The PROBIT Procedure
- Overview
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Getting Started
-
Syntax
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Details
Missing Values Response Level Ordering Computational Method Distributions INEST= SAS-data-set Model Specification Lack-of-Fit Tests Rescaling the Covariance Matrix Tolerance Distribution Inverse Confidence Limits OUTEST= SAS-data-set XDATA= SAS-data-set Traditional High-Resolution Graphics Displayed Output ODS Table Names ODS Graphics
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Examples
- References
| ODS Graphics |
Statistical procedures use ODS Graphics to create graphs as part of their output. ODS Graphics is described in detail in Chapter 21, Statistical Graphics Using ODS.
Before you create graphs, ODS Graphics must be enabled (for example, with the ODS GRAPHICS ON statement). For more information about enabling and disabling ODS Graphics, see the section Enabling and Disabling ODS Graphics in Chapter 21, Statistical Graphics Using ODS.
The overall appearance of graphs is controlled by ODS styles. Styles and other aspects of using ODS Graphics are discussed in the section A Primer on ODS Statistical Graphics in Chapter 21, Statistical Graphics Using ODS.
These ODS graphs are controlled by the PLOTS= option in the PROC statement. You can specify more than one graph request with the PLOTS= option. Table 74.35 summarizes these requests.
Option |
Plot |
|
ALL |
All appropriate plots |
|
CDFPLOT |
Estimated cumulative probability |
|
IPPPLOT |
Inverse predicted probability |
|
LPREDPLOT |
Linear predictor |
|
NONE |
No plot |
|
PREDPPLOT |
Predicted probability |
The following subsections provide information about these graphs.
ODS Graph Names
PROC PROBIT assigns a name to each graph it creates using ODS. You can use these names to reference the graphs when using ODS. The names are listed in Table 74.36.
ODS Graph Name |
Plot Description |
Statement |
PLOTS= Option |
|---|---|---|---|
CDFPlot |
Estimated cumulative probability |
PROC |
CDFPLOT |
IPPPlot |
Inverse predicted probability |
PROC |
IPPPLOT |
LPredPlot |
Linear predictor |
PROC |
LPREDPLOT |
PredPPlot |
Predicted probability |
PROC |
PREDPPLOT |
CDF Plot
For a multinomial model, the predicted cumulative distribution function is defined as
 |
where 
are the indexes of the 
levels of the multinomial response variable, F is the CDF of the distribution used to model the cumulative probabilities, 
is the vector of estimated parameters, 
is the covariate vector, 
are estimated ordinal intercepts with 
, and 
is the threshold parameter, either known or estimated from the model. Let 
be the covariate corresponding to the dose variable and 
be the vector of the rest of the covariates. Let the corresponding estimated parameters be 
and 
. Then
 |
To plot 
as a function of , must be specified. You can use the XDATA= option to provide the values of (see the XDATA= option in the PROC PROBIT statement for details), or use the default values that follow these rules:
If the effect contains a continuous variable (or variables), the overall mean of this effect is used.
If the effect is a single classification variable, the highest level of the variable is used.
The LEVEL= suboption specify the levels of the multinomial response variable for which the CDF curves are requested. There are 
curves for a -level multinomial response variable (for the highest level, it is the constant line 1). You can specify any of them to be plotted by the LEVEL= suboption. See the plot in Output 74.2.6 for an example.
Inverse Predicted Probability Plot
For the binomial model, the response variable is a probability. An estimate of the dose level 
needed for a response of 
is given by
 |
where 
is the cumulative distribution function used to model the probability, is the vector of the rest of the covariates, is the vector of the estimated parameters corresponding to , and is the estimated parameter for the dose variable of interest.
To plot as a function of , must be specified. You can use the XDATA= option to provide the values of (see the XDATA= option in the PROC PROBIT statement for details), or use the default values that follow these rules:
If the effect contains a continuous variable (or variables), the overall mean of this effect is used.
If the effect is a single classification variable, the highest level of the variable is used.
Output 74.4.12 in Example 74.4 shows an inverse predicted probability plot.
Linear Predictor Plot
For both binomial models and multinomial models, the linear predictor 
can be plotted against the first single continuous variable (dose variable) in the MODEL statement.
Let be the covariate of the dose variable, be the vector of the rest of the covariates, be the vector of estimated parameters corresponding to , and be the estimated parameter for the dose variable of interest.
To plot 
as a function of , must be specified. You can use the XDATA= option to provide the values of (see the XDATA= option in the PROC PROBIT statement for details), or use the default values that follow these rules:
If the effect contains a continuous variable (or variables), the overall mean of this effect is used.
If the effect is a single classification variable, the highest level of the variable is used.
For the multinomial model, you can use the LEVEL= suboption to specify the levels for which the linear predictor lines are plotted.
The confidence limits for the predicted values are only available for the binomial model. Output 74.4.13 in Example 74.4 shows a linear predictor plot for a binomial model.
Predicted Probability Plot
The predicted probability is
 |
for the binomial model and
 |
 |
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for the multinomial model with response levels, where is the cumulative distribution function used to model the probability, 
is the vector of the covariates, are the estimated ordinal intercepts with , is the threshold parameter, either known or estimated from the model, and 
is the vector of estimated parameters.
To plot 
(or 
) as a function of a continuous variable , the remaining covariates must be specified. You can use the XDATA= option to provide the values of (see the XDATA= option in the PROC PROBIT statement for details), or use the default values that follow these rules:
If the effect contains a continuous variable (or variables), the overall mean of this effect is used.
If the effect is a single classification variable, the highest level of the variable is used.
For the multinomial model, you can use the LEVEL= suboption to specify the levels for which the linear predictor lines are plotted.
Confidence limits are plotted only for the binomial model. Output 74.1.7 in Example 74.1 shows a predicted probability plot for a binomial model; and Output 74.2.3 in Example 74.2 shows a predicted probability plot for a multinomial model.