Generalized Linear Models Upplaga 1

Generalized Linear Models is a very general class of statistical models that includes many commonly used models as special cases. For example the class of General Linear Models (GLM:s) that includes linear regression, analysis of variance and analysis of covariance, is a special case of GLIM:s. GLIM:s also include log-linear models for analysis of contingency tables, probit/logit regression, Poisson regression, and much more. This book gives an overview of generalized linear models and presents practical examples of their use. Although the approach is applied, the basic theory of generalized linear models is presented in a compact way. The exponential family of distributions is discussed, and we discuss Maximum Likelihood estimation and ways of assessing the fit of the model. Response variables as continuous variables, as binary/binomial variables, as counts and as ordinal response variables are discussed, and many practical examples using the Genmod software of the SAS package are given. Theory and applications of a more complex nature, like quasi-likelihood procedures, repeated measures models, mixed models and analysis of survival data, is also covered.