from abc import abstractmethod
from typing import List, Union
from warnings import warn
import numpy
from scipy.integrate import quad
from . import irt
from .simulation import FiniteSelector, Selector
[docs]
class MaxInfoSelector(Selector):
"""Selector that returns the first non-administered item with maximum information, given an estimated theta
:param r_max: maximum exposure rate for items
"""
def __init__(self, r_max: float = 1):
super().__init__()
self._r_max = r_max
def __str__(self):
return "Maximum Information Selector"
@property
def r_max(self):
return self._r_max
[docs]
def select(
self,
index: int = None,
items: numpy.ndarray = None,
administered_items: List[int] = None,
est_theta: float = None,
**kwargs
) -> Union[int, None]:
"""Returns the index of the next item to be administered.
:param index: the index of the current examinee in the simulator.
:param items: a matrix containing item parameters in the format that `catsim` understands
(see: :py:func:`catsim.cat.generate_item_bank`)
:param administered_items: a list containing the indexes of items that were already administered
:param est_theta: a float containing the current estimated ability
:returns: index of the next item to be applied or `None` if there are no more items in the item bank.
"""
items, administered_items, est_theta = self._prepare_args(
return_items=True,
return_est_theta=True,
index=index,
items=items,
administered_items=administered_items,
est_theta=est_theta,
**kwargs,
)
assert items is not None
assert administered_items is not None
assert est_theta is not None
# sort items by their information value
ordered_items = self._sort_by_info(items, est_theta)
# remove administered ones
valid_indexes = self._get_non_administered(ordered_items, administered_items)
if len(valid_indexes) == 0:
warn("There are no more items to be applied.")
return None
# gets the indexes and information values from the items with r < rmax
valid_indexes_low_r = valid_indexes
if items.shape[1] < 5:
warn(
"This selector needs an item matrix with at least 5 columns, with the last one representing item exposure rate. Since this column is absent, it will presume all items have exposure rates = 0"
)
else:
valid_indexes_low_r = [
index for index in valid_indexes if items[index, 4] < self._r_max
]
# return the item with maximum information from the ones available
if len(valid_indexes_low_r) > 0:
selected_item = valid_indexes_low_r[0]
else:
selected_item = valid_indexes[0]
return selected_item
[docs]
class UrrySelector(Selector):
"""Selector that returns the item whose difficulty parameter is closest to the examinee's ability"""
def __init__(self):
super().__init__()
def __str__(self):
return "Urry Selector"
[docs]
def select(
self,
index: int = None,
items: numpy.ndarray = None,
administered_items: List[int] = None,
est_theta: float = None,
**kwargs
) -> Union[int, None]:
"""Returns the index of the next item to be administered.
:param index: the index of the current examinee in the simulator.
:param items: a matrix containing item parameters in the format that `catsim` understands
(see: :py:func:`catsim.cat.generate_item_bank`)
:param administered_items: a list containing the indexes of items that were already administered
:param est_theta: a float containing the current estimated ability
:returns: index of the next item to be applied or `None` if there are no more items in the item bank.
"""
items, administered_items, est_theta = self._prepare_args(
return_items=True,
return_est_theta=True,
index=index,
items=items,
administered_items=administered_items,
est_theta=est_theta,
**kwargs,
)
assert est_theta is not None
assert administered_items is not None
assert items is not None
ordered_items = self._sort_by_b(items, est_theta)
valid_indexes = self._get_non_administered(ordered_items, administered_items)
if len(valid_indexes) == 0:
warn("There are no more items to be applied.")
return None
return valid_indexes[0]
[docs]
class LinearSelector(FiniteSelector):
"""Selector that returns item indexes in a linear order, simulating a standard
(non-adaptive) test.
:param indexes: the indexes of the items that will be returned in order"""
def __str__(self):
return "Linear Selector"
def __init__(self, indexes: List[int]):
super().__init__(len(indexes))
self._indexes = indexes
self._current = 0
@property
def indexes(self):
return self._indexes
@property
def current(self):
return self._current
[docs]
def select(
self, index: int = None, administered_items: List[int] = None, **kwargs
) -> Union[int, None]:
"""Returns the index of the next item to be administered.
:param index: the index of the current examinee in the simulator.
:param administered_items: a list containing the indexes of items that were already administered
:returns: index of the next item to be applied or `None` if there are no more items in the item bank.
"""
(administered_items,) = self._prepare_args(
index=index, administered_items=administered_items, **kwargs
)
valid_indexes = self._get_non_administered(self._indexes, administered_items)
if len(valid_indexes) == 0:
warn(
f"A new index was asked for, but there are no more item indexes to present.\n"
f"Current item:\t\t\t{self._current}\n"
f"Items to be administered:\t{sorted(self._indexes)} (size: {len(self._indexes)})\n"
f"Administered items:\t\t{sorted(administered_items)} (size: {len(administered_items)})"
)
return None
return valid_indexes[0]
[docs]
class RandomSelector(Selector):
"""Selector that randomly selects items for application.
:param replace: whether to select an item that has already been selected before for this examinee.
"""
def __str__(self):
return "Random Selector"
def __init__(self, replace: bool = False):
super().__init__()
self._replace = replace
[docs]
def select(
self,
index: int = None,
items: numpy.ndarray = None,
administered_items: List[int] = None,
**kwargs
) -> Union[int, None]:
"""Returns the index of the next item to be administered.
:param index: the index of the current examinee in the simulator.
:param items: a matrix containing item parameters in the format that `catsim` understands
(see: :py:func:`catsim.cat.generate_item_bank`)
:param administered_items: a list containing the indexes of items that were already administered
:returns: index of the next item to be applied or `None` if there are no more items in the item bank.
"""
items, administered_items = self._prepare_args(
return_items=True,
index=index,
items=items,
administered_items=administered_items,
**kwargs,
)
assert items is not None
assert administered_items is not None
if len(administered_items) >= items.shape[0] and not self._replace:
warn(
"A new item was asked for, but there are no more items to present.\n"
f"Administered items:\t{len(administered_items)}\nItem bank size:\t{items.shape[0]}"
)
return None
if self._replace:
return numpy.random.choice(items.shape[0])
else:
valid_indexes = self._get_non_administered(
list(range(items.shape[0])), administered_items
)
return numpy.random.choice(valid_indexes)
[docs]
class ClusterSelector(Selector):
"""Cluster-based Item Selection Method.
.. [Men15] Meneghetti, D. R. (2015). Metolodogia de seleção de itens em testes
adaptativos informatizados baseada em agrupamento por similaridade (Mestrado).
Centro Universitário da FEI. Retrieved from
https://www.researchgate.net/publication/283944553_Metodologia_de_selecao_de_itens_em_Testes_Adaptativos_Informatizados_baseada_em_Agrupamento_por_Similaridade
:param clusters: a list containing item cluster memberships
:param r_max: maximum exposure rate for items
:param method: one of the available methods for cluster selection. Given
the estimated theta value at each step:
``item_info``: selects the cluster which has the item
with maximum information;
``cluster_info``: selects the cluster whose items sum of
information is maximum;
``weighted_info``: selects the cluster whose weighted
sum of information is maximum. The weighted equals the
number of items in the cluster;
:param r_control: if `passive` and all items :math:`i` in the selected
cluster have :math:`r_i > r^{max}`, applies the item with
maximum information; if `aggressive`, applies the item
with smallest :math:`r` value.
"""
def __str__(self):
return "Cluster Selector"
@property
def r_max(self):
return self._r_max
@property
def clusters(self):
return self._clusters
@property
def method(self):
return self._method
@property
def r_control(self):
return self._r_control
def __init__(
self,
clusters: List[int],
method: str = "item_info",
r_max: float = 1,
r_control: str = "passive",
):
super().__init__()
available_methods = ["item_info", "cluster_info", "weighted_info"]
if method not in available_methods:
raise ValueError(
f"{method} is not a valid cluster selection method; choose one from {available_methods}"
)
available_rcontrol = ["passive", "aggressive"]
if r_control not in available_rcontrol:
raise ValueError(
f"{r_control} is not a valid item exposure control method; choose one from {available_rcontrol}"
)
self._clusters = clusters
self._method = method
self._r_max = r_max
self._r_control = r_control
[docs]
def select(
self,
index: int = None,
items: numpy.ndarray = None,
administered_items: List[int] = None,
est_theta: float = None,
**kwargs
) -> Union[int, None]:
"""Returns the index of the next item to be administered.
:param index: the index of the current examinee in the simulator.
:param items: a matrix containing item parameters in the format that `catsim` understands
(see: :py:func:`catsim.cat.generate_item_bank`)
:param administered_items: a list containing the indexes of items that were already administered
:param est_theta: a float containing the current estimated ability
:returns: index of the next item to be applied.
"""
items, administered_items, est_theta = self._prepare_args(
return_items=True,
return_est_theta=True,
index=index,
items=items,
administered_items=administered_items,
est_theta=est_theta,
**kwargs,
)
assert items is not None
assert administered_items is not None
assert est_theta is not None
selected_cluster = None
existent_clusters = set(self._clusters)
# this part of the code selects the cluster from which the item at
# the current point of the test will be chosen
if self._method == "item_info":
# get the item indexes sorted by their information value
infos = self._sort_by_info(items, est_theta)
evaluated_clusters = set()
# iterate over every item in order of information value
for i in range(items.shape[0]):
# get the current non-examined item
max_info_item = infos[i]
# if the cluster of the current item has already been fully examined, go to the next item
if self._clusters[max_info_item] in evaluated_clusters:
continue
# get the indexes of all items in the same cluster as the current item
items_in_cluster = numpy.nonzero(
[x == self._clusters[max_info_item] for x in self._clusters]
)[0]
# if all the items in the current cluster have already been administered (it happens, theoretically),
# add this cluster to the list of fully evaluated clusters
if set(items_in_cluster) <= set(administered_items):
evaluated_clusters.add(self._clusters[max_info_item])
# if all clusters have been evaluated, the loop ends and the method returns None somewhere below
if evaluated_clusters == existent_clusters:
break
# else, if there are still items and clusters to be explored, keep going
continue
# if the algorithm gets here, it means this cluster can be used
selected_cluster = self._clusters[max_info_item]
break
elif self._method in ["cluster_info", "weighted_info"]:
# calculates the cluster information, depending on the method
# selected
if self._method == "cluster_info":
cluster_infos = ClusterSelector.sum_cluster_infos(est_theta, items, self._clusters)
else:
cluster_infos = ClusterSelector.weighted_cluster_infos(
est_theta, items, self._clusters
)
# sorts clusters descending by their information values
# this type of sorting was seem on
# http://stackoverflow.com/a/6618543
sorted_clusters = numpy.array(
[
cluster
for (inf_value, cluster) in sorted(
zip(cluster_infos, set(self._clusters)),
key=lambda pair: pair[0],
reverse=True,
)
],
dtype=float,
)
# walks through the sorted clusters in order
for i in range(len(sorted_clusters)):
valid_indexes = numpy.nonzero([r == sorted_clusters[i] for r in items[:, 4]])[0]
# checks if at least one item from this cluster has not
# been administered to this examinee yet
if set(valid_indexes).intersection(administered_items) != set(valid_indexes):
selected_cluster = sorted_clusters[i]
break
# the for loop ends with the cluster that has a) the maximum
# information possible and b) at least one item that has not
# yet been administered
# if the test size gets larger than the item bank size, end the test
if selected_cluster is None:
warn("There are no more items to be applied.")
return None
# in this part, an item is chosen from the cluster that was
# selected above
# gets the indexes and information values from the items in the
# selected cluster that have not been administered
valid_indexes = self._get_non_administered(
numpy.nonzero([cluster == selected_cluster for cluster in self._clusters])[0],
administered_items,
)
# gets the indexes and information values from the items in the
# selected cluster with r < rmax that have not been administered
valid_indexes_low_r = valid_indexes
if items.shape[1] < 5:
warn(
"This selector needs an item matrix with at least 5 columns, with the last one representing item exposure rate. Since this column is absent, it will presume all items have exposure rates = 0"
)
else:
valid_indexes_low_r = [
index
for index in valid_indexes
if items[index, 4] < self._r_max and index not in administered_items
]
if len(valid_indexes_low_r) > 0:
# return the item with maximum information from the ones available
inf_values = irt.inf_hpc(est_theta, items[valid_indexes_low_r])
selected_item = valid_indexes_low_r[numpy.nonzero(inf_values == max(inf_values))[0][0]]
# if all items in the selected cluster have exceed their r values,
# select the one with smallest r, regardless of information
else:
if self._r_control == "passive":
inf_values = irt.inf_hpc(est_theta, items[valid_indexes])
selected_item = valid_indexes[numpy.nonzero(inf_values == max(inf_values))[0][0]]
else:
selected_item = valid_indexes[items[:, 4].index(min(items[:, 4]))]
return selected_item
[docs]
@staticmethod
def sum_cluster_infos(theta: float, items: numpy.ndarray, clusters: List[int]) -> numpy.ndarray:
"""Returns the sum of item information values, separated by cluster
:param theta: an examinee's :math:`\\theta` value
:param items: a matrix containing item parameters in the format that `catsim` understands
(see: :py:func:`catsim.cat.generate_item_bank`)
:param clusters: a list containing item cluster memberships, represented by integers
:returns: array containing the sum of item information values for each cluster"""
cluster_infos = numpy.zeros((len(set(clusters))))
for cluster in set(clusters):
cluster_indexes = numpy.nonzero([c == cluster for c in clusters])[0]
for item in items[cluster_indexes]:
cluster_infos[cluster] += irt.inf(theta, item[0], item[1], item[2], item[3])
return cluster_infos
[docs]
@staticmethod
def weighted_cluster_infos(
theta: float, items: numpy.ndarray, clusters: List[int]
) -> numpy.ndarray:
"""Returns the weighted sum of item information values, separated by cluster.
The weight is the number of items in each cluster.
:param theta: an examinee's :math:`\\theta` value
:param items: a matrix containing item parameters in the format that `catsim` understands
(see: :py:func:`catsim.cat.generate_item_bank`)
:param clusters: a list containing item cluster memberships, represented by integers
:returns: array containing the sum of item information values for each cluster,
divided by the number of items in each cluster"""
cluster_infos = ClusterSelector.sum_cluster_infos(theta, items, clusters)
count = numpy.bincount(clusters)
for i in range(len(cluster_infos)):
cluster_infos[i] /= count[i]
return cluster_infos
[docs]
@staticmethod
def sum_cluster_params(items: numpy.ndarray, c: List[int]):
"""Returns the sum of item parameter values for each cluster
:param items: a matrix containing item parameters in the format that `catsim` understands
(see: :py:func:`catsim.cat.generate_item_bank`)
:param c: a list containing clustering memeberships.
:returns: a matrix containing the sum of each parameter by cluster. Lines are clusters, columns are parameters.
"""
averages = numpy.zeros((numpy.max(c) + 1, 4))
for i in numpy.arange(0, numpy.size(c)):
if c[i] == -1:
continue
averages[c[i], 0] += items[i, 0]
averages[c[i], 1] += items[i, 1]
averages[c[i], 2] += items[i, 2]
averages[c[i], 3] += items[i, 3]
return averages
[docs]
@staticmethod
def avg_cluster_params(items: numpy.ndarray, c: List[int]):
"""Returns the average values of item parameters by cluster
:param items:
:param c: a list containing clustering memeberships.
:returns: a matrix containing the average values of each parameter by cluster.
Lines are clusters, columns are parameters."""
averages = ClusterSelector.sum_cluster_params(items, c)
occurrences = numpy.bincount(numpy.delete(c, numpy.where(c == -1)).astype(numpy.int64))
for counter, i in enumerate(occurrences):
averages[counter, 0] /= i
averages[counter, 1] /= i
averages[counter, 2] /= i
averages[counter, 3] /= i
return averages
[docs]
class StratifiedSelector(FiniteSelector):
def __str__(self):
return "General Stratified Selector"
def __init__(self, test_size, sort_once):
super().__init__(test_size)
self._sort_once = sort_once
self._presorted_items = None
@abstractmethod
def presort_items(self, items: numpy.ndarray) -> numpy.ndarray:
pass
def postsort_items(
self, items: numpy.ndarray, using_simulator_props: bool, **kwargs
) -> numpy.ndarray:
if using_simulator_props:
return self._presorted_items
else:
return self.presort_items(items)
[docs]
def preprocess(self):
self._presorted_items = self.presort_items(self.simulator.items)
[docs]
def select(
self,
index: int = None,
items: numpy.ndarray = None,
administered_items: List[int] = None,
**kwargs
) -> Union[int, None]:
"""Returns the index of the next item to be administered.
:param index: the index of the current examinee in the simulator.
:param items: a matrix containing item parameters
:param administered_items: a list containing the indexes of items that were already administered
:returns: index of the next item to be applied or `None` if there are no more strata to get items from.
"""
items, administered_items, est_theta = self._prepare_args(
return_items=True,
index=index,
items=items,
administered_items=administered_items,
return_est_theta=True,
**kwargs,
)
assert items is not None
assert administered_items is not None
assert est_theta is not None
# select the item in the correct layer, according to the point in the test the examinee is
stratum_index = len(administered_items)
try:
slices, pointer, max_pointer = self._get_stratum(items, stratum_index)
except IndexError:
warn(
f"{self}: test size is larger than was informed to the selector\n"
f"Length of administered items:\t{len(administered_items)}\n"
f"Total length of the test:\t{self._test_size}\n"
f"Number of slices:\t{len(slices)}"
)
return None
using_simulator_props = index is not None
if using_simulator_props and self._sort_once:
sorted_items = self._presorted_items
else:
kwargs["using_simulator_props"] = using_simulator_props
sorted_items = self.postsort_items(items, using_simulator_props, est_theta=est_theta)
# if the selected item has already been administered, select the next one
while sorted_items[pointer] in administered_items:
pointer += 1
if pointer == max_pointer:
raise ValueError(
f"There are no more items to be selected from stratum {slices[len(administered_items)]}"
)
return sorted_items[pointer]
def _get_stratum(self, items: numpy.ndarray, stratum_index: int) -> numpy.ndarray:
slices = numpy.linspace(0, items.shape[0], self._test_size, endpoint=False, dtype="i")
pointer = slices[stratum_index]
max_pointer = (
items.shape[0] if stratum_index == self._test_size - 1 else slices[stratum_index + 1]
)
return slices, pointer, max_pointer
[docs]
class AStratSelector(StratifiedSelector):
"""Implementation of the :math:`\\alpha`-stratified selector proposed by
[Chang99]_, in which the item bank is sorted in ascending order according to the
items discrimination parameter and then separated into :math:`K` strata
(:math:`K` being the test size), each stratum containing gradually higher
average discrimination. The :math:`\\alpha`-stratified selector then selects the
first non-administered item from stratum :math:`k`, in which :math:`k`
represents the position in the test of the current item the examinee is being
presented.
.. image:: ../sphinx/alpha-strat.*
:param test_size: the number of items the test contains. The selector uses this parameter
to create the correct number of strata.
"""
def __str__(self):
return "a-Stratified Selector"
def __init__(self, test_size):
super().__init__(test_size, True)
def presort_items(self, items: numpy.ndarray) -> numpy.ndarray:
return items[:, 0].argsort()
[docs]
class AStratBBlockSelector(StratifiedSelector):
"""Implementation of the :math:`\\alpha`-stratified selector with :math:`b`
blocking proposed by [Chang2001]_, in which the item bank is sorted in ascending
order according to the items difficulty parameter and then separated into
:math:`M` strata, each stratum containing gradually higher average difficulty.
Each of the :math:`M` strata is then again separated into :math:`K`
sub-strata (:math:`k` being the test size), according to their
discrimination. The final item bank is then ordered such that the first
sub-strata of each strata forms the first strata of the new ordered item
bank, and so on. This method tries to balance the distribution of both
parameters between all strata, after perceiving that they are correlated.
.. image:: ../sphinx/b-blocking.*
:param test_size: the number of items the test contains. The selector uses this parameter to
create the correct number of strata.
"""
def __str__(self):
return "a-Stratified b-Blocking Selector"
def __init__(self, test_size):
super().__init__(test_size, True)
def presort_items(self, items: numpy.ndarray) -> numpy.ndarray:
# sort items by their b values, in ascending order
presorted_items = items[:, 1].argsort()
final_indices = []
for stratum_index in range(self._test_size):
slices, pointer, max_pointer = self._get_stratum(items, stratum_index)
indices_current_stratum = presorted_items[pointer:max_pointer]
items_current_stratum = items[indices_current_stratum]
sorted_indices_current_stratum = items_current_stratum[:, 0].argsort()
# sort the items in the current stratum by their discrimination values, in ascending order
global_sorted_indices_current_stratum = indices_current_stratum[
sorted_indices_current_stratum
]
final_indices.extend(global_sorted_indices_current_stratum)
# sort the item bank first by the items maximum information, ascending
# then by their information to the examinee's cuirrent theta, descending
return numpy.array(final_indices)
[docs]
class MaxInfoStratSelector(StratifiedSelector):
"""Implementation of the maximum information stratification (MIS) selector
proposed by [Bar06]_, in which the item bank is sorted in ascending order
according to the items maximum information and then separated into :math:`K`
strata (:math:`K` being the test size), each stratum containing items with
gradually higher maximum information. The MIS selector then selects the first
non-administered item from stratum :math:`k`, in which :math:`k` represents the
position in the test of the current item the examinee is being presented.
.. image:: ../sphinx/mis.*
This method claims to work better than the :math:`a`-stratified method by
[Chang99]_ for the three-parameter logistic model of IRT, since item difficulty
and maximum information are not positioned in the same place in the ability
scale in 3PL.
:param test_size: the number of items the test contains. The selector uses this parameter to
create the correct number of strata.
"""
def __str__(self):
return "Maximum Information Stratification Selector"
def __init__(self, test_size):
super().__init__(test_size, False)
def presort_items(self, items: numpy.ndarray) -> numpy.ndarray:
# get the theta values in which items are maximally informative
theta_maxinfo = irt.max_info_hpc(items)
# get the information values for all items at their maximum points
item_maxinfo = irt.inf_hpc(theta_maxinfo, items)
# globally sort item bank by item max information
return item_maxinfo.argsort()
def postsort_items(
self, items: numpy.ndarray, using_simulator_props: bool, est_theta: float
) -> numpy.ndarray:
# recover items presorted by the first rule
if using_simulator_props:
presorted_items = self._presorted_items
else:
presorted_items = self.presort_items(items)
# run through each stratum and sort items in descending order according to
# their information for the current theta value
final_indices = []
for stratum_index in range(self._test_size):
# grab stratum pointers
slices, pointer, max_pointer = self._get_stratum(items, stratum_index)
item_indices_current_stratum = presorted_items[
pointer:max_pointer
] # item indices for the current stratum
items_current_stratum: numpy.ndarray = items[
item_indices_current_stratum
] # item params for the current stratum
# their information for this theta
info_items_current_stratum_current_theta: numpy.ndarray = irt.inf_hpc(
est_theta, items_current_stratum
)
item_indices_current_stratum_sorted_by_info = item_indices_current_stratum[
(-info_items_current_stratum_current_theta).argsort()
]
final_indices.extend(item_indices_current_stratum_sorted_by_info)
# sort the item bank first by the items maximum information, ascending
# then by their information to the examinee's cuirrent theta, descending
return numpy.array(final_indices)
[docs]
class MaxInfoBBlockSelector(MaxInfoStratSelector):
"""Implementation of the maximum information stratification with :math:`b`
blocking (MIS-B) selector proposed by [Bar06]_, in which the item bank is sorted
in ascending order according to the items difficulty parameter and then
separated into :math:`M` strata, each stratum containing gradually higher
average difficulty.
Each of the :math:`M` strata is then again separated into :math:`K`
sub-strata (:math:`k` being the test size), according to the items maximum
information. The final item bank is then ordered such that the first
sub-strata of each strata forms the first strata of the new ordered item
bank, and so on. This method tries to balance the distribution of both
parameters between all strata and works better than the :math:`a`-stratified
with :math:`b` blocking method by [Chang2001]_ for the three-parameter
logistic model of IRT, since item difficulty and maximum information are not
positioned in the same place in the ability scale in 3PL. This may also
apply, although not mentioned by the authors, for the 4PL.
.. image:: ../sphinx/mis-b.*
:param test_size: the number of items the test contains. The selector uses this parameter to
create the correct number of strata.
"""
def __str__(self):
return "Maximum Information Stratification with b-Blocking Selector"
def presort_items(self, items: numpy.ndarray) -> numpy.ndarray:
# get the theta values in which items are maximally informative
theta_maxinfo = irt.max_info_hpc(items)
# sort items by theta
presorted_items = theta_maxinfo.argsort()
# get the information values for all items at their maximum points
item_maxinfo = irt.inf_hpc(theta_maxinfo, items[presorted_items])
final_indices = []
for stratum_index in range(self._test_size):
slices, pointer, max_pointer = self._get_stratum(items, stratum_index)
indices_current_stratum = presorted_items[pointer:max_pointer]
# sort items in the current stratum by maximum information, in ascending order
sorted_indices_current_stratum = item_maxinfo[indices_current_stratum].argsort()
global_sorted_indices_current_stratum = indices_current_stratum[
sorted_indices_current_stratum
]
final_indices.extend(global_sorted_indices_current_stratum)
# sanity check to make sure all indices are present and unique
assert len(final_indices) == len(set(final_indices))
return numpy.array(final_indices)
[docs]
class The54321Selector(FiniteSelector):
"""Implementation of the 5-4-3-2-1 selector proposed by [McBride83]_, in which,
at each step :math:`k` of a test of size :math:`K`, an item is chosen from a bin
containing the :math:`K-k` most informative items in the bank, given the current
:math:`\\hat\\theta`. As the test progresses, the bin gets smaller and more
informative items have a higher probability of being chosen by the end of the
test, when the estimation of ':math:`\\hat\\theta` is more precise. The
5-4-3-2-1 selector can be viewed as a specialization of the
:py:class:`catsim.selection.RandomesqueSelector`, in which the bin size of most
informative items gets smaller as the test progresses.
:param test_size: the number of items the test contains. The selector uses
this parameter to set the bin size"""
def __str__(self):
return "5-4-3-2-1 Selector"
def __init__(self, test_size):
super().__init__(test_size)
[docs]
def select(
self,
index: int = None,
items: numpy.ndarray = None,
administered_items: List[int] = None,
est_theta: float = None,
**kwargs
) -> Union[int, None]:
"""Returns the index of the next item to be administered.
:param index: the index of the current examinee in the simulator.
:param items: a matrix containing item parameters in the format that `catsim` understands
(see: :py:func:`catsim.cat.generate_item_bank`)
:param administered_items: a list containing the indexes of items that were already administered
:param est_theta: a float containing the current estimated ability
:returns: index of the next item to be applied or `None` if there are no more items in the item bank.
"""
items, administered_items, est_theta = self._prepare_args(
return_items=True,
return_est_theta=True,
index=index,
items=items,
administered_items=administered_items,
est_theta=est_theta,
**kwargs,
)
assert est_theta is not None
assert administered_items is not None
assert items is not None
# sort item indexes by their information value descending and remove indexes of administered items
ordered_items = self._sort_by_info(items, est_theta)
organized_items = self._get_non_administered(ordered_items, administered_items)
if len(organized_items) == 0:
warn("There are no more items to apply.")
return None
bin_size = self._test_size - len(administered_items)
return numpy.random.choice(organized_items[0:bin_size])
[docs]
class RandomesqueSelector(Selector):
"""Implementation of the randomesque selector proposed by [Kingsbury89]_, in which,
at every step of the test, an item is randomly chosen from the :math:`n` most informative
items in the item bank, :math:`n` being a predefined value (originally 5, but user-defined
in this implementation)
:param bin_size: the number of most informative items to be taken into consideration when
randomly selecting one of them.
"""
def __str__(self):
return "Randomesque Selector"
def __init__(self, bin_size):
super().__init__()
self._bin_size = bin_size
@property
def bin_size(self):
return self._bin_size
[docs]
def select(
self,
index: int = None,
items: numpy.ndarray = None,
administered_items: List[int] = None,
est_theta: float = None,
**kwargs
) -> Union[int, None]:
"""Returns the index of the next item to be administered.
:param index: the index of the current examinee in the simulator.
:param items: a matrix containing item parameters in the format that `catsim` understands
(see: :py:func:`catsim.cat.generate_item_bank`)
:param administered_items: a list containing the indexes of items that were already administered
:param est_theta: a float containing the current estimated ability
:returns: index of the next item to be applied or `None` if there are no more items in the item bank.
"""
items, administered_items, est_theta = self._prepare_args(
return_items=True,
return_est_theta=True,
index=index,
items=items,
administered_items=administered_items,
est_theta=est_theta,
**kwargs,
)
assert est_theta is not None
assert administered_items is not None
assert items is not None
# sort item indexes by their information value descending and remove indexes of administered items
ordered_items = self._sort_by_info(items, est_theta)
organized_items = self._get_non_administered(ordered_items, administered_items)
if len(organized_items) == 0:
warn("There are no more items to apply.")
return None
return numpy.random.choice(list(organized_items)[: self._bin_size])
[docs]
class IntervalInfoSelector(Selector):
"""A selector in which, at every step of the test, the item that maximizes
the integral of the information function at a predetermined ``interval``
:math:`\\delta` above and below the current :math:`\\hat\\theta` is chosen.
.. math:: argmax_{i \\in I} \\int_{\\hat\\theta - \\delta}^{\\hat\\theta + \\delta}I_i(\\hat\\theta)
:param interval: the interval of the integral. If no interval is passed, the
integral is computed from :math:`[-\\infty, \\infty]`.
"""
def __str__(self):
return "Interval Information Selector"
def __init__(self, interval: float = None):
super().__init__()
self._interval = interval if interval is not None else numpy.inf
@property
def interval(self):
return self._interval
[docs]
def select(
self,
index: int = None,
items: numpy.ndarray = None,
administered_items: List[int] = None,
est_theta: float = None,
**kwargs
) -> Union[int, None]:
"""Returns the index of the next item to be administered.
:param index: the index of the current examinee in the simulator.
:param items: a matrix containing item parameters in the format that `catsim` understands
(see: :py:func:`catsim.cat.generate_item_bank`)
:param administered_items: a list containing the indexes of items that were already administered
:param est_theta: a float containing the current estimated ability
:returns: index of the next item to be applied or `None` if there are no more items in the item bank.
"""
items, administered_items, est_theta = self._prepare_args(
return_items=True,
return_est_theta=True,
index=index,
items=items,
administered_items=administered_items,
est_theta=est_theta,
**kwargs,
)
assert est_theta is not None
assert administered_items is not None
assert items is not None
# compute the integral of the information function around an examinee's ability
information_integral = numpy.array(
[
quad(
irt.inf,
est_theta - self._interval,
est_theta + self._interval,
args=(item[0], item[1], item[2], item[3]),
)[0]
for item in items
]
)
# sort by that integral in descending order
ordered_items = (-information_integral).argsort()
# remove administered items
organized_items = self._get_non_administered(ordered_items, administered_items)
if len(organized_items) == 0:
warn("There are no more items to apply.")
return None
return organized_items[0]