I am unsure how to go about an exploratory factor analysis for item reduction with multi-level/repeated measure data. My study is a daily diary, 1x a day for 2 weeks. Participants answered many state-level questions, I want to reduce some of these items via EFA. I will then be using those factors in my HLM analyses. Should I be performing the EFA on the state measures as-is (some participants completed more days than others) or should I use the aggregate/mean of the participant's scores for the EFA?
It would most likely not make sense to include all individual data points (from every single time point) in the EFA because of the complexity of the resulting data structure. EFA would likely not give you meaningful and interpretable results for the longitudinal multi-item structure. Could you check the factor structure by using only the first measurement occasion (i.e., cross-sectional data) in the EFA?
I wanted to elaborate on my comment, as I've been in the same situation. However please note I'm not a statistician and this is coming from a very practical viewpoint and I'm not sure what is mathematically the best approach.
I often conduct daily experience studies same as you, though I usually have an ESM protocol (i.e. several measurements per day). I usually use state items derived from the Big Five personality model, and try to have 2-3 items per domain (e.g. "productive" and "responsible" for Conscientiousness). So, prior to analyses I want to combine these items by domain.
I have found these instructions for conducting a multilevel CFA in R lavaan. This approach seems reasonable to me, but it's for CFA - you need to specify the factor structure beforehand. However, you could try a couple of different structures. (In a recent article I saw, the authors used multilevel EFA, but I can't find it now - maybe they used R psych package).
However, my ESM samples are usually too small for any kind of factor analysis, let alone 2-level one. Therefore, I usually just check whether the items that belong to the same trait domain on theoretical basis have high enough within-person correlation using the rmcorr function in R. If so, I average these items. If not, I use them as single items.