I’m more interested in getting the OrderedLogistic functioning and evaluating how much better this model works vs the other models I’ve trained than inference just yet. FWIW here’s a snippet from the Poisson model I was toying with just as an example:
defense_idx, defense = feat_df['defense_team_id'].factorize()
coords['defense'] = defense
with pm.Model(coords=coords) as offense_defense_partial_pooling:
#priors
hfa_effect = pm.Normal('hfa_effect', sigma=.1)
offense_mu = pm.Normal('offense_mu', mu=0, sigma=.5)
offense_sigma = pm.HalfNormal('offense_sigma', sigma=.1)
offense_offset = pm.Normal('offense_offset', mu=0, sigma=.5, dims='offense')
offense_effect = pm.Deterministic('offense_effect', offense_mu + offense_sigma * offense_offset, dims='offense')
defense_mu = pm.Normal('defense_mu', mu=0, sigma=.5)
defense_sigma = pm.HalfNormal('defense_sigma', sigma=.1)
defense_offset = pm.Normal('defense_offset', mu=0, sigma=.5, dims='defense')
defense_effect = pm.Deterministic('defense_effect', defense_mu + defense_sigma * defense_offset, dims='defense')
#likelihood
mu = offense_effect[offense_idx] - defense_effect[defense_idx] + hfa_effect * feat_df['home_ind']
points_rate = pm.Deterministic('points_rate', pm.math.exp(mu), dims='game_id')
points = pm.Poisson('points', mu=points_rate, observed=feat_df['points'], dims='game_id')
pm.model_to_graphviz(offense_defense_partial_pooling)
I would probably end up running the same kind of heirarchical model against the OrderedLogistic likelihood and then I can look at all kinds of things like the impact of distance traveled to away games on offensive/defensive ability, coach effects, FA spending etc. Treating the offensive and defensive effects as things to estimate based on previous seasons and offseason turnover. Just playing with different questions. Is it safe to assume that it’s probably going to be infeasible to approach this problem the way I was originally posting about?