When to use Standard Least Square personality using the attrobute 'random' instead of Mixed Model personality?

[#1]

Hi, I'm trying to make a model with four fixed effects: strain, concentration, their interaction,  day (because I have insufficient experimental days to make it a random effect). The random effects would be replicate nested within plate (intending 96 well plates) and plate nested within day. I understand that I have 2 options to model this in JMP:

1. 'Standard Least Square' personality selecting the random effects as random using 'attributes'

2. 'Mixed Model' personality, the issue with this is that the output doesn't show R^2 values so I am unable to see how much of the variance in the model is explained by my effects. 

Which one would be best to use?

Thank you!

[#2]

Hi @blip555555,

Following our discussion on your previous post, I just looked at the Help section related to Mixed Models. The Mixed Model personality appears to be helpful when you have complex covariance structures.

If you don't have specific covariance structure (setting structure = Residual : no covariance between observations, so the errors are independent), you can build the model either with the Standard Least Square personality with random effects or with the Mixed Model personality, and you will obtain the same results.

For illustration, I tried it with the dataset "Machine", and the two models are the same with the platforms, as the covariance structure is set on "Residual" :

Hope this answer will help you,

[#3]

Dear Victor, 

I see. How do I know if my errors are independent? 

To give some background, I am analysing how antibiotic concentration and bacterial strain influence a fluorescence marker (response variable). My fixed effects are: experimental day (because I didn't conduct the experiment on more than 5 different days), strain, concentration, strain*concentration. My random effects are: replicate nested within plate (account for variation in technical replicates in the same 96-well plate) and plate nested within day (account for variation between plates in the same day). I don't think there's a reason to believe that my errors are dependent after accounting for the variation between replicates and plates. 

Thank you!

[#4]

Hi @blip555555,

You could check several aspects :

• In "Row Diagnostics", you could check the "Residual by Predicted Plot" and "Residual by Row" to check some assumptions behind linear regression models, respectively the constant variance of residuals, and the independance of observations (no specific pattern in the residuals when looking at residuals vs. row).
• You can also look at "Covariance Matrix of Variance Component Estimates" below REML report to check if the covariance between random effects are relatively low.
• Finally, you could also save residuals from the analysis in your datatable, and check the correlations between your residuals and original factors. As the model should have captured the variation from your factors, your residuals should have very low correlations with the original factors.
  You can also use residuals in Control charts, to assess if there may be some strange patterns/values, and possibly link it to factors or specific conditions, and/or assess some slow drifts in residuals that may look suspicious (similar to residual vs. row plot).

Hope this answer will help you,

[#5]

Dear Victor, 

Thank you so much for your replies and sorry for the amountof questions, I'm very new to JMP and statistical modelling in general. I plotted my residuals by predicted as attached below and I also had a look at the covariance matrix components estimates, also attached below. It seems like the standard least square personality with random effects works?

[#6]

Looking at the captures, yes it seems to "work" as the variation of residuals seems random, except the first capture where there seems to be some kind of group effect with no intermediate values ? But this could be the result of your random/blocking effects.

Questions are not a problem, the lack of information in the responses may be. Statistics is not a "yes or no" situation, it's a degree of confidence (and risk) about the decision you want to take based on the information and adequacy of your models. Assessing this situation is difficult if not impossible without the dataset to explore the situation.

If you want to share data in an anonimized way, the option Anonymize Data works well.

Hope this answer will help you,