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Random effects for non-repeated measures data in GLMM

Ross_Metusalem

@jiancao, your GLMM presentation at Midyear involved an example (Example #2) where you specified a random effect for a factor with only one observation per level: There was one observation per subject in a clinical study, but you included Subject as a random effect to account for additional subject-to-subject variability. I learned mixed models in the context of normal response distributions in which repeated measures are required to estimate random effects, so I'm not familiar with this use of random effects.

Two questions:

Why aren't repeated measures necessary to estimate random effects in GLMMs?
Is the use of random effects in GLMMs on non-repeated measures data common in your experience? If it's not common, I'd probably avoid presenting an example like that in GLMM demos and just stick to repeated measures data.

Accepted answers

jiancao

Thank you, Ross, for following up on this!

Q1. Why aren't repeated measures necessary to estimate random effects in GLMMs?

The distributions for the two GLMM models that I showed are Binomial and Poisson. They are considered single-parameter distributions. For Poisson, the parameter is λ, which is the mean and variance; for Binomial, it’s p, and the mean is n*p and variance is n*p*(1-p) where n is sample size. For singles parameter distributions like these GLMM can identify the variation due to random subject variability with cross-sectional data. (These are the only two GLMM models currently available in JMP Pro 17.)

Q2. Is the use of random effects in GLMMs on non-repeated measures data common in your experience? If it's not common, I'd probably avoid presenting an example like that in GLMM demos and just stick to repeated measures data.

A. I haven’t had a lot of experience with GLMM yet in my current role and in my previous jobs, but I can see how GLMM could be useful. For example, split-plot designs are common. The regression model designated by Custom Design is a linear mixed model since it presumes the response is continuous. What if your response is Pass/Fail, or defect counts? You should consider GLMM.

As to whether to demo GLMM, it depends on your audience. If your prospects have never used GLM or LMM, then GLMM may be hard. But if they already know GLM or LMM, then GLMM is a natural upgrade since I would want it.

All comments

jiancao

Thank you, Ross, for following up on this!

Q1. Why aren't repeated measures necessary to estimate random effects in GLMMs?

Ross_Metusalem

Thanks @jiancao. So it sounds like cross-sectional data works with the currently available response distributions in GLMM but if a future version introduces a distribution with a separate scale parameter (e.g. Gamma), then we would require repeated measures data for a GLMM with that distribution.

I agree about the applicability of GLMMs in general. They are going to be popular in a segment of the academic market. I am more curious specifically about demoing an example like your Example #2, where we don't have repeated measures data as we would in a standard mixed model. For people who use GLMMs a lot, perhaps they are familiar with the use of random effects in cross-sectional contexts as in Example #2, but maybe this actually is not common and we'd want to avoid demoing an example like that to avoid confusion or getting too far into the statistical weeds.

jiancao

So it sounds like cross-sectional data works with the currently available response distributions in GLMM but if a future version introduces a distribution with a separate scale parameter (e.g. Gamma), then we would require repeated measures data for a GLMM with that distribution.

Correct.

For people who use GLMMs a lot, perhaps they are familiar with the use of random effects in cross-sectional contexts as in Example #2, but maybe this actually is not common, and we'd want to avoid demoing an example like that to avoid confusion or getting too far into the statistical weeds.

For people who’re familiar with GLMM they will likely ask about distributions like Negative Binomial or repeated structures like AR(1) for within-subject variability both of which I mentioned at the end of my presentation. As for whether to avoid demoing cases like example #2 before JMP Pro 18 comes out, I let you decide.

In my Ex.#3 Manufacturing Defects (this is in the JMP documentation), the count is repeated per Lot but not per Unit. If you only include Lot as a random effect you end up with over-dispersion (i.e., extra variability), so the recommended GLMM model is the one with both Lot and Unit as random effects, which I showed.