Hi!

I have a hard time wrapping my head around a model we’d like to fit.

The objective is to estimate the probability of winning of each member of a board-game group.

The deterministic part of the model would be relatively simple: an intercept per player quantifying the averaged probability of winning, and a series of hierarchical effects: one for game identity, one for the number of players playing.

However, the response is ragged: not every player was present at each game. This leads to another aspect: one player can have a high probability of winning when another is absent, but a lower chance when another is absent. The table would look like :

Would someone have an idea about how to model this? I could create predictors for the presence or absence of a player and fit individual models, but I feel that a multivariate model with all players would be far more interesting (and a statistical challenge for me. We could also use ranks or scores). However, the ragged structure of the response blocks me, and I have no idea about how to formulate a model that could deal with such a structure.

Would anybody have an idea?? The good thing is that we have A LOT of data points for some of the configurations :P

Thanks!

Lucas