GEE vs Hierarchical linear regression I am trying to choose between GEE and hierarchical linear regression for analysis of experimental vignette (2x2 factorial (0/1) design) data. Each respondent (N=160) filled in 2 vignettes, thus the data is nested within respondents (within-subjects design). I want to test the effect of the two factors (and their interaction) on three dependent/outcome variables (scale, 1-10).
I am finding it difficult to decide as in my view hierarchical linear modelling would work, but my supervisor prefers GEE (as there are no distributional assumptions). However, as far as I understand, using GEE I won't get goodness-of-fit measure and no subject-specific estimates.
Do you have any views on which approach would be better?

GEE makes distributional assumptions and is an asymptotic approach, i.e., may require very large N to be accurate.  It's usually worth the effort of carefully specifying the within-subject correlation pattern and using a full maximum likelihood estimation procedure.  Such procedures include mixed effects models and marginal models (marginal over subjects but modeling serial correlation patterns, for example, such as generalized least squares or Markov models).  Tradeoffs of different approaches are described in a table in the longitudinal modeling chapter of RMS course notes.
