Inquiry - Questions regarding Stability Study - Degradation Data Analysis

[#1]

I am a user of JMP 17 and I am currently working on a Stability Study - Degradation Data Analysis.

I have some inquiries and would like to reach out for assistance.

When reviewing the Simple Linear Path results for Model 1~4, I noticed the following:

• In Model 1, the JMP Estimate displays the ANCOVA model excluding the intercept and month terms
  (similar to using the "glm - model - noint option and with out main effect of A" in SAS: Model Y = B + A*B / Noint SS1 solution).
• 
• In Model 2, the results are the same as the ANCOVA model excluding the intercept. (not exist capture file)

With this in mind, I would like to know the method for calculating the p-values for the intercept and slope of each batch in the ANCOVA model for each respective Model. Additionally, I kindly request any relevant references or resources JMP can provide.

If possible, I would greatly appreciate your response to the following questions:

• What is the method for calculating the p-values for the intercept and slope of each batch in the ANCOVA model?
  Could you please provide any relevant references or resources?
• I also have a question regarding the removal of main effects when there is a significant interaction in ANCOVA.
  I have understood that in such cases, the main effects should not be removed. Do you have any appropriate references for this?

Thank you for your attention to my inquiry. If you have any further questions or require additional information, please feel free to let me know. Have a great day.

[#2]

Hi @CovariateIguana :  Good questions. From the start, you have to be very careful comparing JMP Fit Model (or Stability)  results and SAS proc GLM results. They use different model parameterizations so care must be taken when making direct comparisons. See this link for some detail.

https://www.jmp.com/support/help/en/17.1/index.shtml#page/jmp/nominal-factors.shtml#ww65535

That said...in Model 1 JMP is not using "the ANCOVA model excluding the intercept and month terms". JMP is using the full model (each main effect and interaction, with intercept). And, that looks the same as SAS (as you describe) because of the different ways (JMP vs SAS)  the models are parameterized; i.e., SAS proc GLM "Model Y = B + A*B / Noint SS1 solution" is a way to make the output look the same given the different ways JMP and SAS parameterize the model.  If you run the full model in SAS, and the full model in JMP, the parameters will look very different...but the "parameter estimates" can't be compared directly. SAS uses the "Indicator Function Parameterization" that is an optional output in JMP's Fit Model platform. Using the full model in SAS proc GLM, you can use Estimate statements to get the same results as JMP. And, in case this point gets lost; the JMP Fit Model results (full model) are equivalent to the JMP Stability results, and they are both equivalent to SAS proc GLM results (full model). But...and this is the key point, the parameters as shown in the output (JMP Fit Model vs JMP Stability vs SAS proc GLM) are not estimates of the same thing. And, consequently, the p-values, respectively, aren't testing the same hypotheses. You can see this via taking your stability data and running it through JMP Fit Model (full model) and comparing the estimates in "Parameter Estimates" with the estimates in "Indicator Function Parameterization" (which is what SAS proc GLM full model would produce). And compare both of those to the JMP Stability output. They all look different from each other, but they are estimating different things. And further, each of those three sets of parameters can be derived from either of the others. So, in that sense, they are equivalent. You may want to take some time looking at your parameter estimates (in "Parameter Estimates" and "Indicator Function Parameterization" via Fit Model, and "Estimate" via Stability Platform (as you show)) to make sure you (1) understand them and how they are related, and to make sure you (2) understand their respective p-values (i.e., what each null hypothesis is).

And...p-values, are based on Estimate/Stderr having a t distribution (under the null hypothesis); assuming the null hypothesis is true (i.e., parameter=0), p-value = 2 * Prob(T > |Estimate/Stderr|).