def test_ability_eap_abstract(self):
"""Testing eap computation."""
np.random.seed(1002124)
partial_int = np.random.randn(1000, 41)
weight = np.random.randn(41)
theta = np.linspace(-3, 3, 41)
result = _ability_eap_abstract(partial_int, weight, theta)
denom = (partial_int * (weight)).sum(1)
numer = (partial_int * (weight * theta)).sum(1)
expected = numer / denom
np.testing.assert_allclose(result, expected, atol=1e-5, rtol=1e-3)
def grm_mml_eap(dataset, options=None):
"""Estimate parameters for graded response model.
Estimate the discrimination and difficulty parameters for
a graded response model using a mixed Bayesian / Marginal Maximum
Likelihood algorithm, good for small sample sizes
Args:
dataset: [n_items, n_participants] 2d array of measured responses
options: dictionary with updates to default options
Returns:
results_dictionary:
* Discrimination: (1d array) estimate of item discriminations
* Difficulty: (2d array) estimates of item difficulties by item thresholds
* LatentPDF: (object) contains information about the pdf
* Rayleigh_Scale: (int) Rayleigh scale value of the discrimination prior
* AIC: (dictionary) null model and final model AIC value
* BIC: (dictionary) null model and final model BIC value
Options:
* estimate_distribution: Boolean
* number_of_samples: int >= 5
* max_iteration: int
* distribution: callable
* quadrature_bounds: (float, float)
* quadrature_n: int
* hyper_quadrature_n: int
"""
options = validate_estimation_options(options)
cpr_result = condition_polytomous_response(dataset, trim_ends=False)
responses, item_counts, valid_response_mask = cpr_result
invalid_response_mask = ~valid_response_mask
n_items = responses.shape[0]
# Only use LUT
_integral_func = _solve_integral_equations_LUT
_interp_func = create_beta_LUT((.15, 5.05, 500), (-6, 6, 500), options)
# Quadrature Locations
latent_pdf = LatentPDF(options)
theta = latent_pdf.quadrature_locations
# Compute the values needed for integral equations
integral_counts = list()
for ndx in range(n_items):
temp_output = _solve_for_constants(responses[ndx,
valid_response_mask[ndx]])
integral_counts.append(temp_output)
# Initialize difficulty parameters for estimation
betas = np.full((item_counts.sum(), ), -10000.0)
discrimination = np.ones_like(betas)
cumulative_item_counts = item_counts.cumsum()
start_indices = np.roll(cumulative_item_counts, 1)
start_indices[0] = 0
for ndx in range(n_items):
end_ndx = cumulative_item_counts[ndx]
start_ndx = start_indices[ndx] + 1
betas[start_ndx:end_ndx] = np.linspace(-1, 1, item_counts[ndx] - 1)
betas_roll = np.roll(betas, -1)
betas_roll[cumulative_item_counts - 1] = 10000
# Set invalid index to zero, this allows minimal
# changes for invalid data and it is corrected
# during integration
responses[invalid_response_mask] = 0
# Prior Parameters
ray_scale = 1.0
eap_options = {
'distribution': stats.rayleigh(loc=.25, scale=ray_scale).pdf,
'quadrature_n': options['hyper_quadrature_n'],
'quadrature_bounds': (0.25, 5)
}
prior_pdf = LatentPDF(eap_options)
alpha_evaluation = np.zeros((eap_options['quadrature_n'], ))
# Meta-Prior Parameter
hyper_options = {
'distribution': stats.lognorm(loc=0, s=0.25).pdf,
'quadrature_n': options['hyper_quadrature_n'],
'quadrature_bounds': (0.1, 5)
}
hyper_pdf = LatentPDF(hyper_options)
hyper_evaluation = np.zeros((hyper_options['quadrature_n'], ))
base_hyper = (hyper_pdf.weights *
hyper_pdf.null_distribution).astype('float128')
linear_hyper = base_hyper * hyper_pdf.quadrature_locations
for iteration in range(options['max_iteration']):
previous_discrimination = discrimination.copy()
previous_betas = betas.copy()
previous_betas_roll = betas_roll.copy()
# Quadrature evaluation for values that do not change
# This is done during the outer loop to address rounding errors
partial_int = np.ones((responses.shape[1], theta.size))
for item_ndx in range(n_items):
partial_int *= _graded_partial_integral(
theta, betas, betas_roll, discrimination, responses[item_ndx],
invalid_response_mask[item_ndx])
# Estimate the distribution if requested
distribution_x_weight = latent_pdf(partial_int, iteration)
partial_int *= distribution_x_weight
# Update the lookup table if necessary
if (options['estimate_distribution'] and iteration > 0):
new_options = dict(options)
new_options.update({'distribution': latent_pdf.cubic_splines[-1]})
_interp_func = create_beta_LUT((.15, 5.05, 500), (-6, 6, 500),
new_options)
# EAP Discrimination Parameter
discrimination_pdf = stats.rayleigh(loc=0.25, scale=ray_scale).pdf
base_alpha = (prior_pdf.weights * discrimination_pdf(
prior_pdf.quadrature_locations)).astype('float128')
linear_alpha = (base_alpha *
prior_pdf.quadrature_locations).astype('float128')
for item_ndx in range(n_items):
# pylint: disable=cell-var-from-loop
# Indices into linearized difficulty parameters
start_ndx = start_indices[item_ndx]
end_ndx = cumulative_item_counts[item_ndx]
old_values = _graded_partial_integral(
theta, previous_betas, previous_betas_roll,
previous_discrimination, responses[item_ndx],
invalid_response_mask[item_ndx])
partial_int /= old_values
def _local_min_func(estimate):
# Solve integrals for diffiulty estimates
new_betas = _integral_func(estimate, integral_counts[item_ndx],
distribution_x_weight, theta,
_interp_func)
betas[start_ndx + 1:end_ndx] = new_betas
betas_roll[start_ndx:end_ndx - 1] = new_betas
discrimination[start_ndx:end_ndx] = estimate
new_values = _graded_partial_integral(
theta, betas, betas_roll, discrimination,
responses[item_ndx], invalid_response_mask[item_ndx])
new_values *= partial_int
otpt = np.sum(new_values, axis=1)
return np.log(otpt.clip(1e-313, np.inf)).sum()
# Mean Discrimination Value
for ndx, disc_location in enumerate(
prior_pdf.quadrature_locations):
alpha_evaluation[ndx] = _local_min_func(disc_location)
alpha_evaluation -= alpha_evaluation.max()
total_probability = np.exp(alpha_evaluation.astype('float128'))
numerator = np.sum(total_probability * linear_alpha)
denominator = np.sum(total_probability * base_alpha)
alpha_eap = numerator / denominator
# Reset the Value the updated discrimination estimation
_local_min_func(alpha_eap.astype('float64'))
new_values = _graded_partial_integral(
theta, betas, betas_roll, discrimination, responses[item_ndx],
invalid_response_mask[item_ndx])
partial_int *= new_values
# Compute the Hyper prior mean value
for ndx, scale_value in enumerate(hyper_pdf.quadrature_locations):
temp_distribution = stats.rayleigh(loc=0.25, scale=scale_value).pdf
hyper_evaluation[ndx] = np.log(
temp_distribution(discrimination) + 1e-313).sum()
hyper_evaluation -= hyper_evaluation.max()
hyper_evaluation = np.exp(hyper_evaluation.astype('float128'))
ray_scale = (np.sum(hyper_evaluation * linear_hyper) /
np.sum(hyper_evaluation * base_hyper)).astype('float64')
# Check Termination Criterion
if np.abs(previous_discrimination - discrimination).max() < 1e-3:
break
# Recompute partial int for later calculations
partial_int = np.ones((responses.shape[1], theta.size))
for item_ndx in range(n_items):
partial_int *= _graded_partial_integral(
theta, betas, betas_roll, discrimination, responses[item_ndx],
invalid_response_mask[item_ndx])
# Trim difficulties to conform to standard output
# TODO: look where missing values are and place NAN there instead
# of appending them to the end
output_betas = np.full((n_items, item_counts.max() - 1), np.nan)
for ndx, (start_ndx,
end_ndx) in enumerate(zip(start_indices,
cumulative_item_counts)):
output_betas[ndx, :end_ndx - start_ndx - 1] = betas[start_ndx +
1:end_ndx]
# Compute statistics for final iteration
null_metrics = latent_pdf.compute_metrics(
partial_int, latent_pdf.null_distribution * latent_pdf.weights, 0)
full_metrics = latent_pdf.compute_metrics(partial_int,
distribution_x_weight,
latent_pdf.n_points - 3)
# Ability estimates
eap_abilities = _ability_eap_abstract(partial_int, distribution_x_weight,
theta)
return {
'Discrimination': discrimination[start_indices],
'Difficulty': output_betas,
'Ability': eap_abilities,
'LatentPDF': latent_pdf,
'Rayleigh_Scale': ray_scale,
'AIC': {
'final': full_metrics[0],
'null': null_metrics[0],
'delta': null_metrics[0] - full_metrics[0]
},
'BIC': {
'final': full_metrics[1],
'null': null_metrics[1],
'delta': null_metrics[1] - full_metrics[1]
}
}
def gum_mml(dataset, delta_sign=(0, 1), options=None):
"""Estimate parameters for graded unfolding model.
Estimate the discrimination, delta and threshold parameters for
the graded unfolding model using marginal maximum likelihood.
Args:
dataset: [n_items, n_participants] 2d array of measured responses
delta_sign: (tuple) (ndx, sign: [+1 | -1]) sets the sign of the
ndx delta value to positive or negative
options: dictionary with updates to default options
Returns:
discrimination: (1d array) estimates of item discrimination
delta: (1d array) estimates of item folding values
difficulty: (2d array) estimates of item thresholds
Options:
* estimate_distribution: Boolean
* number_of_samples: int >= 5
* max_iteration: int
* distribution: callable
* quadrature_bounds: (float, float)
* quadrature_n: int
"""
options = validate_estimation_options(options)
cpr_result = condition_polytomous_response(dataset,
trim_ends=False,
_reference=0.0)
responses, item_counts, valid_response_mask = cpr_result
invalid_response_mask = ~valid_response_mask
n_items = responses.shape[0]
# Interpolation Locations
# Quadrature Locations
latent_pdf = LatentPDF(options)
theta = latent_pdf.quadrature_locations
# Initialize item parameters for iterations
discrimination = np.ones((n_items, ))
betas = np.full((n_items, item_counts.max() - 1), np.nan)
delta = np.zeros((n_items, ))
partial_int = np.ones((responses.shape[1], theta.size))
# Set initial estimates to evenly spaced
for ndx in range(n_items):
item_length = item_counts[ndx] - 1
betas[ndx, :item_length] = np.linspace(-1, 1, item_length)
# This is the index associated with "folding" about the center
fold_span = ((item_counts[:, None] - 0.5) -
np.arange(betas.shape[1] + 1)[None, :])
# Sets the first value for the
delta_ndx = delta_sign[0]
delta_multiplier = np.sign(delta_sign[1])
# Set invalid index to zero, this allows minimal
# changes for invalid data and it is corrected
# during integration
responses[invalid_response_mask] = 0
#############
# 1. Start the iteration loop
# 2. Estimate Dicriminatin/Difficulty Jointly
# 3. Integrate of theta
# 4. minimize and repeat
#############
for iteration in range(options['max_iteration']):
previous_discrimination = discrimination.copy()
previous_betas = betas.copy()
previous_delta = delta.copy()
# Quadrature evaluation for values that do not change
# This is done during the outer loop to address rounding errors
# and for speed
partial_int = np.ones((responses.shape[1], theta.size))
for item_ndx in range(n_items):
partial_int *= _unfold_partial_integral(
theta, delta[item_ndx], betas[item_ndx],
discrimination[item_ndx], fold_span[item_ndx],
responses[item_ndx], invalid_response_mask[item_ndx])
# Estimate the distribution if requested
distribution_x_weight = latent_pdf(partial_int, iteration)
partial_int *= distribution_x_weight
# Loop over each item and solve for the alpha / beta parameters
for item_ndx in range(n_items):
# pylint: disable=cell-var-from-loop
item_length = item_counts[item_ndx] - 1
# Remove the previous output
old_values = _unfold_partial_integral(
theta, previous_delta[item_ndx], previous_betas[item_ndx],
previous_discrimination[item_ndx], fold_span[item_ndx],
responses[item_ndx], invalid_response_mask[item_ndx])
partial_int /= old_values
new_betas = np.full((betas.shape[1], ), np.nan)
def _local_min_func(estimate):
new_betas[:item_length] = estimate[2:]
new_values = _unfold_partial_integral(
theta, estimate[1], new_betas, estimate[0],
fold_span[item_ndx], responses[item_ndx],
invalid_response_mask[item_ndx])
new_values *= partial_int
otpt = np.sum(new_values, axis=1)
return -np.log(otpt).sum()
# Initial Guess of Item Parameters
initial_guess = np.concatenate(
([discrimination[item_ndx]], [delta[item_ndx]],
betas[item_ndx, :item_length]))
otpt = fmin_slsqp(_local_min_func,
initial_guess,
disp=False,
bounds=[(.25, 4)] + [(-2, 2)] +
[(-6, 6)] * item_length)
discrimination[item_ndx] = otpt[0]
delta[item_ndx] = otpt[1]
betas[item_ndx, :item_length] = otpt[2:]
new_values = _unfold_partial_integral(
theta, delta[item_ndx], betas[item_ndx],
discrimination[item_ndx], fold_span[item_ndx],
responses[item_ndx], invalid_response_mask[item_ndx])
partial_int *= new_values
if np.abs(previous_discrimination - discrimination).max() < 1e-3:
break
# Adjust delta values to conform to delta sign
delta *= np.sign(delta[delta_ndx]) * delta_multiplier
# Recompute partial int for later calculations
partial_int = np.ones((responses.shape[1], theta.size))
for item_ndx in range(n_items):
partial_int *= _unfold_partial_integral(
theta, delta[item_ndx], betas[item_ndx], discrimination[item_ndx],
fold_span[item_ndx], responses[item_ndx],
invalid_response_mask[item_ndx])
# Compute statistics for final iteration
null_metrics = latent_pdf.compute_metrics(
partial_int, latent_pdf.null_distribution * latent_pdf.weights, 0)
full_metrics = latent_pdf.compute_metrics(partial_int,
distribution_x_weight,
latent_pdf.n_points - 3)
# Ability estimates
eap_abilities = _ability_eap_abstract(partial_int, distribution_x_weight,
theta)
return {
'Discrimination':
discrimination,
'Difficulties':
np.c_[betas, np.zeros(
(delta.size, )), -betas[:, ::-1]] + delta[:, None],
'Ability':
eap_abilities,
'Delta':
delta,
'Tau':
betas,
'LatentPDF':
latent_pdf,
'AIC': {
'final': full_metrics[0],
'null': null_metrics[0],
'delta': null_metrics[0] - full_metrics[0]
},
'BIC': {
'final': full_metrics[1],
'null': null_metrics[1],
'delta': null_metrics[1] - full_metrics[1]
}
}
def pcm_mml(dataset, options=None):
"""Estimate parameters for partial credit model.
Estimate the discrimination and difficulty parameters for
the partial credit model using marginal maximum likelihood.
Args:
dataset: [n_items, n_participants] 2d array of measured responses
options: dictionary with updates to default options
Returns:
discrimination: (1d array) estimates of item discrimination
difficulty: (2d array) estimates of item difficulties x item thresholds
Options:
* estimate_distribution: Boolean
* number_of_samples: int >= 5
* max_iteration: int
* distribution: callable
* quadrature_bounds: (float, float)
* quadrature_n: int
"""
options = validate_estimation_options(options)
cpr_result = condition_polytomous_response(dataset,
trim_ends=False,
_reference=0.0)
responses, item_counts, valid_response_mask = cpr_result
invalid_response_mask = ~valid_response_mask
n_items = responses.shape[0]
# Quadrature Locations
latent_pdf = LatentPDF(options)
theta = latent_pdf.quadrature_locations
# Initialize difficulty parameters for estimation
betas = np.full((n_items, item_counts.max()), np.nan)
discrimination = np.ones((n_items, ))
partial_int = np.ones((responses.shape[1], theta.size))
# Not all items need to have the same
# number of response categories
betas[:, 0] = 0
for ndx in range(n_items):
betas[ndx, 1:item_counts[ndx]] = np.linspace(-1, 1,
item_counts[ndx] - 1)
# Set invalid index to zero, this allows minimal
# changes for invalid data and it is corrected
# during integration
responses[invalid_response_mask] = 0
#############
# 1. Start the iteration loop
# 2. Estimate Dicriminatin/Difficulty Jointly
# 3. Integrate of theta
# 4. minimize and repeat
#############
for iteration in range(options['max_iteration']):
previous_discrimination = discrimination.copy()
previous_betas = betas.copy()
# Quadrature evaluation for values that do not change
# This is done during the outer loop to address rounding errors
# and for speed
partial_int = np.ones((responses.shape[1], theta.size))
for item_ndx in range(n_items):
partial_int *= _credit_partial_integral(
theta, betas[item_ndx], discrimination[item_ndx],
responses[item_ndx], invalid_response_mask[item_ndx])
# Estimate the distribution if requested
distribution_x_weight = latent_pdf(partial_int, iteration)
partial_int *= distribution_x_weight
# Loop over each item and solve for the alpha / beta parameters
for item_ndx in range(n_items):
# pylint: disable=cell-var-from-loop
item_length = item_counts[item_ndx]
new_betas = np.zeros((item_length))
# Remove the previous output
old_values = _credit_partial_integral(
theta, previous_betas[item_ndx],
previous_discrimination[item_ndx], responses[item_ndx],
invalid_response_mask[item_ndx])
partial_int /= old_values
def _local_min_func(estimate):
new_betas[1:] = estimate[1:]
new_values = _credit_partial_integral(
theta, new_betas, estimate[0], responses[item_ndx],
invalid_response_mask[item_ndx])
new_values *= partial_int
otpt = np.sum(new_values, axis=1)
return -np.log(otpt).sum()
# Initial Guess of Item Parameters
initial_guess = np.concatenate(
([discrimination[item_ndx]], betas[item_ndx, 1:item_length]))
otpt = fmin_slsqp(_local_min_func,
initial_guess,
disp=False,
bounds=[(.25, 4)] + [(-6, 6)] *
(item_length - 1))
discrimination[item_ndx] = otpt[0]
betas[item_ndx, 1:item_length] = otpt[1:]
new_values = _credit_partial_integral(
theta, betas[item_ndx], discrimination[item_ndx],
responses[item_ndx], invalid_response_mask[item_ndx])
partial_int *= new_values
if np.abs(previous_discrimination - discrimination).max() < 1e-3:
break
# Recompute partial int for later calculations
partial_int = np.ones((responses.shape[1], theta.size))
for item_ndx in range(n_items):
partial_int *= _credit_partial_integral(
theta, betas[item_ndx], discrimination[item_ndx],
responses[item_ndx], invalid_response_mask[item_ndx])
# TODO: look where missing values are and place NAN there instead
# of appending them to the end
# Compute statistics for final iteration
null_metrics = latent_pdf.compute_metrics(
partial_int, latent_pdf.null_distribution * latent_pdf.weights, 0)
full_metrics = latent_pdf.compute_metrics(partial_int,
distribution_x_weight,
latent_pdf.n_points - 3)
# Ability estimates
eap_abilities = _ability_eap_abstract(partial_int, distribution_x_weight,
theta)
return {
'Discrimination': discrimination,
'Difficulty': betas[:, 1:],
'Ability': eap_abilities,
'LatentPDF': latent_pdf,
'AIC': {
'final': full_metrics[0],
'null': null_metrics[0],
'delta': null_metrics[0] - full_metrics[0]
},
'BIC': {
'final': full_metrics[1],
'null': null_metrics[1],
'delta': null_metrics[1] - full_metrics[1]
}
}
def grm_mml(dataset, options=None):
"""Estimate parameters for graded response model.
Estimate the discrimination and difficulty parameters for
a graded response model using marginal maximum likelihood.
Args:
dataset: [n_items, n_participants] 2d array of measured responses
options: dictionary with updates to default options
Returns:
results_dictionary:
* Discrimination: (1d array) estimate of item discriminations
* Difficulty: (2d array) estimates of item diffiulties by item thresholds
* LatentPDF: (object) contains information about the pdf
* AIC: (dictionary) null model and final model AIC value
* BIC: (dictionary) null model and final model BIC value
Options:
* estimate_distribution: Boolean
* number_of_samples: int >= 5
* use_LUT: boolean
* max_iteration: int
* distribution: callable
* quadrature_bounds: (float, float)
* quadrature_n: int
"""
options = validate_estimation_options(options)
cpr_result = condition_polytomous_response(dataset, trim_ends=False)
responses, item_counts, valid_response_mask = cpr_result
invalid_response_mask = ~valid_response_mask
n_items = responses.shape[0]
# Should we use the LUT
_integral_func = _solve_integral_equations
_interp_func = None
if options['use_LUT']:
_integral_func = _solve_integral_equations_LUT
_interp_func = create_beta_LUT((.15, 5.05, 500), (-6, 6, 500), options)
# Quadrature Locations
latent_pdf = LatentPDF(options)
theta = latent_pdf.quadrature_locations
# Compute the values needed for integral equations
integral_counts = list()
for ndx in range(n_items):
temp_output = _solve_for_constants(responses[ndx,
valid_response_mask[ndx]])
integral_counts.append(temp_output)
# Initialize difficulty parameters for estimation
betas = np.full((item_counts.sum(), ), -10000.0)
discrimination = np.ones_like(betas)
cumulative_item_counts = item_counts.cumsum()
start_indices = np.roll(cumulative_item_counts, 1)
start_indices[0] = 0
for ndx in range(n_items):
end_ndx = cumulative_item_counts[ndx]
start_ndx = start_indices[ndx] + 1
betas[start_ndx:end_ndx] = np.linspace(-1, 1, item_counts[ndx] - 1)
betas_roll = np.roll(betas, -1)
betas_roll[cumulative_item_counts - 1] = 10000
# Set invalid index to zero, this allows minimal
# changes for invalid data and it is corrected
# during integration
responses[invalid_response_mask] = 0
#############
# 1. Start the iteration loop
# 2. estimate discrimination
# 3. solve for difficulties
# 4. minimize and repeat
#############
for iteration in range(options['max_iteration']):
previous_discrimination = discrimination.copy()
previous_betas = betas.copy()
previous_betas_roll = betas_roll.copy()
# Quadrature evaluation for values that do not change
# This is done during the outer loop to address rounding errors
partial_int = np.ones((responses.shape[1], theta.size))
for item_ndx in range(n_items):
partial_int *= _graded_partial_integral(
theta, betas, betas_roll, discrimination, responses[item_ndx],
invalid_response_mask[item_ndx])
# Estimate the distribution if requested
distribution_x_weight = latent_pdf(partial_int, iteration)
partial_int *= distribution_x_weight
# Update the lookup table if necessary
if (options['use_LUT'] and options['estimate_distribution']
and iteration > 0):
new_options = dict(options)
new_options.update({'distribution': latent_pdf.cubic_splines[-1]})
_interp_func = create_beta_LUT((.15, 5.05, 500), (-6, 6, 500),
new_options)
for item_ndx in range(n_items):
# pylint: disable=cell-var-from-loop
# Indices into linearized difficulty parameters
start_ndx = start_indices[item_ndx]
end_ndx = cumulative_item_counts[item_ndx]
old_values = _graded_partial_integral(
theta, previous_betas, previous_betas_roll,
previous_discrimination, responses[item_ndx],
invalid_response_mask[item_ndx])
partial_int /= old_values
def _local_min_func(estimate):
# Solve integrals for diffiulty estimates
new_betas = _integral_func(estimate, integral_counts[item_ndx],
distribution_x_weight, theta,
_interp_func)
betas[start_ndx + 1:end_ndx] = new_betas
betas_roll[start_ndx:end_ndx - 1] = new_betas
discrimination[start_ndx:end_ndx] = estimate
new_values = _graded_partial_integral(
theta, betas, betas_roll, discrimination,
responses[item_ndx], invalid_response_mask[item_ndx])
new_values *= partial_int
otpt = np.sum(new_values, axis=1)
return -np.log(otpt).sum()
# Univariate minimization for discrimination parameter
fminbound(_local_min_func, 0.2, 5.0)
new_values = _graded_partial_integral(
theta, betas, betas_roll, discrimination, responses[item_ndx],
invalid_response_mask[item_ndx])
partial_int *= new_values
if np.abs(previous_discrimination - discrimination).max() < 1e-3:
break
# Recompute partial int for later calculations
partial_int = np.ones((responses.shape[1], theta.size))
for item_ndx in range(n_items):
partial_int *= _graded_partial_integral(
theta, betas, betas_roll, discrimination, responses[item_ndx],
invalid_response_mask[item_ndx])
# Trim difficulties to conform to standard output
# TODO: look where missing values are and place NAN there instead
# of appending them to the end
output_betas = np.full((n_items, item_counts.max() - 1), np.nan)
for ndx, (start_ndx,
end_ndx) in enumerate(zip(start_indices,
cumulative_item_counts)):
output_betas[ndx, :end_ndx - start_ndx - 1] = betas[start_ndx +
1:end_ndx]
# Compute statistics for final iteration
null_metrics = latent_pdf.compute_metrics(
partial_int, latent_pdf.null_distribution * latent_pdf.weights, 0)
full_metrics = latent_pdf.compute_metrics(partial_int,
distribution_x_weight,
latent_pdf.n_points - 3)
# Ability estimates
eap_abilities = _ability_eap_abstract(partial_int, distribution_x_weight,
theta)
return {
'Discrimination': discrimination[start_indices],
'Difficulty': output_betas,
'Ability': eap_abilities,
'LatentPDF': latent_pdf,
'AIC': {
'final': full_metrics[0],
'null': null_metrics[0],
'delta': null_metrics[0] - full_metrics[0]
},
'BIC': {
'final': full_metrics[1],
'null': null_metrics[1],
'delta': null_metrics[1] - full_metrics[1]
}
}