Modeling and Multivariate Methods - SAS

212 Performing Logistic Regression on Nominal and Ordinal Responses Chapter 7
Logistic Fit Platform Options
ROC Curve
• columns called Prob[j] for j < r with a formula for the fit to level j
• a column called Most Likely responsename that picks the most likely level of each row based on the
computed probabilities.
For an ordinal response model with r levels, JMP creates
• a column called Linear that contains the formula for a linear combination of the regressors without an
intercept term
• columns called Cum[j], each with a formula for the cumulative probability that the response is less than
or equal to level j, for levels j =1,2,...r -1. There is no Cum[ j =1,2,...r -1] that is 1 for all rows
• columns called Prob[ j =1,2,...r -1], for 1 < j < r, each with the formula for the probability that the
response is level j. Prob[j] is the difference between Cum[j] and Cum[j –1]. Prob[1] is Cum[1], and Prob[r]
is 1–Cum[r –1].
• a column called Most Likely responsename that picks the most likely level of each row based on the
computed probabilities.
Save Quantiles creates columns in the current data table named OrdQ.05, OrdQ.50, and OrdQ.95 that
fit the quantiles for these three probabilities.
Save Expected Value creates a column in the current data table called Ord Expected that is the linear
combination of the response values with the fitted response probabilities for each row and gives the
expected value.
Receiver Operating Characteristic (ROC) curves measure the sorting efficiency of the model’s fitted
probabilities to sort the response levels. ROC curves can also aid in setting criterion points in diagnostic
tests. The higher the curve from the diagonal, the better the fit. An introduction to ROC curves is found in
the Basic Analysis and Graphing book. If the logistic fit has more than two response levels, it produces a
generalized ROC curve (identical to the one in the Partition platform). In such a plot, there is a curve for
each response level, which is the ROC curve of that level versus all other levels. Details on these ROC curves
are found in “Graphs for Goodness of Fit” on page 336 in the “Recursively Partitioning Data” chapter.
Example of an ROC Curve
1. Open the Ingots.jmp sample data table.
2. Select Analyze > Fit Model.
3. Select ready and click Y.
4. Select heat and soak and click Add.
5. Select count and click Freq.
6. Click Run.
7. From the red triangle next to Nominal Logistic Fit, select ROC Curve.
8. Select 1 as the positive level and click OK.