OUTPUT Statement

The LOGISTIC Procedure

OUTPUT Statement

OUTPUT < OUT=SAS-data-set >
< keyword=name ...keyword=name > / < option >;

The OUTPUT statement creates a new SAS data set that contains all the variables in the input data set and, optionally, the estimated linear predictors and their standard error estimates, the estimates of the cumulative or individual response probabilities, and the confidence limits for the cumulative probabilities. Regression diagnostic statistics and estimates of crossvalidated response probabilities are also available for binary response models.

If you use the single-trial syntax, the data set may also contain a variable named _LEVEL_, which indicates the level of the response that the given row of output is referring to. For instance, the value of the cumulative probability variable is the probability that the response variable is as large as the corresponding value of _LEVEL_. For details, see the section "OUT= Output Data Set".

The estimated linear predictor, its standard error estimate, all predicted probabilities, and the confidence limits for the cumulative probabilities are computed for all observations in which the explanatory variables have no missing values, even if the response is missing. By adding observations with missing response values to the input data set, you can compute these statistics for new observations or for settings of the explanatory variables not present in the data without affecting the model fit.

The following list explains specifications in the OUTPUT statement.

OUT= SAS-data-set

names the output data set. If you omit the OUT=option, the output data set is created and given a default name using the DATAn convention.

keyword=name

specifies the statistics to be included in the output data set and names the new variables that contain the statistics. Specify a keyword for each desired statistic (see the following list of keywords), an equal sign, and the name of the new variable or variables to contain the statistic. With the exception of DFBETAS, you can list only one variable after the equal sign. Note that the regression diagnostics are available only for the binary model. Formulas for the statistics are given in the "Linear Predictor, Predicted Probability, and Confidence Limits" section and the "Regression Diagnostics" section. The keywords allowed and the statistics they represent are as follows:

C: confidence interval displacement diagnostic, which measures the influence of individual observations on the regression estimates
CBAR: another confidence interval displacement diagnostic, which measures the overall change in the global regression estimates due to deleting an individual observation
DFBETAS: standardized differences in the regression estimates for assessing the effects of individual observations on the estimated regression parameters in the fitted model. You can specify a list of up to s+1 variable names, where s is the number of explanatory variables in the MODEL statement, or you can specify just the keyword _ALL_. In the former specification, the first variable contains the standardized differences in the intercept estimate, the second variable contains the standardized differences in the parameter estimate for the first explanatory variable in the MODEL statement, and so on. In the latter specification, the DFBETAS statistics are named DFBETA_xxx, where xxx is the name of the regression parameter. For example, if the model contains two variables X1 and X2, the specification DFBETAS=_ALL_ produces three DFBETAS statistics named DFBETA_Intercept, DFBETA_X1, and DFBETA_X2. If an explanatory variable is not included in the final model, the corresponding output variable named in DFBETAS=names contains missing values.
DIFCHISQ: change in the chi-square goodness-of-fit statistic attributable to deleting the individual observation
DIFDEV: change in the deviance attributable to deleting the individual observation
H: diagonal element of the hat matrix for detecting extreme points in the design space
LOWER | L: lower confidence limit for the probability of an event response if events/trials syntax is specified, or the lower confidence limit for the probability that the response is less than or equal to the value of _LEVEL_ if single-trial syntax is specified. See the ALPHA= option.
PREDICTED | PRED | PROB | P: predicted probability of an event response if events/trials syntax is specified, or the predicted probability that the response variable is less than or equal to the value of _LEVEL_ if single-trial syntax is specified (in other words, Pr(Y $\le$ _LEVEL_), where Y is the response variable)
RESCHI: Pearson (Chi) residual for identifying observations that are poorly accounted for by the model
RESDEV: deviance residual for identifying poorly fitted observations
STDXBETA: standard error estimate of XBETA
UPPER | U: upper confidence limit for the probability of an event response if events/trials model is specified, or the upper confidence limit for the probability that the response is less than or equal to the value of _LEVEL_ if single-trial syntax is specified. See the ALPHA=option.
XBETA: estimate of the linear predictor ${\alpha}_i+{\beta}' x$ , where i is the corresponding ordered value of _LEVEL_

PREDPROBS=(keywords)

requests individual, cumulative, or cross-validated predicted probabilities. Descriptions of the keywords are:

INDIVIDUAL | I: requests the predicted probability of each response level. For a response variable Y with three levels, 1, 2, and 3, the individual probabilities are Pr(Y=1), Pr(Y=2), and Pr(Y=3).
CUMULATIVE | C: requests the cumulative predicted probability of each response level. For a response variable Y with three response levels, 1,2, and 3, the cumulative probabilities are Pr(Y $\le$ 1), Pr(Y $\le$ 2), and Pr(Y $\le$ 3). The cumulative probability for the last response level always has the constant value of 1.
CROSSVALIDATE | XVALIDATE | X: requests the cross-validated predicted probability of each response level. These probabilities are derived from the leave-one-out principle; that is, dropping the data of one subject and reestimating the parameter estimates. PROC LOGISTIC uses a less expensive one-step approximation to compute the parameter estimates. Note that, for ordinal models, the cross-validated probabilities are not computed and are set to missing.

You can request any of the three given types of predicted probabilities. For example, you can request both the individual predicted probabilities and the cross-validated probabilities by specifying PREDPROBS=(I X).

When you specify the PREDPROBS= option, two automatic variables _FROM_ and _INTO_ are included for the single-trial syntax and only one variable, _INTO_, is included for the events/trials syntax. The _FROM_ variable contains the formatted value of the observed response. The variable _INTO_ contains the formatted value of the response level with the largest individual predicted probability.

If you specify PREDPROBS=INDIVIDUAL, the OUTPUT data set contains k additional variables representing the individual probabilities, one for each response level, where k is the maximum number of response levels across all BY-groups. The names of these variables have the form IP_xxx, where xxx represents the particular level. The representation depends on the following situations:

If you specify events/trials syntax, xxx is either `Event' or `Nonevent'. Thus, the variable containing the event probabilities is named IP_Event and the variable containing the nonevent probabilities is named IP_Nonevent.
If you specify the single-trial syntax with more than one BY group, xxx is 1 for the first ordered level of the response, 2 for the second ordered level of the response, ..., etc., as given in the Response Profile table. The variable containing the predicted probabilities Pr(Y=1) is named IP_1, where Y is the response variable. Similarly, IP_2 is the name of the variable containing the predicted probabilities Pr(Y=2), and so on.
If you specify the single-trial syntax with no BY-group processing, xxx is the left-justified formatted value of the response level (the value may be truncated so that IP_xxx does not exceed 32 characters.) For example, if Y is the response variable with response levels `None', `Mild', and `Severe', the variables representing individual probabilities Pr(Y='None'), P(Y='Mild'), and P(Y='Severe') are named IP_None, IP_Mild, and IP_Severe, respectively.

If you specify PREDPROBS=CUMULATIVE, the OUTPUT data set contains k additional variables representing the cumulative probabilities, one for each response level, where k is the maximum number of response levels across all BY-groups. The names of these variables have the form CP_xxx, where xxx represents the particular response level. The naming convention is similar to that given by PREDPROBS=INDIVIDUAL. The PREDPROB=CUMULATIVE values are the same as those output by the PREDPROB=keyword, but are arranged in variables on each output observation rather thin in multiple output observations.

If you specify PREDPROBS=CROSSVALIDATE, the OUTPUT data set contains k additional variables representing the cross-validated predicted probabilities of the k response levels, where k is the maximum number of response levels across all BY-groups.

The names of these variables have the form XP_xxx, where xxx represents the particular level. The representation is the same as that given by PREDPROBS=INDIVIDUAL except that for the events/trials syntax there are four variables for the cross-validated predicted probabilities instead of two:

XP_EVENT_R1E: is the cross validated predicated probability of an event when a current event trial is removed.
XP_NONEVENT_R1E: is the cross validated predicated probability of a nonevent when a current event trial is removed.
XP_EVENT_R1N: is the cross validated predicated probability of an event when a current nonevent trial is removed.
XP_NONEVENT_R1N: is the cross validated predicated probability of a nonevent when a current nonevent trial is removed.

The cross-validated predicted probabilities are precisely those used in the CTABLE option. Refer to the "Predicted Probability of an Event for Classification" section for details of the computation.

You can specify the following option after a slash.

ALPHA=value

sets the confidence level used for the confidence limits for the appropriate response probabilities. The quantity value must be between 0 and 1. By default, ALPHA=0.05, which results in the calculation of a 95% confidence interval.

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