Examples for using mixed models in physics & engineering

Question

Could you highlight useful examples when it makes sense to use mixed models in physics / engineering?

I still wonder when I should use a mixed model and when not.

Answer 1

As I see it, there is no reason why these models cannot be used in these domains. My feeling is that there is a degree of techniques falling in and out of fashion. Often students will learn the techniques of their lecturers, mentors and colleagues, and I suspect in recent years LMM have gained traction in certain disciplines but not yet in others.

Here are a few examples of their applications to engineering and physics, along with one of my own applications in business.

• Productivity estimation of bulldozers using GLMM here they are modelling productivity of bulldozers, including different properties of the bulldozer and the operator. They consider soil type as a random effect.

• In my own work I have used LMM to estimate the time it takes workers to complete some process. Very roughly speaking: We want to know whether some change in the process (treatment) leads to a reduction in time to complete the process. A huge source of variability is the worker themselves, some are naturally a lot faster than others, therefore the specific worker is a random effect.

• Here is an example in engineering. An Analysis of defective products in auto parts factories with generalized linear mixed models I was not able to load a copy of the paper. However from reading the abstract I can imagine how they might be useful here. The data was collected from 12 machines and so you could imagine it might make sense to have machine as a random effect. You would have to read the article to be sure what they do though.

• Spatiotemporal dynamics of NO2 concentration with linear mixed models: A Bangladesh case study Published in the journal of physics and chemistry of the earth. I highlight this as the journal name specifically mentions physics and chemistry.

---

Update following Ben’s comment. I am not sure I can give a good answer for when to use them. For most of the examples above I tried to explain how they might be used there, because I think a good way to learn is to see examples and then as you become familiar with the examples, you will start to see how your potential use cases match examples you have seen before. I am not sure whether you have done many tutorials/hands on examples using these models, but I think working through a few of these would really help you to see how and why they are useful. I would recommend this tutorial, and note also the ‘What’ section gives an explanation of why you might want to use them. There is also this answer. To quote from the current top answer

“I believe that a multilevel model makes sense when there is reason to believe that observations are not necessarily independent of one another. Whatever "cluster" accounts for this non-independence can be modeled.”

In my use case my observations are the times it takes workers to complete some task. The times are not independent, and times from the same worker are likely to be similar (some workers are fast, some are slow). To account for this I group the times by the worker. The overall point of this was to determine whether some treatment had led to a speed-up.