Macro for Fitting Nonlinear Models to Poisson Distributed Data

摘要

Models are considered in which the dependent variable y is a count that follows the Poisson distribution. The expected value of y is represented with a regression function that describes the relation between the expected count, the predictor variables, and the parameters. Estimates of the parameters can be obtained using iteratively weighted least squares (IWLS). The IWLS procedure is equivalent to using the method of scoring to obtain a root of the likelihood equations. Poisson regression models include linear, log-linear, quasi-linear, and intrinsically nonlinear regression functions. This approach allows the analyst to concentrate on determining the most appropriate form of the regression function without regard for computational complexity. The SAS procedures NLIN and MATRIX can be used to obtain ML estimates, their estimated asymptotic covariance matrix, and diagnostic measures that can be used to aid the analyst in detecting outlying responses and extreme points in the model space. An example, using an intrinsically nonlinear model (derived from the theory of Dual Radiation Action), is used to illustrate the ML estimation, hypothesis testing, and regression diagnostics techniques. (ERA citation 10:011927)