Effect Wald Tests
You can also request profile likelihood confidence intervals for the model parameters. When you select the Confidence Intervals command, a dialog prompts you to enter α to compute the 1 – α confidence intervals, or you can use the default of α = 0.05. Each confidence limit requires a set of iterations in the model fit and can be expensive. Furthermore, the effort does not always succeed in finding limits.
Parameter Estimates with Confidence Intervals
When you select Odds Ratios, a report appears showing Unit Odds Ratios and Range Odds Ratios, as shown in Odds Ratios.
Odds Ratios
where r1 and r1 are the two response levels
Note that exp(βi(Xi + 1)) = exp(βiXi) exp(βi). This shows that if Xi changes by a unit amount, the odds is multiplied by exp(βi), which we label the unit odds ratio. As Xi changes over its whole range, the odds are multiplied by exp((Xhigh - Xlow)βi) which we label the range odds ratio. For binary responses, the log odds ratio for flipped response levels involves only changing the sign of the parameter, so you might want the reciprocal of the reported value to focus on the last response level instead of the first.
In the Dose Response.jmp sample data table, the dose varies between 1 and 12.
 1 Select Help > Sample Data Library and open Dose Response.jmp.
 2 Select Analyze > Fit Model.
 3 Select response and click Y.
 4 Select dose and click Add.
 5 Click Run.
 6
Odds Ratios
The unit odds ratio for dose is 1.606 (which is exp(0.474)) and indicates that the odds of getting a Y = 0 rather than Y = 1 improves by a factor of 1.606 for each increase of one unit of dose. The range odds ratio for dose is 183.8 (exp((12-1)*0.474)) and indicates that the odds improve by a factor of 183.8 as dose is varied between 1 and 12.
For a two-level response, the Inverse Prediction command finds the x value that results in a specified probability.
 1 Select Help > Sample Data Library and open Ingots.jmp.
 2 Select Analyze > Fit Y by X.
 3 Select ready and click Y, Response.
 4 Select heat and click X, Factor.
 5 Select count and click Freq.
 6 Click OK.
Logistic Probability Plot
 7 From the red triangle menu next to Logistic Fit, select Inverse Prediction.
 8 For Probability, type 0.9.
 9 Click OK.
Inverse Prediction Plot
However, if you have another regressor variable (Soak), you must use the Fit Model platform, as follows:
 1 From the Ingots.jmp sample data table, select Analyze > Fit Model.
 2 Select ready and click Y.
 3 Select heat and soak and click Add.
 4 Select count and click Freq.
 5 Click Run.
 6 From the red triangle next to Nominal Logistic Fit, select Inverse Prediction.
Then the Inverse Prediction command displays the Inverse Prediction window shown in The Inverse Prediction Window and Table, for requesting the probability of obtaining a given value for one independent variable. To complete the dialog, click and type values in the editable X and Probability columns. Enter a value for a single X (heat or soak) and the probabilities that you want for the prediction. Set the remaining independent variable to missing by clicking in its X field and deleting. The missing regressor is the value that it will predict.
The Inverse Prediction Window and Table
See the appendix Statistical Details for more details about inverse prediction.
If you have ordinal or nominal response models, the Save Probability Formula command creates new data table columns.
If the response is numeric and has the ordinal modeling type, the Save Quantiles and Save Expected Values commands are also available.
The Save commands create the following new columns:
 • columns called Lin[j] that contain a linear combination of the regressors for response levels j = 1, 2, ... r - 1
 • a column called Prob[r], with a formula for the fit to the last level, r
 • 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.
 • 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.
creates columns in the current data table named OrdQ.05, OrdQ.50, and OrdQ.95 that fit the quantiles for these three probabilities.
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 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 Partition chapter of the Specialized Models book.
 1 Select Help > Sample Data Library and open Ingots.jmp.
 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
 8
ROC Curve
Produces a lift curve for the model. A lift curve shows the same information as an ROC curve, but in a way to dramatize the richness of the ordering at the beginning. The Y-axis shows the ratio of how rich that portion of the population is in the chosen response level compared to the rate of that response level as a whole. See the Partition chapter of the Specialized Models book for more details about lift curves. See the Specialized Models book for details about lift curves.
Lift Curve shows the lift curve for the same model specified for the ROC curve (ROC Curve).
Lift Curve