# logistic mixed effects model

I am trying to replicate the findings of a paper that has the following setup:

The paper aims to test whether the recall rates were better for words learned from in-group members than from out-group members. After the learners hear the words, they are asked to answer "Did X say this?" questions as either YES or NO, which includes all combinations of member-word pairs. Their in-group bias is measured too. Then the accuracy of the participants is calculated.

The authors ran a logistic mixed-effects model with accuracy per trial as the dependent measure and fixed effects for group membership (in-group [reference level] vs. out-group), in-group bias, and their interaction. They added per participant and per items random intercepts and by participant slope for group membership.

I am not very familiar with the mixed-effects models and I thought that a repeated-measures ANOVA might work as well. What is the added value of regression models here?

Thank you!

## 1 Answer

Repeated measures ANOVA (rmANOVA) is a special case of a mixed effects model. In this case it would not be appropriate to use rmANOVA for the following reasons:

1. According to the description: "per participant and per items random intercepts" - this sounds very much like crossed random effects, which rmANOVA cannot handle

2. Since they also say "by participant slope for group membership" this means they fitted random slopes, so this would also not be handled by rmANOVA

3. Since the outcome is binary ("YES or No") they have used a logistic model. rmANOVA is for a continuous outcome, not a binary data one.

• Thank you for your explanation! May I also ask slightly differently? Assume that the outcome was continuous and forget about what the authors actually did. Would the rmANOVA be still inappropriate? Thank you @RobertLong Commented Jun 8, 2021 at 20:22
• You're welcome :) No, because it appears that there are repeated measures within participant and items, and these are crossed. It wouldn't matter if they were nested rather than crossed, because rmANOVA doesn't handle crossed or nested random effects. It is better to think a bit more generally in this kind of situation. If you understand what a mixed effects model is doing, and what it can be used for, then you can apply it too lots of situations. It's a bit similar to thinking about regular ANOVA being as a special case of the linear regression model. Commented Jun 8, 2021 at 20:28
• Now I understood it better. Perhaps I have to deepen my understanding of the mixed-effects models first to understand it even better :) Commented Jun 8, 2021 at 20:35
• I saw your sentence "A similar scenario where crossed random effects occur is when individual observations are nested within two factors simultaneously, which commonly occurs with so-called repeated measures subject-item data. Typically each subject is measured multiple times with different items and these same items are measured/tested by different subjects" in another post. I wonder whether the items themselves can truly be regarded as a crossed random effect (at least in this scenario, as the items are asking the same thing, except for the subject of the items) Commented Jun 11, 2021 at 8:53