Introduction Hello everybody! Recently, there’s been a lot of talk about meta-analysis, and here I would just like to quickly show that Bayesian multilevel modeling nicely takes care of your meta-analysis needs, and that it is easy to do in R with the rstan and brms packages. As you’ll see, meta-analysis is a special case of Bayesian multilevel modeling when you are unable or unwilling to put a prior distribution on the meta-analytic effect size estimate.

Experimental investigations commonly begin with a hypothesis, an expectation of what one might find: “We hypothesize that alcohol leads to slower reactions to events in a driving simulator.” Data is then collected and analyzed to specifically address this hypothesis. Almost always, the support for or against the hypothesis is statistical, not intraocular (Krantz, 1999). However, the prevailing statistical paradigm—null hypothesis significance testing (NHST)—never tests the researcher’s offered hypothesis, but instead the “null hypothesis”: That there is no relationship between alcohol consumption and reaction time.

In this post, I address the following problem: How to obtain regression lines and their associated confidence intervals at the average and individual-specific levels, in a two-level multilevel linear regression.
Background Visualization is perhaps the most effective way of communicating the results of a statistical model. For regression models, two figures are commonly used: The coefficient plot shows the coefficients of a model graphically, and can be used to replace or augment a model summary table.

The average psychologist’s statistical toolkit is expanding. Multilevel (mixed effects) models are now routinely used where 10 years ago repeated measures ANOVA prevailed. Bayesian statistics are coming. Isn’t this fantastic?
Well, yes and no. Here is a quote about the use of multilevel models by psycholinguists:
At a recent workshop on mixed-effects models, a prominent psycholinguist memorably quipped that encouraging psycholinguists to use linear mixed-effects models was like giving shotguns to toddlers.

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