Hi,

I am fitting individual growth models using nlme (multilevel models with
repeated measurements nested within the individual).  I have already
calculated PRV statistics at each level, and now I am trying to calculate
the Pseudo R-squared for the models (an overall summary of the total
outcome variability explained).  Singer and Willett (2003) recommend
calculating Pseudo R-squared in multilevel modeling by squaring the sample
correlation between observed and predicted values (across the sample for
each person on each occasion of measurement).

My question is which set of predicted values should I use from nlme in that
calculation?  From my models in nlme, I receive two sets of fitted values.
 Reading the description of the fitted lme values (
http://stat.ethz.ch/R-manual/R-patched/library/nlme/html/fitted.lme.html),
there appear to be two sets of fitted values that correspond to levels of
grouping, where the first set of fitted values (Level 0) correspond to the
population fitted values and it moves to more innermore groupings as the
levels increase (e.g., I suppose Level 1 corresponds to the
individual-level fitted values in my data).

I'm not sure I understand the distinction between population fitted values
and individual-level fitted values because each individual and each
measurement occasion has an estimate for both (population and individual
fitted estimates).  Could you please explain the distinction and which one
I should be using to calculate the Pseudo R-squared as suggested by Singer
and Willett (2003)?  Thanks so much for your help!

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