This example uses the AdverseR.jmp sample data table to illustrate an ordinal logistic regression. Suppose you want to model the severity of an adverse event as a function of treatment duration value.
1.
Open the AdverseR.jmp sample data table.
2.
Right-click on the icon to the left of ADR SEVERITY and change the modeling type to ordinal.
3.
Select Analyze > Fit Y by X.
4.
Select ADR SEVERITY and click Y, Response.
5.
Select ADR DURATION and click X, Factor.
6.
Example of Ordinal Logistic Report
In the plot, markers for the data are drawn at their x-coordinate. When several data points appear at the same y position, the points are jittered. That is, small spaces appear between the data points so you can see each point more clearly.
For details about the Whole Model Test report and the Parameter Estimates report, see The Logistic Report. In the Parameter Estimates report, an intercept parameter is estimated for every response level except the last, but there is only one slope parameter. The intercept parameters show the spacing of the response levels. They always increase monotonically.
This example uses the Car Physical Data.jmp sample data table to show an additional example of a logistic plot. Suppose you want to use weight to predict car size (Type) for 116 cars. Car size can be one of the following, from smallest to largest: Sporty, Small, Compact, Medium, or Large.
1.
Open the Car Physical Data.jmp sample data table.
2.
In the Columns panel, right-click on the icon to the left of Type, and select Ordinal.
3.
Right-click on Type, and select Column Info.
6.
7.
Select Analyze > Fit Y by X.
8.
Select Type and click Y, Response.
9.
Select Weight and click X, Factor.
10.
Example of Type by Weight Logistic Plot
In Example of Type by Weight Logistic Plot, note the following observations:
Markers for the data are drawn at their x-coordinate, with the y position jittered randomly within the range corresponding to the response category for that row.
If the x -variable has no effect on the response, then the fitted lines are horizontal and the probabilities are constant for each response across the continuous factor range. Examples of Sample Data Table and Logistic Plot Showing No y by x Relationship shows a logistic plot where Weight is not useful for predicting Type.
Examples of Sample Data Table and Logistic Plot Showing No y by x Relationship
Examples of Sample Data Table and Logistic Plot Showing an Almost Perfect y by x Relationship
1.
Open the Penicillin.jmp sample data table.
2.
Select Analyze > Fit Y by X.
3.
Select Response and click Y, Response.
4.
Select In(Dose) and click X, Factor.
Notice that JMP automatically fills in Count for Freq. Count was previously assigned the role of Freq.
5.
7.
Select Cured as the positive.
8.
The results for the response by In(Dose) example are shown here. The ROC curve plots the probabilities described above, for predicting response. Note that in the ROC Table, the row with the highest Sens-(1-Spec) is marked with an asterisk.
Examples of ROC Curve and Table
In a study of rabbits who were given penicillin, you want to know what dose of penicillin results in a 0.5 probability of curing a rabbit. In this case, the inverse prediction for 0.5 is called the ED50, the effective dose corresponding to a 50% survival rate. Use the crosshair tool to visually approximate an inverse prediction.
To see which value of In(dose) is equally likely either to cure or to be lethal, proceed as follows:
1.
Open the Penicillin.jmp sample data table.
2.
Select Analyze > Fit Y by X.
3.
Select Response and click Y, Response.
4.
Select In(Dose) and click X, Factor.
Notice that JMP automatically fills in Count for Freq. Count was previously assigned the role of Freq.
5.
8.
Move the cross-hair intersection to the prediction line, and read the In(dose) value that shows on the horizontal axis.
In this example, a rabbit with a In(dose) of approximately -0.9 is equally likely to be cured as it is to die.
Example of Crosshair Tool on Logistic Plot
If your response has exactly two levels, the Inverse Prediction option enables you to request an exact inverse prediction. You are given the x value corresponding to a given probability of the lower response category, as well as a confidence interval for that x value.
To use the Inverse Prediction option, proceed as follows:
1.
Open the Penicillin.jmp sample data table.
2.
Select Analyze > Fit Y by X.
3.
Select Response and click Y, Response.
4.
Select In(Dose) and click X, Factor.
Notice that JMP automatically fills in Count for Freq. Count was previously assigned the role of Freq.
5.
7.
Type 0.95 for the Confidence Level.
8.
Select Two sided for the confidence interval.
10.
Inverse Prediction Window
Example of Inverse Prediction Plot
The estimates of the x values and the confidence intervals are shown in the report as well as in the probability plot. For example, the value of ln(Dose) that results in a 90% probability of being cured is estimated to be between -0.526 and 0.783.