EXACT Statement

The LOGISTIC Procedure

EXACT Statement

EXACT <'label'>< Intercept >< effects >< / options > ;

The EXACT statement performs the exact tests of the parameters for the specified effects and optionally estimates the parameters and outputs the exact conditional distributions. You can specify the keyword INTERCEPT and any effects in the MODEL statement. Inference on parameters for the specified effects is performed by conditioning on the sufficient statistics of all the other model parameters (possibly including the intercept).

You can specify several EXACT statements, but they must follow the MODEL statement. Each statement can optionally include an identifying label. If several EXACT statements are specified, any statement without a label is assigned a label of the form "Exactn", where "n" indicates the nth EXACT statement. The label is included in the headers of the exact analysis tables.

The CONTRAST, TEST, and UNITS statements do not apply to the exact analyses. Exact analyses are not performed when you specify a WEIGHT statement, a link other than LINK=LOGIT, an offset variable, the NOFIT option, or a model-selection method.

The effects specified in the MODEL statement can have at most 32 parameters. If you have too many observations with the same covariate values, an integer overflow may occur and computations will cease.

The following options can be specified in each EXACT statement after a slash (/):

ALPHA=p

specifies the level of significance p for 100(1-p)% confidence limits for the parameters or odds ratios. The value p must be between 0 and 1. If the ALPHA= option is not specified, p is equal to 0.05 or the value of the ALPHA= option in the PROC LOGISTIC statement.

ESTIMATE < =keyword >

estimates the individual parameters (conditional on all other parameters) for the effects specified in the EXACT statement. For each parameter, a point estimate, a confidence interval, and a p-value for a two-sided test that the parameter is zero are displayed. Note that the two-sided p-value is twice the one-sided p-value. You can optionally specify one of the following keywords:

PARM: specifies that the parameters be estimated. This is the default.
ODDS: specifies that the odds ratios be estimated. For classification variables, use of the reference parameterization (the PARAM=REF option in the CLASS statement) is recommended.
BOTH: specifies that the parameters and odds ratios be estimated.

JOINT

performs the joint test that all of the parameters for the EXACT statement are simultaneously equal to zero along with tests that the parameters of the individual variables are zero. The joint test of all the parameters is indicated in the "Conditional Exact Tests" table by the label "Joint."

JOINTONLY

performs only the joint test that all of the parameters for the EXACT statement are simultaneously equal to zero. The test is indicated in the "Conditional Exact Tests" table by the label "Joint." When this option is specified, tests for the parameters of the individual variables are not performed.

ONESIDED

requests one-sided confidence intervals and p-values for the individual parameter estimates and odds ratios. The one-sided p-value is the smaller of the left and right tail probabilities for the observed sufficient statistic for the parameter under the null hypothesis that the parameter is zero. The two-sided p-values (default) are twice the one-sided p-values.

OUTDIST=SAS-data-set

names the SAS data set containing the exact conditional distributions. This data set contains all of the exact conditional distributions required to process the corresponding EXACT statement. The data set contains the possible sufficient statistics for the parameters of the effects specified in the EXACT statement, the counts, and, when hypothesis tests are performed on the parameters, the probability of occurrence and the score value for each sufficient statistic. When you request an OUTDIST= data set, the observed sufficient statistics are displayed in the "Sufficient Statistics" table. See the "OUTDIST= Output Data Set" section for more information.

Examples

In the following example, two exact tests are computed: one is for x1 and the other is for x2. The test for x1 is based on the exact conditional distribution of the sufficient statistic for the x1 parameter given the observed values of the sufficient statistics for the intercept, x2, and x3 parameters; likewise, the test for x2 is conditional on the observed sufficient statistics for the intercept, x1, and x3:
```
                 
   proc logistic;
      model y = x1 x2 x3;
      exact x1 x2; 
   run;
```
If x3 is a CLASS variable with three levels and the reference parameterization is specified, then there are two associated parameters. If you submit the C13 statement, an individual test that the parameter of x1 is zero and a joint test for testing that the two parameters of x3 are both zero is performed. If you specify the CJ13 statement, both of these tests and a joint test that all the parameters for the EXACT statement are zero are performed. If you request the CE3 statement, then a joint test for testing that the two parameters of x3 are both zero is performed, and estimates for each of the two parameters are produced:
```
                 
   class x3 / param=ref;
   exact 'C13'  x1 x3; 
   exact 'CJ13' x1 x3 / joint; 
   exact 'CE3'  x3    / estimate;
```
You can specify multiple EXACT statements in the same PROC LOGISTIC invocation. PROC LOGISTIC determines, from all the EXACT statements, the distinct conditional distributions that need to be evaluated. For example, only one exact conditional distribution is required for the following two EXACT statements:
```
   exact x1 / estimate=parm;
   exact x1 / estimate=parm onesided;
```
For each EXACT statement, individual tests for the parameters of the specified effects are computed unless the JOINTONLY option is specified. Consider the following EXACT statements:
```
   exact 'E12' x1 x2 / estimate;
   exact 'E1'  x1    / estimate;
   exact 'E2'  x2    / estimate;
   exact 'J12' x1 x2 / joint;
```
In the E12 statement, the parameters for x1 and x2 are estimated and tested separately. Specifying the E12 statement is equivalent to specifying both the E1 and E2 statements. In the J12 statement, the joint test for the parameters of x1 and x2 is computed as well as the individual tests for x1 and x2.
All exact conditional distributions for the tests and estimates computed in a single EXACT statement are output to the corresponding OUTDIST= data set. For example, consider the following EXACT statements:
```
   exact 'O1'   x1    /           outdist=o1;
   exact 'OJ12' x1 x2 / jointonly outdist=oj12;
   exact 'OA12' x1 x2 / joint     outdist=oa12;
   exact 'OE12' x1 x2 / estimate  outdist=oe12;
```
The O1 statement outputs a single exact conditional distribution. The OJ12 statement outputs only the joint distribution for x1 and x2. The OA12 statement outputs three conditional distributions: one for x1, one for x2, and one jointly for x1 and x2. The OE12 statement outputs two conditional distributions: one for x1 and the other for x2. Data set oe12 contains both the x1 and x2 variables; the distribution for x1 has missing values in the x2 column while the distribution for x2 has missing values in the x1 column.
See the "OUTDIST= Output Data Set" section for more information.

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