Hey all,
with three weeks more understanding - here my summary for what helped me.
- In general, the problem is overdetermined with collinearity (-> wrong title)
- In general I want multiple levels where I want to quantify \mu and \sigma per individual contributor. This is a random effects / linear mixed effects model.
- Linear Regressions do not work well with collinearity. Regularization helps.
- a Super easy way of estimating just the \mu is via a linear model that you can define with OrdinalEncoder solve with e.g. Bayesian Ridge or a RidgeRegressor that contains the afore mentioned Regularization
- with bayesian modeling, an L2 regularization can be achieved by specifying a gaussian prior see here or here. So there is actually no need to try to implement constraints.
- ultimate goal for me are multiple levels (generic). Generic definitions can easily be generated with bambi (BAyesian Model-Building Interface)
- Linear Mixed Effects Models by statsmodels are no option, since they can do only up to two levels…