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1 Statistics 601, Fall 2005 Lab 5 Notes In this lab we will discuss the use of Newton-Raphson algorithms for numerical maximization of likelihood or log likelihood functions. You will be given access to a generic Newton-Raphson algorithm for R or Splus. We will illustrate maximum likelihood estimation with a simulated beta example. We will then discuss writing a function for derivatives of a gamma model for use with a Newton-Raphson algorithm. Also included in the lab assignment is the use of maximum likelihood for estimation of a generalized linear model. We will be covering this in lecture over the next couple of periods. Lab 5 Assignment On the course web page under “Laboratory Materials” are links to files that contain a generic Newton-Raphson algorithm, and a menu-driven package for generalized linear models. Also on the course web page under “Data” is a link to a file that contains values simulated from two gamma distributions. The file contains two columns of 50 values each. The first column should be considered data from Group 1 and the second column data from Group 2. 1. Find maximum likelihood estimates for gamma models formulated for these data. Test whether the groups should be considered significantly different. Produce Wald theory intervals for model parameters. Display your results. 2. Find your own example of data to which it might be reasonable to fit a generalized linear model (published examples are fine). Using any computational tool you wish (the functions provided, built-in S or R functions, SAS, whatever) estimate models, summarize results, and depict the data and model fit graphically.