As part of an RCT with 100 participants in each arm we use a 5-point likert scale to assess change an outcome over time in each arm (two independent groups, each measured at two time points).

We therefore have baseline and end of study data for two independent groups and would like to assess which group showed greatest improvement over time. I hear different arguments regarding if you can/cannot use a mixed-model ANOVA for likert data, but I am not sure of the non-parametric equivalent? As there are 100 responses each time, I have also seen that the mean result could start to resemble scale-type data, and therefore a parametric test is absolutely fine.

Any advice would be appreciated.