ROC Curves

This procedure is a useful way to evaluate the performance of classification schemes in which there is one variable with two categories by which subjects are classified.

Example. It is in a bank's interest to correctly classify customers into those customers who will and will not default on their loans, so special methods are developed for making these decisions. ROC curves can be used to evaluate how well these methods perform.

Statistics. Area under the ROC curve with confidence interval and coordinate points of the ROC curve. Plots: ROC curve.

Methods. The estimate of the area under the ROC curve can be computed either nonparametrically or parametrically using a binegative exponential model.

ROC Curve Data Considerations

The old ROC Curve procedure supports the statistical inference about a single ROC curve. This may also be recovered by the new ROC Analysis procedure. Furthermore, the new ROC Analysis procedure can compare two ROC curves generated from either independent groups or paired subjects.

Data. Test variables are quantitative. Test variables are often composed of probabilities from discriminant analysis or logistic regression or composed of scores on an arbitrary scale indicating a rater's "strength of conviction" that a subject falls into one category or another category. The state variable can be of any type and indicates the true category to which a subject belongs. The value of the state variable indicates which category should be considered positive.

Assumptions. It is assumed that increasing numbers on the rater scale represent the increasing belief that the subject belongs to one category, while decreasing numbers on the scale represent the increasing belief that the subject belongs to the other category. The user must choose which direction is positive. It is also assumed that the true category to which each subject belongs is known.

To Obtain an ROC Curve

This feature requires the Statistics Base option.

  1. From the menus choose:

    Analyze > Classify > ROC Curve...

  2. Select one or more test probability variables.
  3. Select one state variable.
  4. Identify the positive value for the state variable.

This procedure pastes ROC command syntax.