Question

How do the rules applied to a cost matrix differ from those applied to a profit matrix?

Answer 1

A cost matrix (error matrix) is also useful when specific classification errors are more severe than others. The Classification mining function tries to avoid classification errors with a high error weight. The trade-off of avoiding 'expensive' classification errors is an increased number of 'cheap' classification errors. Thus, the number of errors increases while the cost of the errors decreases in comparison with the same classification without a cost matrix. Weights specified must be greater than or equal to zero. The default weight is 1. The cost matrix diagonal must be zero.

You can assign error weights to misclassifications by specifying a cost matrix. The following table shows an example of a cost matrix. In this example, the following class labels are used:

• High risk
• Low risk
• Safe

The error weight for classifying customer data as Safe, when it is actually High risk, is 7.0. The misclassification of Low risk as Safe has only an error weight of 3.0.

A profit matrix can be used with categorical responses. A profit matrix is used to assign costs to undesirable outcomes and profits to desirable outcomes. You can assign profit and cost values to each combination of actual and predicted response categories. To specify the costs of classifying into an alternative category, enter values in the Undecided column. To save your assignments to the response column as a property, check Save to column as property. Leaving this option unchecked applies the Profit Matrix only to the current Partition report.

Probability Threshold Specification for Profit Matrix

When the response is binary, instead of entering weights into the profit matrix, you can specify a probability threshold in the Profit Matrix window. For details about how values are calculated for the profit matrix, see Profit Matrix in the Using JMP book.

Target

The level whose probability is modeled.

Probability Threshold

A threshold for the probability of the target level. If the probability that an observation falls into the target level exceeds the probability threshold, the observation is classified into that level.

When you define costs using the Specify Profit Matrix option and then select Show Fit Details, a Decision Matrix report appears.