Contour Profile in JMP
Contour Profiler in JMP displays the prediction formula of the fitted model as contour lines, allowing you to examine the relationship between factors (X) and characteristic values (Y).
In particular, in the development and manufacturing stages of pharmaceuticals, it is recommended to construct a design space* by representing the relationship between factors and characteristics with contour lines using the experimental design method in the QbD (Quality by Design) concept. In doing so, JMP often uses the "contour profile" shown above.
*Multidimensional combination and interaction of input variables (e.g. raw material properties) and process parameters proven to ensure quality (from ICH Q8)
From time to time, from Japanese customers I want to display the predicted response values with a color gradation in the "Contour profile" as shown below. We may receive a request.
Unfortunately, JMP does not have the option to add a color gradient like the one above in the Contour Profiler.
Even in the case of multi-characteristics (multiple Ys), "Contour Profile" can be drawn by superimposing multiple characteristics as follows.
At this time, if you can add color gradation to multiple characteristics, The graph will be difficult to understand.
Contour lines of color gradation drawn with "Contour chart"
To draw the contour lines with color gradation shown at the beginning in JMP requires a little ingenuity.
As an example, let's use JMP's sample data "Bounce Data.jmp" and fit a response surface model to the characteristic Y "coefficient of restitution", and we want to make the response surface a contour line with a color gradation.
It starts with the [Contour Profile] displayed in the [Fit Model] report.
The contour lines displayed here are plotted with the value of the factor "Silane" fixed at 50, with "Silica" on the horizontal axis and "Silane" on the vertical axis.
Operations that create color gradient contours
1. From the red triangle button to the left of the report "Contour Profile" [Simulator] , change the number of iterations to 1, the progression of silica and sulfur to the arithmetic progression of position parameters, and set the number of steps to 100, as shown in the figure below. (The sequence remains "fixed" because in this example Silane is the factor fixing the value.)
2. Under "Simulator" Create table Click the button.
Then, the data table on the right side of the above figure is output. This data table is created as follows:
Divide the range of "Silica" (0.7-1.7) into 100 evenly spaced
Divide the range of "sulfur" (1.8-2.8) into 100 evenly spaced
⇒ Create 10,000 (=100 x 100) grids with silica on the horizontal axis and sulfur on the vertical axis, and enter the predicted value for each grid in "Restitution coefficient"
3.For the data table created in step 2. Graph > Contour Plot , specify [X] and [Y] as shown below, and check "Fill display area".
A contour plot is created. If necessary, right-click the legend displayed on the right and specify the color theme, the number of labels (how many to color), etc.
To display more value labels on the contour lines, click the red triangle button at the top left of the report. [contour label] Choose.
Color Gradient Contours Drawn in Graph Builder
Above, we showed how to use the "Contour Chart" platform, but you can also use the "Graph Builder" to create the data table created in step 2.
Which one is better depends on your preference, but please be aware that there are display limitations compared to the "Contour Plot", such as not being able to add value labels to the contour lines with the "Graph Builder".
by Naohiro Masukawa, JMP Japan
