Mixed model terminology

[#1]

Hi All,

I'm working through a paper where I am looking at fish swimming performance and am controlling for individual nested within species. I have two different types of tests I am running using the mixed model personality and I need help describing (naming, characterizing) those models when I write up my paper. In the journals I have submitted to I get a lot of reviews complaining that they don't understand what I am doing with my data because they are unfamiliar with JMP and the mixed model platform.

In the first test I am looking for differences between species in several input variables/body metrics (maximum bending curvature, duration of turn, etc).

In the model my fixed effect is Species and my random effect is Individual nested within species. If I didn't have individual as a random effect this would be a simple T-test, but I am unsure what to call it when I control for individual variation.

The second test is a linear model, in this case my fixed effects are species, bending curvature, and turn duration (and the full factorial of interactions), again with the random effect of individual nested in species. I'm assuming I can just call this a linear mixed model.

Thanks,

Stephen

[#2]

Terminology can be confusing, and unfortunately isn't universal.  I don't exactly know what you mean by "am controlling for individual nested within species". Controlling for a random effect? Perhaps this helps:

https://www.jmp.com/support/help/en/16.1/?os=mac&source=application&utm_source=helpmenu&utm_medium=a...

[#3]

I had this issue some time ago while attempting to estimate a hierarchical linear model (HLM) for publication. i get the impression that different programs are using different terminologies as well as different estimation methods and algorithms (not sure if there are any copy rights or patents).

My solution at the time was going through the prominent book in the field (education) and estimate the example models with their sample data. Once i obtained the exact results I was sure i was using the models acceptable in the field and can confidently use their conventional terminology.

The lack of communication between disciplines means that each has their own terminology. For commercial issues i would guess it would be very difficult to find an explicit translation of the terminology from one software to another. these reasons put together also make it almost impossible to find a professional that would be able to pull this kind of answer off the cuff.

[#4]

Hi,

Mixed models can be confusing. And the terminology is also quite confusing. However, I am not sure that the terminology in JMP is very different from the terminology in SAS or R, for example.

In any case, I am wondering if you really need to use mixed models for your analysis. Why do you need to add an effect for individuals? An example where you might do this is if you are measuring the response across several timepoints for the same set of individuals ("repeated measures"). But most of the time it does not make sense to add an effect for individuals.

It might help if you can attach example data sets to illustrate the type of analyses that you need to do.

I hope that helps,

Phil

[#5]

The main model that I am doing is a linear model looking at the relationship between body shape variables (how much curvature the fish has when bending and how fast it bends) and swimming performance variables (how much does the fish a fish turn and how fast) and comparing the results between species with different body shapes. The criticisms I've gotten in the past have related to not controlling for variation among individuals within species. The reviewers are concerned that my data is driven by the behavior of one or a few individuals and not the species as a whole.

Including individual as a random effect in the linear mixed model makes sense. I figured I should still include individual as a random effect when I am comparing the means of the different species in the dependent variables of the linear mixed model.

I've attached my data with a script file with the models I am trying to run.

[#6]

That helps, thanks.

Why do you have multiple observations (rows) for each individual?  

[#7]

I recorded 15 independent turns for each individual.

[#8]

Okay. Now it makes much more sense as to why you need to add an effect for individual.

Standard regression assumes that all observations are independent. That would be the case if each row in your table were a unique individual.

Because you have multiple observations for each individual, the observations are not independent. Observations within each individual could be expected to be more similar.

One way to ensure that the model is appropriate is to add a random effect for Individual. This should be nested within species because the individuals are unique to each species (of course). A fixed effect for Individual would not make sense because individuals are randomly drawn representatives from a distribution of a larger population rather than controllable levels of a variable.

It seems like you understand all of this because that is what you have done with your models. 

So now the question is: what are your reviewers not understanding? How would they have you model the data?

As I said before, I am pretty sure that the terminology used by JMP for mixed models is the same as used in other software. (I did a module on mixed models as part of my MSc where we used R. I repeated all the examples in JMP and I do not remember any difference in the reported outputs)

[#9]

So I need to do two different models. One is the linear mixed model where I have continuous and categorical fixed effects in addition to the random nested effect. 

The other model includes only the categorical fixed effect (species) and the continuous response (the body shape variables), I assume I need to include individual as a random nested effect again. In this case does it matter if I use standard least squares with REML or mixed model personalities? I'm leaning toward SLS+REML

[#10 · Accepted solution]

Yes, including individual as a random effect (nested under species) is appropriate for your data. As I said, if you don't include Individual, that would imply that each row of data is a completely independent measurement, and that is not the case.

SLS + REML will work fine for your example.

Fit Mixed gives the opportunity to use more complex covariance structures but I don't think you want to get into that complexity. (If you do, then @jiancao has done some great presentations at Discovery about this)