Need help with Repeated MeasurementsHi,
a customer has the following situation:
several Products (X_1, V_1_0 to V_1_19) will be tested with 5 culture dishes each (X_3, 1 to 5) over 4 times (X_14-X_17, e.g. 0, 12, 48,...h). There are several factors they want to know which of them and how they influences the results (X_4-X_7) .
How to best set up this model? Using MANOVA or using LS with Random Effects? When stacking and adding the factors to my model it has singularity issues.
Please stick to JMP functionality first.
I also thought about FDE but I think the data is to few to get a good model in my eyes.
@DonMcCormack @julian
Re: Need help with Repeated MeasurementsHi Martin,
I am a bit confused by the data (it may be due to the anonymization process). I would back up a step and make sure the client has a clear statement of what they are trying to do. Here are some various questions that came to mind as I tried to make sense of the data...
1. Should each product be considered together or individually?
2. What is the outcome of interest? Is it the measured value at each time point or is it a growth rate or the time that the growth reaches a certain point, or a % change (to make comparisons across products)?
3. It looks like X14 = response for time point 1, X15 = response for time point 2, etc. (which matches your stacked use of the data). Can you replace with the time values?
4. the X4 - X7 look to be specific levels per product - put on a standardized scale??
5. I believe you are trying to understand the impact of X4 - X7 on the responses as shown in the attached screen grab...
6. maybe FDE would work after you do steps 3 and 4?
Re: Need help with Repeated MeasurementsHi @karencopeland ,
I try to answer the questions.
1. Should each product be considered together or individually?
The products (X_1) are classified by product types (X_2)
2. What is the outcome of interest? Is it the measured value at each time point or is it a growth rate or the time that the growth reaches a certain point, or a % change (to make comparisons across products)?
I'll check this again, but what I understood she wants to know for each product if the factors X4-X7 are necessary and how they affect the result of the cultures. The ideal behaviour is flat for the first 3 time points until the last time point which should be high. If all is flat it did not work.
3. It looks like X14 = response for time point 1, X15 = response for time point 2, etc. (which matches your stacked use of the data). Can you replace with the time values?
0, 4, 24, 168 min
4. the X4 - X7 look to be specific levels per product - put on a standardized scale??
You can think of an experiment where one product has one setting of X_4-X_7 and will be tested in 5 culture dishes in parallel, each measured at 4 time points. The next product has another different setting of X_4-X_7 and again being tested in 5 culture dishes and measured 4 times.
That said, the 5 dishes are used to see the variation occuring for one setting. And the products are treated by the 4 factors and it is of interest what affects the outcome most and how does that differ for each product. e.g. if a high setting of X_4 would have a positive effect on product A is it also true for product B or should it be not used there
5. I believe you are trying to understand the impact of X4 - X7 on the responses as shown in the attached screen grab...
yes, but I get too few degrees of freedom to check for this
6. maybe FDE would work after you do steps 3 and 4?
I think the models are not accurate enough with just up to 2 knots to be set. (see attached file StackedForFDE). I briefly checked standardization but I couldn't see a benefit for the model here.
Re: Need help with Repeated MeasurementsIn terms of MANOVA vs. mixed models, I defer to Statistical Method for the analysis of Repeated measurements (C.S. Davis, 2002, Springer) who indicates MANOVA is under powered relative to mixed models. Personally, I find MANOVA harder to interpret and prefer a linear modeling approach. That said, you'll be limited with respect to the covariance structures in JMP, with only compound symmetry available. JMP Pro has a standard set of covariance structures for repeated measures but not nearly as many as SAS. I did a Discovery paper a few years back dealing with this topic. BTW, there's a chapter in the Davis book on growth curve modeling.
FDE? I think it would be a viable option, but you may run into issues if people ask about statistically differences. Additionally, depending on the industry, there may be standard models that are used because the parameters have particular interpretations.
Is this coming from a regulated industry? If so, there might be a standard operating procedure for modeling the data.
Re: Need help with Repeated MeasurementsAfter looking at the data and comments a bit more closely, I think you're going to have issues trying to fit this data at all. The responses appear to be very discrete percentage values, which may be better fit by considering them ordinal. If you do treat them as continuous, you'll need to use a non Gaussian mixed model (Beta?). The levels are unique to the product, so you only can fit the factors or the product levels, but not both.
Re: Need help with Repeated MeasurementsI looked at the data. The model with subject being a random effect as you specified for the repeated measures that assumes a CS structure can actually be fit with the removal of four fixed effects, X4-X7. There is a total lack of variability on these fixed effects per subject id X__3[X__1] , which is shown in the in the JMP Singularity Report.
Re: Need help with Repeated MeasurementsThis is a case of trying to model before understanding the data. It appears that each product is a unique combination of X4 - X7, some products work (i.e., they hit 100 units prior to the end of the time) and some don't. The question is then, can we figure out which combinations of X4 -X7 are "good" and which are "bad". I don't see this fitting into a clean model ....
