How does JMP do BoxCox transformations?

[#1]

I have recently been converting JMP formulas into Excel using the python code option. I have been unable to actually transfer any formula (MLR) involving a BoxCox transformation. It have manually done the calculations following the formula and have gone numbers in the multimillions instead of 100 thousands where it should be. If someone knows if the formula is already converted back or If I need to and what I need to do to apply the inverse BoxCox to get it back in normal terms. I don't know if I am missing something or if the Python Code through the publish formula option is missing something. I was hoping that someone could explain how JMP preforms the Box Cox transformation so that I can better understand it to potentially fix it. I tried to attach the code of the formula but it wouldn't allow me to post. Any help would be appreciated.

[#2]

Documentation and formula for Box-Cox transformation is available here: https://www.jmp.com/support/help/en/18.2/index.shtml#page/jmp/boxcox-y-transformation.shtml

[#3]

Thank this did help me better understand BoxCox transformations in general but not how JMP does them necessarily. The following question I believe would help me understand.  The numbers that JMP shows in the Parameter Estimates section, for a BoxCox formula, are those just BoxCox transformed or have they already been inverse transformed back into understandable units?

[#4]

@DWS  If all you do is select "Box Cox Transformation" under the "Factor Profiling" menu, then no transformation is applied and the parameter estimates are based on Y. But if you further Refit with the box-cox transformation (red triangle in the "Box Cox Transformations" output), the parameter estimates are based on the transformed Y. 

[#5]

OK, just to be clear, the formula that is give after I have clicked "Refit with Transformation", in that new menu , that formula and that parameter estimates are not transformed then inverse transformed back into real units but are left in transformed units. If this is the case then is is possible to know the formula JMP uses to inverse transform them because, it does give inverse normal units in the save column prediction formula? or should I apply a normal inverse transformation? Also, do you know this from experience? or is this written somewhere because I could not find it anywhere. Sorry for the number of questions.

[#6]

@DWS : As you can see, when you refit and save the prediction formula it is back transformed so the predictions are in the original scale of Y. And the formula in that new column is the back-transformation formula you seek. I'm not sure if this is in the JMP help or not (but I can see what it is doing in my own work)  I'm not sure what you are asking about the parameter estimates though; they do not get transformed in any way; only Y does.

[#7]

Okay, In let me give you an example of just one X variable and intercept between the two formulas. Non BoxCox: Intercept: 254,077 X1: -44,880. Same formula and variable after BoxCox: Intercept: 61,472,780 X1; -43,139. You see my issue. These numbers are taken from the parameter estimate and verified in the formula editor. All the x variables are the same they are not too far off from their non transformed counter parts but the intercept is very off. I don't know why this is and I cannot think of how this could even be possible.

[#8]

@DWS  What is your lambda in the BC transformation? And how many X's do you have? Can you take a pic of both sets of parameter estimates?

[#9]

[#10]

@DWS   Oh dear. I think back-transforming is the least of your worries. Before you can think about interpreting coefficients (especially one of over 50), you’ll want to make sure the terms you have in your model can be estimated with the data you have. Some estimates are biased, some are zeroed. That indicates you are trying to estimate some parameters wrt X’s that are highly correlated, and/or some that are not estimable because the structure of your data doesn’t support estimating the terms you are trying to estimate. Your VIF’s in your parameter estimate table (if they aren’t visible, right mouse click on the parm estimates table to choose them) will help you identify multi-collinearity (correlation). For example, if X1 and X2 move together, then including both in the model makes both of their coefficients unreliable wrt interpretation…so one of them should be excluded as a candidate in the model. 

Also, if lambda = -0.002, it may be easier to use the LN transformation; it’s easier to interpret, and -0.002 is very close to 0 (lambda=0 corresponds to the LN transformation). 

Edit: more here.

https://community.jmp.com/t5/Discussions/Parameter-Estimates-being-zerod/m-p/751701