The problem here is that there is no consensus method. There are papers out there that point out that linear modeling techniques are very robust to the assumption of normality. There are other papers out there that insist that since Likert scales are ordinal, rather than rational, you should not use any methods that assume normality of the residuals. So what to do?
If you are good at interpreting multinomial data and the various odds ratios involved, then you might consider using PROC GLIMMIX with a multinomial distribution and a G side structure that handles the repeated nature of the data.
If you are willing to trust in the robustness to assumptions, and you can make a case that either a) the gap between the scores is linear or b) you can weight each score by some utility factor, then a repeated measures analysis of variance will work.
SteveDenham.
