# Best way to model repeated measure differences across groups

Let's say I have three groups, each consisting of two individuals. Each group answers questions together, and each member independently reports their confidence in their groups' answers. I want to see if one kind of group has members that are more confident in their collective answer than members of other groups.

On the one hand, this is a repeated measures problem since the same question is asked multiple times ("what is your confidence?" on a 0-100 scale). But the measures actually relate to different questions. There's a temporal component to the problem, since confidence likely evolves over time. It's also multi-level (individual + group characteristics).

The most trivial way of dealing with this is by averaging each individual's confidence across all the questions at the group-level and doing a simple comparison of means. I'm afraid this loses a lot of interesting information, however. What is the best way to model this?

• Have you heard of repeated measures ANOVA? Commented Oct 23, 2018 at 5:21
• yes, doesn't apply to my problem. Commented Oct 23, 2018 at 13:41
• " one kind of group". How many kinds do you have? Commented Oct 26, 2018 at 2:59
• There are technically 'four' groups from an individual level perspective. Participants are paired up on the basis of some variable (sex). What is random is whether you are paired up with a male or a female partner. So four groups in total (MM, FF, MF, FM). Commented Oct 26, 2018 at 3:04

$$\text{confidence}_{tik}=\pi_{0ik}+\pi_{1ik}(\text{time})+e_{tik}$$ where $$\pi_{0ik}=\beta_{00k}+\beta_{01k}(\text{sex})+r_{0ik}$$ and $$\pi_{1ik}=\beta_{10k}+\beta_{11k}(\text{sex})+r_{1ik}$$ with $$\beta_{00k}=\gamma_{000}+\gamma_{001}(\text{group})+U_{00k}$$ and $$\beta_{01k}=\gamma_{010}+\gamma_{011}(\text{group})+U_{01k}$$ and $$\beta_{10k}=\gamma_{100}+\gamma_{101}(\text{group})+U_{10k}$$ and $$\beta_{11k}=\gamma_{110}+\gamma_{111}(\text{group})+U_{11k}$$ such that $$\text{confidence}_{tik}=\gamma_{000}+\gamma_{001}(\text{group})+\gamma_{010}(\text{sex})+\gamma_{011}(\text{group})(\text{sex})+\gamma_{100}(\text{time})+\gamma_{101}(\text{group})(\text{time})+\gamma_{110}(\text{sex})(\text{time})+\gamma_{111}(\text{group})(\text{sex})(\text{time})+U_{00k}+U_{01k}(\text{sex})+U_{10k}(t)+U_{11k}(\text{sex})(\text{time})+r_{0ik}+r_{1ik}(t)+e_{tik}$$
However, you should look at the proportional variance explained by the levels and by each variable. Nonetheless, I presume the $$(\text{group})(\text{sex})(\text{time})$$ three-way interaction will yield very interesting results.
Edit (thanks to a_statistician for catching some issues): The $$U$$ parameters are level-2 random effects and level-2 by level-1 random interaction effects.
• Where is $r_{01k}$ and $r_{1ik}$ in the final equation? What are the $U$ terms? Commented Oct 28, 2018 at 2:16