There was an interesting thread on twitter about linear mixed models (LMMs) that someone made me aware of recently. (I stopped following twitter because of its general inanity, but this thread is worth commenting on.) The gist of the complaints (trying to recreate this list from memory) were. My list is an amalgamation of comments from different people; I think that the thread started here:
Inspired by @IrisVanRooij, I want to express some concerns that may be controversial and even outrageous to some but I feel we at least should have a discussion. I'm wondering if statistics in psycholinguistics could use a rethink. It feels like the tail now wags the dog.
— Fernanda Ferreira (@fernandaedi) December 20, 2020
To summarize the complaints:
- LMMs take too long to fit (cf. repeated measures ANOVA). This slows down student output.
- Too much time is spent on thinking about what the right analysis is.
- The interpretation of LMMs can change dramatically depending on which model you fit.
- Reviewers will always object to whatever analysis one does and demand a different one. Often which analysis one does doesn't matter as regards interpretation.
- The lme4 package exhibits all kinds of weird and unstable behavior. Should we trust its output?
- The focus has shifted away from substantive theoretical issues within psych* to statistical methods, but psych* people cannot be statisticians and can never know enough. This led to the colorful comment that doing statistics should be like taking a crap---it shouldn't become the center of your entire existence.
Indeed, a mathematical psychologist I know, someone who knows what they're doing, once told me that if you cannot answer your question with a paired t-test, you are asking the wrong question. In fact, if I go back to my existing data-sets that I have published between 2002 and 2020, almost all of them can be reasonably analyzed using a series of paired t-tests.
There is a presupposition that lies behind the above complaints: the purpose of data analysis is to find out whether an effect is significant or not. Once one understands that that's not the primary purpose of a statistical analysis, things start to make more sense. The problem is that it's just very hard to comprehend this point; this is because the idea of null hypothesis significance testing is very deeply entrenched in our minds. Walking away from it feels impossible.
Here are some thoughts about the above objections.
1. If you want the simplicity of paired t-tests and repeated measures ANOVA, absolutely go for it. But release your data and code, and be open to others analyzing your data differently. I think it's perfectly fine to spend your entire life doing just paired t-tests and publishing the resulting t and p-values. Of course, you are still fitting linear mixed models, but heavily simplified ones. Sometimes it won't matter whether you fit a complicated model or a simple one, but sometimes it will. It has happened to me that a paired t-test was exactly the wrong thing to do, and I spent a lot of time trying to model the data differently. Should one care about these edge cases? I think this is a subjective decision that each one of us has to make individually. Here is another example of a simple two-condition study where a complicated model that took forever to fit gave new insight into the underlying process generating the data. The problem here comes down to the goal of a statistical analysis. If we accept the premise that statistical significance is the goal, then we should just go ahead and fit that paired t-test. If, instead, the goal is to model the generative process, then you will start losing time. What position you take really depends on what you want to achieve.
2. There is no one right analysis, and reviewers will always object to whatever analysis you present. The reason that reviewers propose alternative analyses has nothing to do with the inherent flexibility of statistical methods. It has to do with academics being contrarians. I notice this in my own behavior: if my student does X, I want them to do Y!=X. If they do Y, I want them to do X!=Y. I suspect that academics are a self-selected lot, and one thing they are good at is objecting to whatever someone else says or does. So, the fact that reviewers keep asking for different analyses is just the price one has to pay for dealing with academics, it's not an inherent problem with statistics per se. Notice that reviewers also object to the logic of a paper, and to the writing. We are so used to dealing with those things that we don't realize it's the same type of reaction we are seeing to the statistical analyses.
3. If you want speed and still want to fit linear mixed models, use the right tools. There are plenty of ways to fit linear mixed models fast. rstanarm, LMMs in Julia, etc. E.g., Doug Bates, Phillip Alday, and Reinhold Kliegl taught a one-week course on fitting LMMs super fast in Julia: see here.
4. The interpretation of linear mixed models depends on model specification. This surprises many people, but the surprise is due to the fact that people have a very incomplete understanding of what they are doing. If you cannot be bothered to study linear mixed modeling theory (understandable, life is short), stick to paired t-tests.
5. lme4's unstable and weird behavior is problematic, but this is not enough reason to abandon linear mixed models. The weirdness of messages, and the inconsistencies of lme4 are really frustrating, one has to admit that. Perhaps this is the price one has to pay for free software (although, having used non-free software like Word, SPSS, Excel, I'm not so sure there is any advantage). But the fact is that LMMs give you the power to incorporate variance components in a sensible way, and lme4 does the job, if you know what you are doing. Like any other instrument one thinks about using as a professional, if you can't be bothered to learn to use it, then just use some simpler method you do know how to use. E.g., I can't use fMRI; I don't have access to the equipment. I'm forced to work with simpler methods, and I have to live with that. If you want more control over your hierarchical models than lme4 provides, learn Stan. E.g., see our chapter on hierarchical models here.
Personally, I think that it is possible to learn enough statistics to be able to use linear mixed models competently; one doesn't need to become a statistician. The curriculum I think one needs in psych and related areas is encapsulated in our summer school on statistical methods, which we run annually at Potsdam. It's a time commitment, but it's worth it. I have seen many people go from zero knowledge to fitting sophisticated hierarchical models, so I know that people can learn all this without it taking over their entire life.
Probably the biggest problem behind all these complaints is the misunderstanding surrounding null hypothesis significance testing. Unfortunately,p-values will rarely tell you anything useful, significant or not, unless you are willing to put in serious time and effort (the very thing people want to avoid doing). So it really not going to matter much whether you compute them using paired t-tests or linear mixed models.
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