# Is there a non-parametric, two-way, continuous data ANOVA for replicated repeated measures?

I have data of multiple factors. Let's call them: size (2 levels), geometry (2 levels) and time (242 levels but I can limit my focus to 3 levels, which are relevant). I also have a measure (dependent variable) called "distance", which is continuous.

Description: I measured the distance of the cells to starting point in different geometries, different pore sizes over time. There are multiple measurements for each group. It looks like that the distribution of the distances of these groups are different from each other.

I would like to know, if distance can be predicted by size and geometry. My data is not normally distributed, so I would like to apply a non-parametric test. It would be great to include all time points to compare "curves" or time-course but if not possible, it is enough to do the test on 3 relevant time points. I am using R.

I think I cannot use: Friedman test, as it is for non-replicated data. Kruskal Wallis, as it is one-way (last resort?). OLR, as it is for ordinal data, not continuous.

• Did you measure the exact same cells at the different time points, i.e., do you have repeated measures? Can you show some histograms for groups and time points? I would possibly try fitting a GLM, possibly a GLMM. The question would only be what distribution and link function to use. – Roland Jan 30 '19 at 15:17
• I don't have paired measurements. These are the "same" cells but they are not "connected". I don't identify each cell. These are repeated measures in the sense that I have time-course data. (I read somewhere that this "can" be taken as repeated measures.). I will try to add some histograms. – Genom Jan 30 '19 at 15:22
• A mixed model would also work. – user2974951 Jan 30 '19 at 15:38
• @user2974951 How does the mixed model work? – Genom Jan 30 '19 at 15:47