Summary : Using the Model to Make Predictions

Predicted Probabilities

Because the model attempts to predict cumulative probabilities rather than category membership, two steps are required to get predicted categories. First, for each case, the probabilities must be estimated for each category. Second, those probabilities must be used to select the most likely outcome category for each case.

The probabilities themselves are estimated by using the predictor values for a case in the model equations and taking the inverse of the link function. The result is the cumulative probability for each group, conditional on the pattern of predictor values for the case. The probabilities for individual categories can then be derived by taking the differences of the cumulative probabilities for the groups in order. In other words, the probability for the first category is the first cumulative probability; the probability for the second category is the second cumulative probability minus the first; the probability for the third category is the third cumulative probability minus the second; and so on.

From Probabilities to Predicted Category Values

For each case, the predicted outcome category is simply the category with the highest probability, given the pattern of predictor values for that case. For example, suppose you have an applicant who wants a 48-month loan (duration), is 22 years old (age), has one credit with the bank (numcred), has no other installment debt (othnstal), and owns her home (housng). Inserting these values into the prediction equations, this applicant has predicted values of -2.78, -1.95, 0.63, and 0.97. (Remember that there is one equation for each category except the last.) Taking the inverse of the complementary log-log link function gives the cumulative probabilities of .06, 0.13, 0.85, and 0.93 (and, of course, 1.0 for the last category). Taking differences gives the following individual category probabilities: category 1: .06, category 2: 0.13-0.06=0.07, category 3: 0.85-0.13=0.72, category 4: 0.93-0.85=0.08, and category 5: 1.0-0.93=0.07. Clearly, category 3 (debt payments current) is the most likely category for this case according to the model, with a predicted probability of 0.72. Thus, you would predict that this applicant would keep her payments current and the account would not become critical.

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