The PROBIT Procedure
- Overview
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Getting Started
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SyntaxPROC PROBIT StatementBY StatementCDFPLOT StatementCLASS StatementEFFECTPLOT StatementESTIMATE StatementINSET StatementIPPPLOT StatementLPREDPLOT StatementLSMEANS StatementLSMESTIMATE StatementMODEL StatementOUTPUT StatementPREDPPLOT StatementSLICE StatementSTORE StatementTEST StatementWEIGHT Statement
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DetailsMissing ValuesResponse Level OrderingComputational MethodDistributionsINEST= SAS-data-setModel SpecificationLack-of-Fit TestsRescaling the Covariance MatrixTolerance DistributionInverse Confidence LimitsOUTEST= SAS-data-setXDATA= SAS-data-setTraditional High-Resolution GraphicsDisplayed OutputODS Table NamesODS Graphics
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Examples
- References
Rescaling the Covariance Matrix
One way of correcting overdispersion is to multiply the covariance matrix by a dispersion parameter. You can supply the value of the dispersion parameter directly, or you can estimate the dispersion parameter based on either the Pearson’s chi-square statistic or the deviance for the fitted model.
The Pearson’s chi-square statistic 
and the deviance 
are defined in the section Lack-of-Fit Tests. If the SCALE= option is specified in the MODEL statement, the dispersion parameter is estimated by
![\[ \widehat{\sigma }^2 = \left\{ \begin{array}{ll} \chi _ P^2/(m(k-1)-q) & \mbox{ SCALE=PEARSON} \\ \chi _ D^2/(m(k-1)-q) & \mbox{ SCALE=DEVIANCE} \\ (\Argument{constant})^2 & \mbox{ SCALE=\Argument{constant} } \end{array} \right. \]](images/statug_probit0098.png) |
In order for the Pearson’s statistic and the deviance to be distributed as chi-square, there must be sufficient replication within the subpopulations. When this is not true, the data are sparse, and the p-values for these statistics are not valid and should be ignored. Similarly, these statistics, divided by their degrees of freedom, cannot serve as indicators of overdispersion. A large difference between the Pearson’s statistic and the deviance provides some evidence that the data are too sparse to use either statistic.
You can use the AGGREGATE (or AGGREGATE=) option to define the subpopulation profiles. If you do not specify this option, each observation is regarded as coming from a separate subpopulation. For events/trials syntax, each observation represents n Bernoulli trials, where n is the value of the trials variable; for single-trial syntax, each observation represents a single trial. Without the AGGREGATE (or AGGREGATE=) option, the Pearson’s chi-square statistic and the deviance are calculated only for events/trials syntax.
Note that the parameter estimates are not changed by this method. However, their standard errors are adjusted for overdispersion, affecting their significance tests.