API

AbstractItemResponseModels.Continuous Type

Continous <: ResponseType

Defines that an ItemResponseModel has a continous response variable.

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AbstractItemResponseModels.Dichotomous Type

Dichotomous <: ResponseType

Defines that an ItemResponseModel has a binary response variable.

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AbstractItemResponseModels.DistributionEstimate Type

DistributionEstimate <: EstimationType

Defines that the parameters of an ItemResponseModel are estimated by a distribution. Thus, parameters for a model with estimation_type(model) == DistributionEstimate are probability distributions that implement common interface functions for distributions, e.g. rand, mean, or quantile.

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AbstractItemResponseModels.EstimationType Type

EstimationType

The EstimationType of an ItemResponseModel describes the type of parameter estimation for the model.

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AbstractItemResponseModels.ItemResponseModel Type

ItemResponseModel

An abstract type representing an item response theory model.

Each implementation T <: ItemResponseModel must define the following traits:

• response_type: A valid ResponseType

• person_dimensionality: The number of dimensions for the person parameters

• item_dimensionality: The number of dimensions for the item parameters

• estimation_type: A valid EstimationType

Additionally T <: ItemResponseModel must implement the following interface:

• irf: An item response function returning the probability that a person with given ability estimate will answer an item with a particular response.

• iif: An item information function returning the information of answering with a particular response on an item given an ability estimate.

• expected_score: An expected score function returning the expected score for one or multiple items, given an ability estimate.

• information: An information function returning the information of one or multiple items, given an ability estimate.

• fit: A function fitting an item response model of type T to observed data.

• get_item_locations: A function returning the item locations for a given item.

• get_person_locations: A function returning the person locations for a given person.

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AbstractItemResponseModels.Nominal Type

Nominal <: ResponseType

Defines that an ItemResponseModel has an unordered categorical response variable.

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AbstractItemResponseModels.Ordinal Type

Ordinal <: ResponseType

Defines that an ItemResponseModel has an ordered categorical response variable.

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AbstractItemResponseModels.PointEstimate Type

PointEstimate <: EstimationType

Defines that the parameters of an ItemResponseModel are estimated by a single point estimate. Thus, parameters for a model with estimation_type(model) == PointEstimate are single real-valued numbers.

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AbstractItemResponseModels.ResponseType Type

ResponseType

The ResponseType defines the scale level of item responses for a given ItemResponseModel.

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AbstractItemResponseModels.SamplingEstimate Type

SamplingEstimate <: EstimationType

Defines that the parameters of an ItemResponseModel are estimated by a sampling procedure. Thus, parameters for a model with estimation_type(model) == SamplingEstimate are vectors of real-valued numbers where the length of the parameter vector is equal to the number of samples drawn.

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AbstractItemResponseModels.check_response_type Method

check_response_type(::T, itr) where {T<:ResponseType}

Check if the responses in itr are valid for ResponseType T.

If all responses are valid, nothing is returned.

If any invalid responses are found, a DomainError is thrown.

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AbstractItemResponseModels.dimensionality Method

dimensionality

Return a tuple of the dimensions for an ItemResponseModel where the first element corresponds to the person dimensionality and the second element to the item dimensionality.

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AbstractItemResponseModels.each_item_index Method

each_item_index(model::ItemResponseModel)

Create an iterable object visiting each item index of an item response model.

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AbstractItemResponseModels.each_person_index Method

each_person_index(model::ItemResponseModel)

Create an iterable object visiting each person index of an item response model.

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AbstractItemResponseModels.estimation_type Method

estimation_type(model::ItemResponseModel)

Return the EstimationType of an [ItemResponseModel].

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AbstractItemResponseModels.expected_score Function

expected_score(model::ItemResponseModel, theta; scoring_function)
expected_score(model::ItemResponseModel, theta, is; scoring_function)

Calculate the expected score of an ItemResponseModel.

Arguments

• model: An ItemResponseModel

• theta: The person parameter value(s)

• is: One or multiple item identifiers. If is is omitted, the expected score for the whole test is returned.

Keyword arguments

• scoring_function: A binary function of the form f(y, ctx) = x, mapping all possible response values y to

a value x. The argument ctx contains the current item context.

Return values

If estimation_type(model) == PointEstimate then expected_score must return a single scalar value.

If estimation_type(model) == SamplingEstimate then expected_score must return a vector of values with the length equal to the number of samples drawn.

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AbstractItemResponseModels.get_item_locations Method

get_item_locations(model::ItemResponseModel, i)

Get the item locations for an item from an ItemResponseModel.

Arguments

• model: An ItemResponseModel

• i: A unique item identifier

Return values

If item_dimensionality(model) == Univariate and estimation_type(model) == PointEstimate then get_item_locations must return a single scalar value.

If item_dimensionality(model) == Multivariate and estimation_type(model) == PointEstimate then get_item_locations must return a vector of values corresponding to the dimensionality of the item parameters.

If item_dimensionality(model) == Univariate and estimation_type(model) == SamplingEstimate then get_item_locations must return a vector of values with the length equal to the number of samples drawn.

If item_dimensionality(model) == Multivariate and estimation_type(model) == SamplingEstimate then get_item_locations must return a matrix with rows corresponding to the drawn samples and columns corresponding to the dimension of the item parameter.

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AbstractItemResponseModels.get_person_locations Method

get_person_locations(model::ItemResponseModel, p)

Get the person locations for an person from an ItemResponseModel.

Arguments

• model: An ItemResponseModel

• p: A unique person identifier

Return values

If person_dimensionality(model) == Univariate and estimation_type(model) == PointEstimate then get_person_locations must return a single scalar value.

If person_dimensionality(model) == Multivariate and estimation_type(model) == PointEstimate then get_person_locations must return a vector of values corresponding to the dimensionality of the person parameters.

If person_dimensionality(model) == Univariate and estimation_type(model) == SamplingEstimate then get_person_locations must return a vector of values with the length equal to the number of samples drawn.

If person_dimensionality(model) == Multivariate and estimation_type(model) == SamplingEstimate then get_person_locations must return a matrix with rows corresponding to the drawn samples and columns corresponding to the dimension of the person parameter.

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AbstractItemResponseModels.iif Function

iif(model::ItemResponseModel, theta, i)
iif(model::ItemResponseModel, theta, i, y)

Arguments

• model: An ItemResponseModel

• theta: The person parameter value(s)

• i: A unique item identifier

• y: Response value(s)

Return values

If estimation_type(model) == PointEstimate then the item information function must return a scalar value.

If estimation_type(model) == SamplingEstimate then the item information function must return a vector of values with the length equal to the number of samples drawn.

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AbstractItemResponseModels.information Function

information(model::ItemResponseModel, theta; scoring_function)
information(model::ItemResponseModel, theta, is; scoring_function)

Calculate the information of an ItemResponseModel.

Arguments

• theta: The person parameter value(s)

• is: One or multiple item identifiers. If is is omitted, the information of the whole test (test information) is returned.

Keyword arguments

• scoring_function: A binary function of the form f(y, ctx) = x, mapping all possible response values y to

a value x. The argument ctx contains the current item context.

Return values

If estimatione_type(model) == PointEstimate then information must return a single scalar value.

If estimation_type(model) == SamplingEstimate then information must return a vector of values with the length equal to the number of samples drawn.

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AbstractItemResponseModels.irf Function

irf(model::ItemResponseModel, theta, i)
irf(model::ItemResponseModel, theta, i, y)

Evaluate the item response function of an ItemResponseModel.

Arguments

• model: An ItemResponseModel

• theta: The person parameter value(s)

• i: A unique item identifier

• y: Response value(s)

Return values

If estimation_type(model) == PointEstimate then the item response function must return a scalar value.

If estimation_type(model) == SamplingEstimate then the item response function must return a vector of values with the length equal to the number of samples.

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AbstractItemResponseModels.item_dimensionality Method

item_dimensionality(model::ItemResponseModel)

Return the number of dimensions for the item parameters of an ItemResponseModel as an integer.

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AbstractItemResponseModels.person_dimensionality Method

person_dimensionality(model::ItemResponseModel)

Return the number of dimensions for the person parameters of an ItemResponseModel as an integer.

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AbstractItemResponseModels.response_type Method

response_type(model::ItemResponseModel)
response_type(::Type{<:ItemResponseModel})

Return the ResponseType of an ItemResponseModel.

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StatsAPI.fit Function

fit(::Type{T}, data::AbstractMatrix, args...; kwargs...)

Fit an item response model to response data.

Arguments

• data: The observed response data. If data is a response matrix, the columns must describe items and rows describe persons.

• args...: Additional arguments required to fit the ItemResponseModel

Keyword arguments

• kwargs...: Additional keyword arguments required to fit the ItemResponseModel

Return values

A fitted model with T <: ItemResponseModel.

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AbstractItemResponseModels.Tests.FakeIRM Type

FakeIRM{RT<:ResponseType,PD<:Dimensionality,ID<:Dimensionality}

A minimal implementation of ItemResponseModel for interface testing.

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AbstractItemResponseModels.Tests.test_interface Method

test_interface(T::Type{<:ItemResponseModel}, data, args...; kwargs...)

Test the implementation of an item response model interface.

Arguments

• T: The implemented model type

• data: observed data

• args...: Additional arguments passed to fit

Keyword arguments

• kwargs...: Additional keyword arguments passed to fit

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