This chapter contains examples that illustrate the use of GMBO/PECAN. The data used for the first series of examples are taken from the book on generalized additive models by Hastie and Tibshirani (Hastie and Tibshirani 1990). The data concern risk factors for kyphosis, a forward flexion of the spine in excess of 40 percent from vertical, following laminectomy (a corrective spinal surgery). For each of 83 patients, the data set includes a binary indicator of the occurrence of kyphosis (kyphosis), age in months at the time of the operation (age), and two variables related to the nature of the surgery. These latter variables are the starting vertebrae level (start) and the number of vertebrae levels involved (number). The data are stored in a file called KYPHOSIS.DAT and can be read without explicit format specification, that is, the fields are separated by blanks or tabs. All of the examples in which these data are used are logistic regression models. These examples also illustrate various methods for the computation of test statistics and confidence bounds and show how to obtain generalized regression diagnostics for logistic regression models.
The second series of examples illustrates the use of the alternative link functions available in GMBO/PECAN. With these alternative links it is possible to model binomial probabilities using complementary log-log, identity, or log links. The data used in these examples have been used by Wacholder(Wacholder 1986) to illustrate the use of alternatives to logistic regression. The covariates are alcohol consumption (three levels), socioeconomic status (three levels), and a binary indicator of smoking status. The data have been reduced to 18 observations, one for each combination of categories defined by covariates. The data include the total number of people (n) and the number of cases (n) for each cell. The covariates are not included in the data set but, as will be illustrated below, can be generated using the generate labels function.