We have conducted the following research in order to understand the process of parameter estimation in generalized linear models. In the beginning we lay theoretical foundations with exponential family and derive some of it's properties. Then we define generalized linear models, inspect some more important cases and define multiple methods for parameter estimation, taking a closer look at the maximum likelihood method. We go on to derive maximum likelihood equations in the logistic model and generalize the result for the exponential family. As an alternative, we derive the same equations also for the probit model and comment on the advantages of using canonical link functions. The second part focuses on numerical methods. We derive the Newton method and comment on its possible issues. We also define the Fisher's scoring algorithm and prove the equivalence of the methods for canonical distribution models.
Theory is then put to work in the last part of the research. We compare probit and logit models and comment on the differences between the two.
|
