Regression and Generalized Linear Models - Department of ….pdf

Regression and Generalized Linear Models by Soumita Lahiri Sourish Saha Department of Statistics, University of Florida Contents 1 Linear Regression 3 1.1 Simple Linear Regression . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Multiple Linear Regression . . . . . . . . . . . . . . . . . . . . . . . 5 2 Generalized Linear Models 6 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 Examples of exponential family distribution . . . . . . . . . . . . . 7 2.3 What is a Generalized Linear Model (GLM) ? . . . . . . . . . . . . 8 2.4 Criteria For Assessing Goodness Of Fit . . . . . . . . . . . . . . . . 9 3 Models for Polytomous Data 12 3.1 Types of Variables/Measurement Scales . . . . . . . . . . . . . . . . 13 3.1.1 Continuous - Discrete Variables . . . . . . . . . . . . . . . . 13 3.1.2 Nominal - Ordinal Scales . . . . . . . . . . . . . . . . . . . . 13 3.2 Common Distributions for Categorical/Polytomous Data . . . . . . 14 3.2.1 Binomial Distribution . . . . . . . . . . . . . . . . . . . . . 14 3.2.2 Multinomial Distribution . . . . . . . . . . . . . . . . . . . . 15 3.2.3 Poisson Distribution . . . . . . . . . . . . . . . . . . . . . . 15 3.3 Models for Ordinal Data . . . . . . . . .