# Design Question: MLM with varying numbers of responses within Random Effects

I have a question about MLM; this is within the context of analysing some data for my PhD. I'm going to frame the question in this context so that it is easier to understand. In my experiment, I manipulate my IV (which has five levels) between-subjects. This IV determines how many stimuli participants encode (i.e. Set Size); Thus they encode 1,2,3,5 or 10 stimuli. Then later in the experiment, I test participants on what they encoded. Participants in the Set Size 1 group are tested on only 1 item, but participants in Set Size groups 2,3,5 and 10 are tested on 2,3,5 and 10 items respectively. This means that I collect multiple data points from each participant within the Set Size 2 -10 groups, but I collect only one data point from participants in the Set Size 1 group. The outcome variable, where they are asked if to choose what they encoded before, is a dichotomous variable (Correct/Incorrect).

I want to compare performance between the five set size groups. I can calculate a group average for accuracy and compare these with a lm (assuming that assumptions are not violated), but I was thinking of running a mixed effects logistic regression using glmer, and I will nest responses within Participant. This way I can account for the repeated measures design. In this case, my model will now predict the likelihood or probability of making a correct decision.

My question is about what an MLM 'does' in such a situation? How does it handle the one level of the Fixed Effect where participants only provided one response. What happens when I cluster data by participant where is only data point per participant in one level of the Fixed effect, but multiple data points per participant in other levels of the effect effect. (Apologies in advance if I am using the incorrect terms etc.)

• welcome to CV! I want to make sure I properly understand your set-up; as you note, if you've got repeated measurements in general a MLM is a better way to proceed so I think you're definitely on the right track here. I don't know anything about the science here -- what do you mean by a participant "encoding" a stimuli? Does this mean that participant $i$ performs $S_i$ tasks, where $S_i \in \{1, 2, 3, 5, 10\}$ is the Set Size, so you get $S_i$ observations on person $i$? Are there any other IVs? – jld Apr 19 '18 at 17:36