rasch_model_pymc3

rasch_model.py

with pm.Model() as model:
    
    ## Independent priors
    alpha = pm.Normal('Person', mu = 0, sigma = 3, shape = (1, len(data)))
    gamma = pm.Normal('Question', mu = 0, sigma = 3, shape = (data.shape[1], 1))
    
    ## Log-Likelihood
    def logp(d):
        v1 = tt.transpose(d) * tt.log(tt.nnet.sigmoid(alpha - (gamma - gamma.mean(0))))
        v2 = tt.transpose((1-d)) * tt.log(1 - tt.nnet.sigmoid(alpha - (gamma - gamma.mean(0))))
        
        return v1 + v2
    
    
    
    ll = pm.DensityDist('ll', logp, observed = {'d': data.values})
    trace = pm.sample(1500, cores=-1, step = pm.NUTS())
    trace = trace[250:]
pm.traceplot(trace);
trace = pm.trace_to_dataframe(trace)

I'm studying item response theory. It's not a clear implementation, but I build a sample code of this gist on Medium.

see here