This updated edition provides a unifying framework for many commonly-used multivariate statistical methods including multiple regression and analysis of variance or covariance for continuous response data.

Contenu

Part 1 Background; scope; notation; distributions derived from normal distribution. Part 2 Model fitting: plant growth sample; birthweight sample; notation for linear models; exercises. Part 3 Exponential family of distributions and generalized linear models: exponential family of distributions; generalized linear models. Part 4 Estimation: method of maximum likelihood; method of least squares; estimation for generalized linear models; example of simple linear regression for Poisson responses; MINITAB program for simple linear regression with Poisson responses; GLIM. Part 5 Inference: sampling introduction for scores; sampling distribution for maximum likelihood estimators; confidence intervals for the model parameters; adequacy of a model; sampling distribution for the log-likelihood statistic; log-likelihood ratio statistic (deviance); assessing goodness of fit; hypothesis testing; residuals. Part 6 Multiple regression: maximum likelihood estimation; least squares estimation; log-likelihood ratio statistic; multiple correlation coefficient and R; numerical example; residual plots; orthogonality; collinearity; model selection; non-linear regression. Part 7 Analysis of variance and covariance: basic results; one-factor ANOVA; two-factor ANOVA with replication; crossed and nested factors; more complicated models; choice of constraint equations and dummy variables; analysis of covariance. Part 8 Binary variables and logistic regression: probability distributions; generalized linear models; dose response models; general logistic regression; maximum likelihood estimation and the log-likelihood ratio statistic; other criteria for goodness of fit; least squares methods; remarks. Part 9 Contingency tables and log-linear models: probability distributions; log-linear models; maximum likelihood estimation; hypothesis testing and goodness of fit; numerical examples; remarks. Appendices: conventional parametrizations with sum-to-zero constraints; corner-point parametrizations; three response variables; two response variables and one explanatory variable; one response variable and two explanatory variables.