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INTRODUCING THE GENERALIZED LINEAR MODELS

This paper deals with the Generalized Linear Models, an extension of the linear modeling process that allows models to be fit to data that follow probability distributions other than the Normal distribution, such as the Poisson, Binomial, Multinomial, and etc. Also, the Generalized Linear Models can be used for a non-linear distribution. In the first chapter, we will begin by discussing the past problem of looking at the data using the simple linear regression models. We then introduce the Generalized Linear Models (GLM), and the characteristics of GLM to give a better understanding of the model. First, we discuss the components of GLM and the simple linear regression models. It is easier to compare both models when we understand the basic components of them. Then we discuss the Link Function, one of the major characteristics of GLM which allows the model to follow distributions other than Normal. Finally, we move to the Simpson’s paradox and the Interaction test, yet another important aspect when we discuss GLM modeling. It helps us to understand the importance of GLM and multivariate tests when analyzing datasets with multiple parameters. Chapter 3 discusses about The “Optimal” model. It is useful to understand what exactly the “Optimal” model is and what kind of procedures should be taken to achieve the “Best” model for GLM modeling process. The auto insurance dataset is introduced for modeling example in chapter 4. GLM modeling software called EMBLEM was used for the modeling process. In EMBLEM, many useful applications including the statistics test for significance of each parameter, Interaction tests for multiple parameters, and many other functions are available for better and easier modeling. Since it is important to understand which application should be used for certain process, the process for GLM modeling will also be discussed in this chapter.