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<h3 class="section">15.7 LOGISTIC REGRESSION</h3>

<a name="index-LOGISTIC-REGRESSION"></a>
<a name="index-logistic-regression"></a>
<a name="index-bivariate-logistic-regression"></a>

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<pre class="display">LOGISTIC REGRESSION [VARIABLES =] <var>dependent_var</var> WITH <var>predictors</var>

     [/CATEGORICAL = <var>categorical_predictors</var>]

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

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

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

     [/MISSING = {INCLUDE|EXCLUDE}]
</pre></div>

<p>Bivariate Logistic Regression is used when you want to explain a dichotomous dependent
variable in terms of one or more predictor variables.
</p>
<p>The minimum command is
</p><div class="example">
<pre class="example">LOGISTIC REGRESSION <var>y</var> WITH <var>x1</var> <var>x2</var> &hellip; <var>xn</var>.
</pre></div>
<p>Here, <var>y</var> is the dependent variable, which must be dichotomous and <var>x1</var> &hellip; <var>xn</var>
are the predictor variables whose coefficients the procedure estimates.
</p>
<p>By default, a constant term is included in the model.
Hence, the full model is
<em>{\bf y} 
= b_0 + b_1 {\bf x_1} 
+ b_2 {\bf x_2} 
+ \dots
+ b_n {\bf x_n}
</em>
</p>
<p>Predictor variables which are categorical in nature should be listed on the <code>/CATEGORICAL</code> subcommand.
Simple variables as well as interactions between variables may be listed here.
</p>
<p>If you want a model without the constant term <em>b_0</em>, use the keyword <code>/ORIGIN</code>.
<code>/NOCONST</code> is a synonym for <code>/ORIGIN</code>.
</p>
<p>An iterative Newton-Raphson procedure is used to fit the model.
The <code>/CRITERIA</code> subcommand is used to specify the stopping criteria of the procedure,
and other parameters.
The value of <var>cut_point</var> is used in the classification table.  It is the 
threshold above which predicted values are considered to be 1.  Values
of <var>cut_point</var> 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:
</p><ul>
<li> The number of iterations exceeds <var>max_iterations</var>.  
      The default value of <var>max_iterations</var> is 20.
</li><li> The change in the all coefficient estimates are less than <var>min_delta</var>.
The default value of <var>min_delta</var> is 0.001.
</li><li> The magnitude of change in the likelihood estimate is less than <var>min_likelihood_delta</var>.
The default value of <var>min_delta</var> is zero.
This means that this criterion is disabled.
</li><li> The differential of the estimated probability for all cases is less than <var>min_epsilon</var>.
In other words, the probabilities are close to zero or one.
The default value of <var>min_epsilon</var> is 0.00000001.
</li></ul>


<p>The <code>PRINT</code> subcommand controls the display of optional statistics.
Currently there is one such option, <code>CI</code>, which indicates that the 
confidence interval of the odds ratio should be displayed as well as its value.
<code>CI</code> should be followed by an integer in parentheses, to indicate the
confidence level of the desired confidence interval.
</p>
<p>The <code>MISSING</code> subcommand determines the handling of missing
variables.  
If <code>INCLUDE</code> is set, then user-missing values are included in the
calculations, but system-missing values are not.
If <code>EXCLUDE</code> is set, which is the default, user-missing
values are excluded as well as system-missing values. 
This is the default.
</p>
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