I agree with all that @Mark_Bailey has shared. To add my two cents, if you don't have JMP Pro, here's an idea for you to consider where you don't have to invoke informative missing on a platform dialog specification window, but get the moral equivalent of said invocation in the modeling analysis...the 'missingness' will be sort of hidden and not as efficiently/neatly displayed in tabular or data visualizations...but it will be in there.
First a bit of an explanation of how JMP handles 'missingness' for nominal variables/effects. In general the concept is called 'informative missing' throughout the JMP ecosystem. The primary presumption wrt to informative missing is that there is INFORMATION within the system of study that leads to the observation being missing. Maybe an underlying cause? Commonality? Or lurking common variable that leads to the missing observation?
For example, suppose one were to survey a bunch of fishermen about how many fish they caught and you were trying to model effects that influence the number of fish caught. In the survey one of the questions is 'fishing method'. And there are three options for respondents to pick from; 1. trolling, 2. spin casting, 3. still fishing. Respondents are given the option to leave a field blank...that is it's now 'missing' within the observation. Now let's suppose for some reason the respondents that tend to have the highest fish caught counts are also those that chose to NOT ANSWER THE QUESTION. And this makes some sense doesn't it? Fisherman are notorious for keeping their secrets so there is information wrt to the study when respondents leave out the answer. So now one would want to try and understand the underlying mechanism behind why the data is missing to better understand the entire system.
Now here's my suggestion within JMP. If you are willing to presume there is information in the 'missingness'...and this is a big presumption...then you can replace the missing cells with a psuedo value nominal value that is common in each missing cell. For analysis purposes, informative missing in JMP/JMP Pro generally treats the missingness as another level of the nominal variable. Hence it will be included in any effects that include that term. Here's the JMP documentation regarding informative missing within the Partition platform that is NOT part of JMP Pro. So make sure you closely examine each modeling platform dialogue specification box you are thinking of using...you may NOT have to mess with your data table after all:
https://www.jmp.com/support/help/en/15.2/#page/jmp/informative-missing-2.shtml