Which analysis for incomplete block design with repeated measure?

I have a question on analyzing data from an incomplete block design. Participants have been randomly assigned to 1 out of 8 procedures each consisting of two cases. The cases differed on three variables (all nominal). Cases were counterbalanced in such a way that if a participant was assigned to the case with variables 1, 1 and 1, you would automatically get case 2, 2, and 2 as a second case. Outcome for each of these cases was based on the likelihood of a specific outcome (interval). I am not interested in the effect of each participant on the outcome (hence the randomization) but rather in the effect of each of the three manipulated variables on the estimated likelihood.
This means I have incomplete data for each participant. Is it possible to use an ANOVA to analyze the data? And if so, do I have to deal with (and if yes, how) the ‘repeated measures’ for each participant?

Thanks in advance!