def test_trim_response_set(self):
"""Testing trim of all yes/no values."""
np.random.seed(439)
dataset = np.random.rand(10, 300)
counts = np.random.rand(300)
# Pass through
new_set, new_counts = trim_response_set_and_counts(dataset, counts)
np.testing.assert_array_equal(dataset, new_set)
np.testing.assert_array_equal(counts, new_counts)
# Make first column zeros
dataset[:, 0] = 0
new_set, new_counts = trim_response_set_and_counts(dataset, counts)
np.testing.assert_array_equal(dataset[:, 1:], new_set)
np.testing.assert_array_equal(counts[1:], new_counts)
# Make last column all 1
dataset[:, -1] = 1
new_set, new_counts = trim_response_set_and_counts(dataset, counts)
np.testing.assert_array_equal(dataset[:, 1:-1], new_set)
np.testing.assert_array_equal(counts[1:-1], new_counts)
# Test when bad value is present
dataset = np.ones((10, 300), dtype=int)
dataset[0] = -1
dataset[0, 0] = INVALID_RESPONSE
counts = np.random.randint(0, 10, 300)
new_set, new_counts = trim_response_set_and_counts(dataset, counts)
self.assertEqual(new_set.shape[1], dataset.shape[1] - 1)
np.testing.assert_array_equal(dataset[:, 1:], new_set)
np.testing.assert_array_equal(counts[1:], new_counts)
def rasch_conditional(dataset, discrimination=1, options=None):
""" Estimates the difficulty parameters in a Rasch IRT model
Args:
dataset: [items x participants] matrix of True/False Values
discrimination: scalar of discrimination used in model (default to 1)
options: dictionary with updates to default options
Returns:
difficulty: (1d array) estimates of item difficulties
Options:
* max_iteration: int
Notes:
This function sets the sum of difficulty parameters to
zero for identification purposes
"""
options = validate_estimation_options(options)
n_items = dataset.shape[0]
unique_sets, counts = np.unique(dataset, axis=1, return_counts=True)
# Initialize all the difficulty parameters to zeros
# Set an identifying_mean to zero
##TODO: Add option to specifiy position
betas = np.zeros((n_items, ))
identifying_mean = 0.0
# Remove the zero and full count values
unique_sets, counts = trim_response_set_and_counts(unique_sets, counts)
response_set_sums = unique_sets.sum(axis=0)
for iteration in range(options['max_iteration']):
previous_betas = betas.copy()
for ndx in range(n_items):
partial_conv = _symmetric_functions(np.delete(betas, ndx))
def min_func(estimate):
betas[ndx] = estimate
full_convolution = np.convolve([1, np.exp(-estimate)], partial_conv)
denominator = full_convolution[response_set_sums]
return (np.sum(unique_sets * betas[:,None], axis=0).dot(counts) +
np.log(denominator).dot(counts))
# Solve for the difficulty parameter
betas[ndx] = fminbound(min_func, -5, 5)
# recenter
betas += (identifying_mean - betas.mean())
# Check termination criterion
if np.abs(betas - previous_betas).max() < 1e-3:
break
return {'Discrimination': discrimination,
'Difficulty': betas / discrimination}
def _jml_abstract(dataset, _item_min_func, discrimination=1, max_iter=25):
""" Defines common framework for joint maximum likelihood
estimation in dichotomous models."""
unique_sets, counts = np.unique(dataset, axis=1, return_counts=True)
n_items, _ = unique_sets.shape
# Use easy model to seed guess
alphas = np.full((n_items, ), discrimination,
dtype='float') # discrimination
betas = mml_approx(dataset, alphas) # difficulty
# Remove the zero and full count values
unique_sets, counts = trim_response_set_and_counts(unique_sets, counts)
n_takers = unique_sets.shape[1]
the_sign = convert_responses_to_kernel_sign(unique_sets)
thetas = np.zeros((n_takers, ))
for iteration in range(max_iter):
previous_betas = betas.copy()
#####################
# STEP 1
# Estimate theta, given betas
# Loops over all persons
#####################
for ndx in range(n_takers):
# pylint: disable=cell-var-from-loop
scalar = the_sign[:, ndx] * alphas
def _theta_min(theta):
otpt = np.exp(scalar * (theta - betas))
return np.log1p(otpt).sum()
# Solves for the ability for each person
thetas[ndx] = fminbound(_theta_min, -6, 6)
# Recenter theta to identify model
thetas -= thetas.mean()
thetas /= thetas.std(ddof=1)
#####################
# STEP 2
# Estimate Item Parameters
# given Theta,
#####################
alphas, betas = _item_min_func(n_items, alphas, thetas, betas,
the_sign, counts)
if (np.abs(previous_betas - betas).max() < 1e-3):
break
return {'Discrimination': alphas, 'Difficulty': betas}
def test_trim_response_set(self):
"""Testing trim of all yes/no values."""
np.random.seed(439)
dataset = np.random.rand(10, 300)
counts = np.random.rand(300)
# Pass through
new_set, new_counts = trim_response_set_and_counts(dataset, counts)
np.testing.assert_array_equal(dataset, new_set)
np.testing.assert_array_equal(counts, new_counts)
# Make first column zeros
dataset[:, 0] = 0
new_set, new_counts = trim_response_set_and_counts(dataset, counts)
np.testing.assert_array_equal(dataset[:, 1:], new_set)
np.testing.assert_array_equal(counts[1:], new_counts)
# Make last column all 1
dataset[:, -1] = 1
new_set, new_counts = trim_response_set_and_counts(dataset, counts)
np.testing.assert_array_equal(dataset[:, 1:-1], new_set)
np.testing.assert_array_equal(counts[1:-1], new_counts)
# Test when array contains nans
mask = np.random.rand(*dataset.shape) < 0.1
dataset[mask] = np.nan
# There are responses with zero variance
locations = np.where(np.nanstd(dataset, axis=0) == 0)
self.assertTrue(locations[0].size > 0)
new_set, new_counts = trim_response_set_and_counts(dataset, counts)
locations = np.where(np.nanstd(new_set, axis=0) == 0)
self.assertTrue(locations[0].size == 0)