Common Errors in Statistics (and How to Avoid Them), 4th Edition

BINOMIAL OUTCOMES

Suppose your firm plans to bid on a contract. You hope your firm’s bid will be lower than that submitted by other firms, yet high enough to provide your firm a substantial profit if you win, a simple model of the Bernoulli outcome of success is logit[p] = log[p/(1 − p)] = μ + α$ + z, where p is the probability of success and $ represents the dollar value of the bid.

More commonly , the logistic model (which employs the logit function) is used for prediction purposes when the outcome is a binomial variable. Will the patient improve or get worse? In evaluating predictors for inclusion in the model, one begins with a univariate analysis on a variable-by-variable basis. (Of course, only variables that might have a potential cause- and effect-relationship with the outcome should be considered.) For categorical, and ordinal variables, Hosmer and Lemeshow [2001] recommend this be done via a 2 × k contingency table employing a likelihood ratio chi-square test. If there are cells with zero values, do one of the following:

1. Collapse that category with adjacent categories.

2. Stratify the model based on the results of that cell (note that this is done automatically via decision trees, which were considered in Chapter 13).

When making use of all the remaining predictors in the model, avoid overmatching as in the example of the leukemia study described under the heading ...