15.18 ROC

ROC     var_list BY state_var (state_value)
        /PLOT = { CURVE [(REFERENCE)], NONE }
        /PRINT = [ SE ] [ COORDINATES ]
        /CRITERIA = [ CUTOFF({INCLUDE,EXCLUDE}) ]
          [ TESTPOS ({LARGE,SMALL}) ]
          [ CI (confidence) ]
          [ DISTRIBUTION ({FREE, NEGEXPO }) ]
        /MISSING={EXCLUDE,INCLUDE}

The ROC command is used to plot the receiver operating characteristic curve of a dataset, and to estimate the area under the curve. This is useful for analysing the efficacy of a variable as a predictor of a state of nature.

The mandatory var_list is the list of predictor variables. The variable state_var is the variable whose values represent the actual states, and state_value is the value of this variable which represents the positive state.

The optional subcommand PLOT is used to determine if and how the ROC curve is drawn. The keyword CURVE means that the ROC curve should be drawn, and the optional keyword REFERENCE, which should be enclosed in parentheses, says that the diagonal reference line should be drawn. If the keyword NONE is given, then no ROC curve is drawn. By default, the curve is drawn with no reference line.

The optional subcommand PRINT determines which additional tables should be printed. Two additional tables are available. The SE keyword says that standard error of the area under the curve should be printed as well as the area itself. In addition, a p-value for the null hypothesis that the area under the curve equals 0.5 is printed. The COORDINATES keyword says that a table of coordinates of the ROC curve should be printed.

The CRITERIA subcommand has four optional parameters:

• The TESTPOS parameter may be LARGE or SMALL. LARGE is the default, and says that larger values in the predictor variables are to be considered positive. SMALL indicates that smaller values should be considered positive.
• The CI parameter specifies the confidence interval that should be printed. It has no effect if the SE keyword in the PRINT subcommand has not been given.
• The DISTRIBUTION parameter determines the method to be used when estimating the area under the curve. There are two possibilities, viz: FREE and NEGEXPO. The FREE method uses a non-parametric estimate, and the NEGEXPO method a bi-negative exponential distribution estimate. The NEGEXPO method should only be used when the number of positive actual states is equal to the number of negative actual states. The default is FREE.
• The CUTOFF parameter is for compatibility and is ignored.

The MISSING subcommand determines whether user missing values are to be included or excluded in the analysis. The default behaviour is to exclude them. Cases are excluded on a listwise basis; if any of the variables in var_list or if the variable state_var is missing, then the entire case is excluded.