Linear models versus mixed linear models
Hi community,
There has been a lot of discussion of the advanges of Bayesian versus frequentist statistics in psychology, but there has been relatively few discussions on the advantages of linear mixed effects models over linear models. In cognitive psychology, for example, researchers generally analyze mean RT data from each subject and condition by (i) conducting an omnibus ANOVA and (ii) computing contrasts (or post-hoc tests, depending on a priori hypotheses). This is what textbooks (e.g., Howell) teach. In addition, ANOVA and linear regressions are developed in separate chapters (e.g., Howell), and students generally discover the link between the two analyses late in their university curriculum (or in the texbook).
A friend of mine, researcher in economy, recently asked me the following question: "Why do you guys generally use linear instead of mixed linear models, and why do you guys teach ANOVAs separately from linear regression in psychology?" Frankly, I don't see any good reason for both.
We spend hours collecting hundreds of trials, to compute an arbitrary summary statistic (the mean) that we submit to a linear model. Why not getting rid of this practice, and systematically compute mixed linear models (whether frequentist or Bayesian) on raw data ? In this respect, I note that mixed linear models are not yet included in JASP, (though I am aware that they will be part of a future release), so I guess they have not been a priority for developers, and there must be a good reason for that since you guys are amazing statisticians.
I would appreciate hearing your thoughts on this.
Mathieu
Comments
Hi Mathieu,
Yes, they will be part of the next release, which is about a month away.
There is probably no good scientific reason against mixed effects models, but then again, good scientific reasons do not always win (e.g., the field is still dominated by p-values). If you press me, I may try and argue that ANOVA models are easier to understand, apply, and teach. I mean, you'd present the binomial model first before you tell students about generalized linear mixed effects models. Also, when you average data within a subject you loose information; but in return, you gain a certain robustness. Finally, people might argue that in most situations, it won't matter much. That said, I do like these models and they'll be in the next version of JASP. (Actually, the Bayesian "ANOVA" currently in JASP is in fact a linear mixed effect model.) Also, the visual modeling module we just added also does mixed models.
Cheers,
E.J.