[R-sig-ME] sums of squares and F values in anova

[Alexandra Kuznetsova]

Dear lme4 authors,

I have a question regarding the calculation of sums of squares in anova for lmerMod object. I know that there were some discussions regarding how they are calculated (but still remains unclear to me..).

As far as I understand the way they are calculated is similar to the way they are calculated in lm objects, that is transforming Y into orthogonal Q space, and then computing sums of squares for the independent effects.

I have found in your  JSS paper "Fitting linear mixed effects models using lme4" some explanations (in equations 67 and 68). Would it be possible to give some more comments on these equations? 
And what about the partial (type 3) sums of squares -  is there a way to calculate them using the same way?

Hope my questions were clear!
Thank you in advance!

Alexandra Kuznetsova