I am running an econometric analysis on how some factors (gender, income level, being a student...) might affect the degree of cooperation in a weakest-link game setting. My dependent variable (the level of cooperation chosen) can have three values (1, 2 or 3) and at first I ran a random effects multinomial logistic regression, declaring the dataset as a panel using the round number as the t variable and the player number as the id variable. However, as the cooperation levels are ranked, I thought that running a rank ordered logit might be more suitable for this matter. Furthermore, I am also considering running a bayesian multilevel model as it might allow me to control for group specific effects (the degree of cooperation of a player is likely to depend on the cooperation that the other players he/she is matched demonstrate). Do you think it is proper to use this last specification for what I am analysing?