Hello everyone, I think I am stuck on a specification problem and struggling to find a way out.
- Problem definition: A total of 154 subjects are measured eight times each (dependent variable perceived_cost, measured using a single item 11 point scale) after being asked to chose among two available options of a non-labelled product.
The predictors that characterize each option are two dummy variables (respectively, monetary and nonnonmonetary cost of the product, both with high and low level). These two independent variables combined together create four possible different combinations, mon_high, mon_low, nmon_high, nmon_low. Each participant is offered one binary option for eight times in a row (I look at these as if they were 8 time periods). As there are 4 product combinations and 8 measurements, there is a sort of repeated measures: every respondent typically selects one condition more than once and sometimes a condition is never chosen. With reference to the dependent variable, the four conditions are hypothesized to be ordered (i.e. perceived cost should be mon_high&nmon_high > mon_high&nmon_low > mon_low&nmon_high > mon_low&nmon_low). In summary, we have 1 observation for each "time period" for each participant (repeated measures) and participants that can have more than one measurement per condition and/or no measurements for some other condition.
- My baseline research question is: I'd like to check that the level of the dv perceived_cost is different for different conditions and specifically that it follows the hypothesized order mon_high&nmon_high > mon_high&nmon_low > mon_low&nmon_high > mon_low&nmon_low.
- Analysis problem: given the structure of the data, at the subject level I have missing data and nonnormal distributions so I can't simply run a repeated measures ANOVA. So, I thought I could have run a mixed model with repetitions and after reshaping the data long my plan was to run the following:

mixed perceived_cost 4conditions##Sessions || SubjectId:, var reml
contrast 4conditions##Sessions
margins 4conditions##Sessions
contrast 4Sessions##conditions, effect
contrast 4conditions##Sessions, effect

where 4conditions is discrete from 1 to 4 reflecting the four conditions, Sessions is discrete with eight values from 1 to 8.
However, I realized that this specification would probably be fine if each participant would be exposed to one condition only, but this is not my case as SubjectIds changes across conditions. Now I'm (quite) lost about how to tackle this problem and ask for help: any suggestion about the right way to go? Thank you very much.