Simulate Responses in JMP 13 is revamped to be more useful
The Simulate Responses feature throughout various design of experiments (DOE) platforms has always been a useful tool for generating a set of responses according to a specified model. I use it frequently for the simulated responses in Fit Model (or other appropriate platforms), as a way to check that the model is being fit as expected. Prior to JMP 13, Simulate Responses had limitations:
Simulation was limited to linear regression models with normal errors.
The ability to simulate responses was tied to the DOE window and the Simulate Responses window. If you closed either window, you would have to make a new data table to simulate responses again.
If you wanted to run a Monte Carlo simulation study using simulated responses (that is, simulating a large number of responses from the specified model and collecting results), there was no easy way to do so using the simulated responses from the DOE platform.
Simulate Responses in JMP 13
The look and feel of the Simulate Responses dialog remains the same in JMP 13. But to address the limitations I mentioned above, some new features have been added. That's the focus of the rest of this post.
Different distributions for the response
There are times when conducting an experiment that the response is not continuous, but instead either pass/fail or count data. In JMP 13, in addition to a linear regression model with normal errors, you now also have the ability to simulate responses that follow a Binomial or Poisson distribution.
Relaunching the Simulate Responses dialog
As discussed above, because Simulate Responses was tied to the DOE platform, there was no easy way to relaunch the Simulate Responses dialog once either was closed. In JMP 13, Simulate Responses is tied to the data table. A table script, called DOE Simulate, relaunches the simulation dialog.Automatic formula creation
In my view, the most powerful new aspect of the revamped Simulate Responses can be easy to miss. I’ll demonstrate with a simple example, a 12-run Custom Design with four continuous factors (X1-X4). When you select Simulate Responses from the hotspot in a DOE platform and you create a data table, you now end up with two columns for each response that have the same values initially. The second one, Y Simulated (where Y is the name of the response), gets updated each time the Apply button is clicked in the dialog. Why the need for two columns?
If you right-click on the column name, you see that Y Simulated is actually a Formula Column. The column Y has no formula – it is simply filled in during the data table creation -- the idea being that you fill your own response values there when collecting data.
If you examine the formula, you see the responses are generated based on the model specified in the Simulate Responses dialog:
This means that you can also simulate responses by clicking the Apply button within the formula editor. Note that this formula is automatically created by the Simulate Responses dialog. Suppose you change the coefficients and distribution, like this:
When you click the Apply button, your Y Simulated column now has count data.
The script updates the underlying formula to reflect the new model:Simulation studies
Why am I so excited about this aspect of Simulate Responses? Simulation studies. For users comfortable using JSL, the automatic formula only requires the use of Eval Formula to simulate a new response, and then gathering the desired information via scripting. What’s more, if you have JMP Pro 13, this formula allows you to perform one-click Monte Carlo simulations (akin to the one-click bootstrap).
Stay tuned for a blog post by Ryan Parker explaining how to use this new Simulate feature. In a future blog post, I’ll show just how easy it is to perform empirical power calculations using the new Simulate Responses with one-click Simulate.