### 15.8 LOGISTIC REGRESSION

    LOGISTIC REGRESSION [VARIABLES =] dependent_var WITH predictors

         [/CATEGORICAL = categorical_predictors]

         [{/NOCONST | /ORIGIN | /NOORIGIN }]

         [/PRINT = [SUMMARY] [DEFAULT] [CI(confidence)] [ALL]]

         [/CRITERIA = [BCON(min_delta)] [ITERATE(max_interations)]
                      [LCON(min_likelihood_delta)] [EPS(min_epsilon)]
                      [CUT(cut_point)]]

         [/MISSING = {INCLUDE|EXCLUDE}]

Bivariate Logistic Regression is used when you want to explain a dichotomous dependent variable in terms of one or more predictor variables.

The minimum command is

    LOGISTIC REGRESSION y WITH x1 x2 … xn.

Here, y is the dependent variable, which must be dichotomous and x1 … xn are the predictor variables whose coefficients the procedure estimates.

By default, a constant term is included in the model. Hence, the full model is {\bf y} = b_0 + b_1 {\bf x_1} + b_2 {\bf x_2} + \dots + b_n {\bf x_n}

Predictor variables which are categorical in nature should be listed on the `/CATEGORICAL` subcommand. Simple variables as well as interactions between variables may be listed here.

If you want a model without the constant term b_0, use the keyword `/ORIGIN`. `/NOCONST` is a synonym for `/ORIGIN`.

An iterative Newton-Raphson procedure is used to fit the model. The `/CRITERIA` subcommand is used to specify the stopping criteria of the procedure, and other parameters. The value of cut_point is used in the classification table. It is the threshold above which predicted values are considered to be 1. Values of cut_point must lie in the range [0,1]. During iterations, if any one of the stopping criteria are satisfied, the procedure is considered complete. The stopping criteria are:

- The number of iterations exceeds max_iterations. The default value of max_iterations is 20.
- The change in the all coefficient estimates are less than min_delta. The default value of min_delta is 0.001.
- The magnitude of change in the likelihood estimate is less than min_likelihood_delta. The default value of min_delta is zero. This means that this criterion is disabled.
- The differential of the estimated probability for all cases is less than min_epsilon. In other words, the probabilities are close to zero or one. The default value of min_epsilon is 0.00000001.

The `PRINT` subcommand controls the display of optional statistics. Currently there is one such option, `CI`, which indicates that the confidence interval of the odds ratio should be displayed as well as its value. `CI` should be followed by an integer in parentheses, to indicate the confidence level of the desired confidence interval.

The `MISSING` subcommand determines the handling of missing variables. If `INCLUDE` is set, then user-missing values are included in the calculations, but system-missing values are not. If `EXCLUDE` is set, which is the default, user-missing values are excluded as well as system-missing values. This is the default.