How to use SAS® to fit Multiple Logistic Regression Models

When response outcomes are continuous error terms in models are normally distributed and a standard normal distribution function is adequate. The logistic distribution function which is very similar to the normal distribution function is required when the response variable is binary. Parameters of a logistic response function are often estimated using the method of maximum likelihood (ML). One of the problems with ML estimation is that, no closed-form solution exists for the values of the parameters that maximize the loglikelihood function. Hence sophisticated computer-intensive numerical search procedures (i.e: Newton Raphson) are required to find ML estimates of parameters. This paper is a step by step guide to develop a multiple logistic regression model for data sets with binary response variable using PROC LOGISTIC in SAS®. Since PROC LOGISTIC requires uniform coding and does not accommodate missing data, data need be corrected for missing values and for outliers, those can reduce the efficiency of ML estimation. In addition, best subset among 25 predictor variables was selected. This step is useful to increase the speed of ML estimation. Complete model diagnostics tests, sensitivity and residual analyses were performed. ML parameter estimation was significant at 5%level. P-value of Hosmer and Lemeshow goodness of fit test was 0.9545. Model had a maximum adjusted R-square value equal to 0.78, showed 93.2% sensitivity and 79.5% specificity. Residuals from the model did not show significant patterns and were normally distributed. Odds ratios of the predictor variables supported the conclusions drawn from ML estimation.