	score statistic, parameter estimate
	observed and expected Fisher information
	likelihood ratio statistics
	nuisance parameters and composite hypotheses
	reading: Binary Data Appendix 1; GLM Appendix 1.

Binary data
	covariate classes and contingency tables
	binomial distribution
	link functions and parameter interpretation
	retrospective sampling; BD section 4.2, 4.3; GLM section 4.3
	parameter estimation
	deviance function
	sparseness
	extrapolation (point estimation vs interval estimation)
	over-dispersion: BD section 3.2; GLM section 4.5
	reading: BD chapter 2; GLM chapter4 

Polytomous data
	measurement scales nominal, ordinal, interval, nested
	multinomial distribution
	quadratic forms and generalized inverses
	multinomial log likelihood
	parameter estimation
	over-dispersion
	paired preferences and the Bradley-Terry model formula
	reading: BD sections 5.1-5.4; GLM chapter 5

Log-linear models
	Poisson distribution
	relative potency and Fieller's method
	Contingency tables; independence and conditional independence
	over-dispersion
	multiple responses
	reading: BD sections 5.5-5.6; GLM chapter 6

Conditional and marginal likelihoods
	Gaussian marginal likelihood: REML
	2x2 tables
	matched pairs and quasi-symmetry
	odds-ratio regression and hypergeometric distribution
	reading: BD sections 2.3-2.5, A1.8; GLM chapter 7

Quasi-likelihood and estimating functions
	reading: GLM chapter 9

Distance-matrix methods
	Wishart matrix and Wishart distance matrix
	Trees rooted and unrooted
	Projection methods