I've deigned an experiment in which participants read 24 narratives and guess if they are written by men or women and rate their own confidence. I thus have 24 binary repeated measures. I have the following predictors: participant gender and response to a scale about gender identity (participant based), and also 6 narrative content ratings of the narratives (vary by narrative but not by participants) and finally participants' confidence (varies by participant and by narrative). I've been using GEE in SPSS because my reading suggests this is the most accessible way for me to run what is effectively a repeated measures logistic regression. But I may have a mediation between confidence and some of the narrative variables. Should I be using a different approach? Is structural equation modelling appropriate here? I have access to STATA and AMOS, but no experience with either.
To get at questions of mediation, structural equation modeling is probably your best bet. To account for the clustering of data within participants, you can use multilevel structural equation modeling (MSEM). Level 1 would contain narratives and their descriptors (e.g., content ratings and confidence levels), whereas Level 2 would contain participants and their descriptors (e.g., gender).
You can read more about mediation in MSEM in this article:
Preacher, K. J., Zyphur, M. J., & Zhang, Z. (2010). A general multilevel SEM framework for assessing multilevel mediation. Psychological Methods, 15(3), 209–233.
I have conducted MSEM before using the Mplus program. Not sure about STATA/AMOS.