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Bayesian 2PL implementation with PyMC3
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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,)) | |
slopes = pm.Normal("slopes", mu=0, | |
sigma=1, | |
shape=(5,)) | |
# Transformed parameter | |
deltas = [] | |
for s_idx, q_idx in student_question_map: | |
s = students[s_idx,] | |
q = questions[q_idx,] | |
d = slopes[q_idx] | |
deltas.append( d * (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", "slopes"] ,compact=False) |
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