def test_log_likelihood():
"""
Computes the log-likelihood "by hand" for a simple example and ensures
that the one returned by xlogit is the same
"""
P = 1 # Without panel data
betas = np.array([.1, .1, .1, .1])
X_, y_ = X.reshape(N, P, J, K), y.reshape(N, P, J, 1)
# Compute log likelihood using xlogit
model = MixedLogit()
model._rvidx, model._rvdist = np.array([True, True]), np.array(['n', 'n'])
draws = model._get_halton_draws(N, R, K) # (N,Kr,R)
panel_info = np.ones((N, P))
obtained_loglik, _ = model._loglik_gradient(betas, X_, y_, panel_info,
draws, None, None)
# Compute expected log likelihood "by hand"
Br = betas[None, [0, 1], None] + draws * betas[None, [2, 3], None]
eXB = np.exp(np.einsum('npjk,nkr -> npjr', X_, Br))
p = eXB / np.sum(eXB, axis=2, keepdims=True)
expected_loglik = -np.sum(
np.log((y_ * p).sum(axis=2).prod(axis=1).mean(axis=1)))
assert pytest.approx(expected_loglik, obtained_loglik)
def test_log_likelihood():
"""
Computes the log-likelihood "by hand" for a simple example and ensures
that the one returned by xlogit is the same
"""
betas = np.array([.1, .1, .1, .1])
X_, y_ = X.reshape(N, J, K), y.reshape(N, J, 1)
# Compute log likelihood using xlogit
model = MixedLogit()
model._rvidx, model._rvdist = np.array([True, True]), np.array(['n', 'n'])
draws = model._generate_halton_draws(N, R, K) # (N,Kr,R)
obtained_loglik = model._loglik_gradient(betas,
X_,
y_,
None,
draws,
None,
None, {
'samples': N,
'draws': R
},
return_gradient=False)
# Compute expected log likelihood "by hand"
Br = betas[None, [0, 1], None] + draws * betas[None, [2, 3], None]
eXB = np.exp(np.einsum('njk,nkr -> njr', X_, Br))
p = eXB / np.sum(eXB, axis=1, keepdims=True)
expected_loglik = -np.sum(np.log((y_ * p).sum(axis=1).mean(axis=1)))
assert expected_loglik == pytest.approx(obtained_loglik)
