Sufficient DF's- NonEstimable error message for Full Factorial

[#1]

I have a dataset with 4 treatments (Locations) that were repeated for 3 Years. When I run a full factorial (Year, Location, Year*Location) I get the nonEstimable error message, as seen below. When I analyze just Year and Location with no interaction, I do get results as seen below. Now when I don't select a By element in the Fit Model control panel, specifically don't select Cultivar as a By element, I do get a result for the full factorial, as seen below.

1) Do I not have enough degrees of freedom to test the Full Factorial with a By element? Is why I am getting the NonEstimable message. I know the message has to do with confounding factors but to be honest I don't know what I am supposed to do as a solution.

(I have pasted some of my data to give an idea of what I am working with, please note the sample size being small and unbalanced for example)

2) If my DFs are too low, are there any solutions/alternatives to testing the interaction?

Full factorial- nonestimable:

No interaction:

Full factorial without By element:

Data snapshot:

[#2]

This may relate to a later discussion so I link it to it, as there are some answers which might be helpful: Re: How many DFs are required to test X number of main effects - JMP Fit Model

[#3]

1) Looking at your (incomplete) table, I have a strong suspicion your missing values are making it impossible to estimate the interactions, e.g. there is only 1 Tieton value for Brown Snout (Year 2012), so if you analyse By Cultivar, it will be possible to estimate the effect of Tieton for Brown Snout, but not the interaction of Tieton*Year since there is only 1 year available for Tieton. Your DF has been used up to estimate the effect of Tieton, you cannot get Tieton*Year.

I assume the other cultivars in the rest of your data table haves values for Tietion for the other years. This gives you the DFs you need to estimate Tieton*Year, but only if you do not analyse By: Cultivar.

2) If you had more terms in your model, you could remove the non significant terms, which would pool the data and allow you to estimate your interctions, but since it is not your case if you do By: Cultivar...  the closest thing you can do is to a model with Cultivar, but not Cultivar*Year or Cultivar*Location or Cultivar*Year*Location. It is equivalent to saying the interactions between Cultivar and other factors are non significant. This may allow the model build to estimate all the other terms: Year, Location, Cultivar, Year*Location. It will depend on how many missing values you have in your data table.