Source code for catsim.selection

from abc import abstractmethod
from warnings import warn

import numpy
from scipy.integrate import quad

from . import irt
from .simulation import Selector, FiniteSelector


def _nearest(array: list, value) -> numpy.ndarray:
    """Returns the indexes of values in `array` that are closest to `value`
    
    :param array: an array of numeric values
    :param value: a numerical value
    :return: an array containing the indexes of numbers in `array`,
             according to how close their are to `value`
    """
    array = numpy.asarray(array)
    return numpy.abs(array - value).argsort()


[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 = None, est_theta: float = None, **kwargs ) -> int: """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 proficiency :returns: index of the next item to be applied or `None` if there are no more items in the item bank. """ if (index is None or self.simulator is None ) and (items is None or administered_items is None or est_theta is None): raise ValueError( 'Either pass an index for the simulator or all of the other optional parameters to use this component independently.' ) if items is None and administered_items is None and est_theta is None: items = self.simulator.items administered_items = self.simulator.administered_items[index] est_theta = self.simulator.latest_estimations[index] # first, we'll order items by their information value if irt.detect_model(items) <= 2: # when the logistic model has the number of parameters <= 2, # all items have highest information where theta = b ordered_items = _nearest(items[:, 1], est_theta) else: # else, we'll have to calculate the theta value where information is maximum inf_values = irt.max_info_hpc(items) ordered_items = _nearest(inf_values, est_theta) valid_indexes = [x for x in ordered_items if x not in 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 proficiency""" 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 = None, est_theta: float = None, **kwargs ) -> int: """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 proficiency :returns: index of the next item to be applied or `None` if there are no more items in the item bank. """ if (index is None or self.simulator is None ) and (items is None or administered_items is None or est_theta is None): raise ValueError( 'Either pass an index for the simulator or all of the other optional parameters to use this component independently.' ) if items is None and administered_items is None and est_theta is None: items = self.simulator.items administered_items = self.simulator.administered_items[index] est_theta = self.simulator.latest_estimations[index] ordered_items = _nearest(items[:, 1], est_theta) valid_indexes = [x for x in ordered_items if x not in 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): 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 = None, **kwargs) -> int: """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. """ if (index is None or self.simulator is None) and (administered_items is None): raise ValueError( 'Either pass an index for the simulator or all of the other optional parameters to use this component independently.' ) if administered_items is None: administered_items = self.simulator.administered_items[index] if set(self._indexes) <= set(administered_items): warn( 'A new index was asked for, but there are no more item indexes to present.\nCurrent item:\t\t\t{0}\nItems to be administered:\t{1} (size: {2})\nAdministered items:\t\t{3} (size: {4})' .format( self._current, sorted(self._indexes), len(self._indexes), sorted(administered_items), len(administered_items) ) ) return None selected_item = [x for x in self._indexes if x not in administered_items][0] return selected_item
[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 = None, **kwargs ) -> int: """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. """ if (index is None or self.simulator is None) and (items is None or administered_items is None): raise ValueError( 'Either pass an index for the simulator or all of the other optional parameters to use this component independently.' ) if items is None and administered_items is None: items = self.simulator.items administered_items = self.simulator.administered_items[index] 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.\nAdministered items:\t{0}\nItem bank size:\t{1}' .format(len(administered_items), items.shape[0]) ) return None if self._replace: return numpy.random.choice(items.shape[0]) else: return numpy.random.choice(list(set(range(items.shape[0])) - set(administered_items)))
[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, 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( '{0} is not a valid cluster selection method; choose one from {1}'.format( method, available_methods ) ) available_rcontrol = ['passive', 'aggressive'] if r_control not in available_rcontrol: raise ValueError( '{0} is not a valid item exposure control method; choose one from {1}'.format( r_control, 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 = None, est_theta: float = None, **kwargs ) -> int: """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 proficiency :returns: index of the next item to be applied. """ if (index is None or self.simulator is None ) and (items is None or administered_items is None or est_theta is None): raise ValueError( 'Either pass an index for the simulator or all of the other optional parameters to use this component independently.' ) if items is None and administered_items is None and est_theta is None: items = self.simulator.items administered_items = self.simulator.administered_items[index] est_theta = self.simulator.latest_estimations[index] 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 = _nearest(irt.max_info_hpc(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 = [ index for index in numpy.nonzero([cluster == selected_cluster for cluster in self._clusters])[0] if index not in 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) -> 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) -> 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): """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): """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): super().__init__(test_size) self._organized_items = None @staticmethod @abstractmethod def sort_items(items: numpy.ndarray) -> numpy.ndarray: pass
[docs] def preprocess(self): # sort item indexes by their discrimination value self._organized_items = __class__.sort_items(self.simulator.items)
[docs] def select( self, index: int = None, items: numpy.ndarray = None, administered_items: list = None, **kwargs ) -> int: """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. """ if (index is None or self.simulator is None) and (items is None or administered_items is None): raise ValueError( 'Either pass an index for the simulator or all of the other optional parameters to use this component independently.' ) if items is None and administered_items is None: items = self.simulator.items administered_items = self.simulator.administered_items[index] # select the item in the correct layer, according to the point in the test the examinee is slices = numpy.linspace(0, items.shape[0], self._test_size, endpoint=False, dtype='i') try: pointer = slices[len(administered_items)] max_pointer = items.shape[0] if len( administered_items ) == self._test_size - 1 else slices[len(administered_items) + 1] except IndexError: warn( "{0}: test size is larger than was informed to the selector\nLength of administered items:\t{1}\nTotal length of the test:\t{2}\nNumber of slices:\t{3}" .format(self, len(administered_items), self._test_size, len(slices)) ) return None organized_items = self._organized_items if self._organized_items is not None else self.sort_items( items ) # if the selected item has already been administered, select the next one while organized_items[pointer] in administered_items: pointer += 1 if pointer == max_pointer: raise ValueError( 'There are no more items to be selected from stratum {0}'.format( slices[len(administered_items)] ) ) return organized_items[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) @staticmethod def sort_items(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) @staticmethod def sort_items(items: numpy.ndarray) -> numpy.ndarray: return numpy.lexsort((items[:, 0], items[:, 1]))
[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 proficiency 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) @staticmethod def sort_items(items: numpy.ndarray) -> numpy.ndarray: maxinfo = irt.max_info_hpc(items) return irt.inf_hpc(maxinfo, items).argsort()
[docs]class MaxInfoBBlockSelector(StratifiedSelector): """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 proficiency 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 __init__(self, test_size): super().__init__(test_size) @staticmethod def sort_items(items: numpy.ndarray) -> numpy.ndarray: maxinfo = irt.max_info_hpc(items) return numpy.lexsort((irt.inf_hpc(maxinfo, items), maxinfo))
[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 = None, est_theta: float = None, **kwargs ) -> int: """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 proficiency :returns: index of the next item to be applied or `None` if there are no more items in the item bank. """ if (index is None or self.simulator is None ) and (items is None or administered_items is None or est_theta is None): raise ValueError( 'Either pass an index for the simulator or all of the other optional parameters to use this component independently.' ) if items is None and administered_items is None and est_theta is None: items = self.simulator.items administered_items = self.simulator.administered_items[index] est_theta = self.simulator.latest_estimations[index] # sort item indexes by their information value descending and remove indexes of administered items organized_items = [ x for x in (-irt.inf_hpc(est_theta, items)).argsort() if x not in administered_items ] bin_size = self._test_size - len(administered_items) if len(organized_items) == 0: warn('There are no more items to apply.') return None 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 = None, est_theta: float = None, **kwargs ) -> int: """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 proficiency :returns: index of the next item to be applied or `None` if there are no more items in the item bank. """ if (index is None or self.simulator is None ) and (items is None or administered_items is None or est_theta is None): raise ValueError( 'Either pass an index for the simulator or all of the other optional parameters to use this component independently.' ) if items is None and administered_items is None and est_theta is None: items = self.simulator.items administered_items = self.simulator.administered_items[index] est_theta = self.simulator.latest_estimations[index] # sort item indexes by their information value descending and remove indexes of administered items organized_items = [ x for x in (-irt.inf_hpc(est_theta, items)).argsort() if x not in 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 calculated 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 = None, est_theta: float = None, **kwargs ) -> int: """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 proficiency :returns: index of the next item to be applied or `None` if there are no more items in the item bank. """ if (index is None or self.simulator is None ) and (items is None or administered_items is None or est_theta is None): raise ValueError( 'Either pass an index for the simulator or all of the other optional parameters to use this component independently.' ) if items is None and administered_items is None and est_theta is None: items = self.simulator.items administered_items = self.simulator.administered_items[index] est_theta = self.simulator.latest_estimations[index] # sort item indexes by the integral of the information function descending and remove indexes of administered items organized_items = [ x for x in ( -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 ] ) ).argsort() if x not in administered_items ] if len(organized_items) == 0: warn('There are no more items to apply.') return None return list(organized_items)[0]