### 15.10 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 x1xn 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.