Bayesian 1PL implementation in PyMC3

irt_1pl.py

import pymc3 as pm
from theano import tensor as tt
import arviz as az
import numpy as np

# Binary, correct answer array
scores = np.array([1,1,1,0,0,0
    ]).flatten()

# (student:question) tuples
# order corresponds to scores 
student_question_map = [(0,1), (0,2), (0,3),
         (1,2), (1,3),
         (3,4)]

with pm.Model() as model:
    # Priors
    questions = pm.Normal("questions", mu=0,
                                  sigma=1, 
                                  shape=(5,))
    students = pm.Normal("students", mu=0, 
                                  sigma=1, 
                                  shape=(5,))
    slope = pm.Normal("slope", mu=0, 
                                  sigma=1)
    
    # Transformed parameter
    deltas = []
    for s_idx, q_idx in student_question_map:
      s = students[s_idx,]
      q = questions[q_idx,] 
      deltas.append( slope * (s - q) )
    
    thetas = pm.Deterministic("theta", tt.nnet.sigmoid(deltas))   
    # Likelihood
    kij = pm.Bernoulli("kij", p=thetas, observed=scores)
    trace = pm.sample(chains=4, )

az.plot_trace(trace, var_names=["questions", "students", "slope"] ,compact=False)