An introduction to generalized linear models

TLDR: In this paper, the authors propose a method of maximum likelihood estimation method of least squares estimation for generalized linear models for simple linear regression with Poisson responses GLIM, which is based on the MINITAB program.

Abstract: 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.