Dear List, I am trying to analyze a dataset where I have 1 continuous between-item variable (C), and 2 factorial within-item variables (3- and 2-level: F3, F2). I'm interested in whether slope of C is different from 0 at different combinations of F3 and F2, and whether it varies between these combinations. And unfortunately I need a decent anova-like table with p-values. The reason is that 1) this analysis is going to be repeated 9 times for different parts of the data (not comparable), so such an omnibus table will give a good overview of which places need a follow up with simpler models; 2) this is the norm in my field of reseach, although usually with factorial variables only. I'm wondering how to do it properly in R without falling into any pitfalls, avoiding violations of any assumptions (like sphericity) and what is the most apropriate type of sum of squares for this analysis. The 2 solutions I found so far are: based on nlme::lme():
res.lme = nlme::lme(data=d, y ~ C * F3 * F2, random = ~ 1|item/F3/F2) anova(res.lme) for type I SS Anova(res.lme, type="II/III") # for type II/III SS
based on lmerTest package:
res.lmertest = lmerTest::lmer(data=d, y ~ C * F3 * F2 + (1|item)) anova(res.lmertest) # for type III SS
I also considered running repeated-measures ANCOVA using aov() with nested error terms, but that wouldn't protect me against sphericity assumption violations. I also considered using car::Anova() for running a repeated-measures MANCOVA analysis, but if I got this thread right (http://thread.gmane.org/gmane.comp.lang.r.general/270271/focus=270275), this is (at present) not possible to do. Are these ways of analyzing data valid? Concerning the type of SS: I tried to read all discussions in this list on this topic. If I got it right, since I'm interested in interactions of C with other factors in the first place, in my case using SS type III would make sense - is this a good logic? Many thanks for help, Jakub