This module provides abstract and concrete item banks, which store information about items and their parameters such as difficulty, most typically resulting from fitting an Item-Response Theory (IRT) model.

struct BSplineItemBank <: AbstractItemBank

This item bank implements the a bank with B-spline based item-responses with dichotomous responses.

References:

• Maximum Marginal Likelihood Estimation of a Monotonic Polynomial Generalized Partial Credit Model Winsberg, S., Thissen, D. and Wainer, H. (1984) ETS Research Report Series.

struct BooleanResponse <: ResponseType

A boolean/dichotomous response.

This item bank corresponds to the most commonly found version of MIRT in the literature. Its items feature multidimensional discriminations and its learners multidimensional abilities, but item difficulties are single-dimensional.

abstract type ContinuousDomain <: DomainType

A continuous domain.

struct DichotomousPointsItemBank{DomainT} <: PointsItemBank

• xs::Any

• ys::Matrix{Float64}

An item bank where all items have IRFs computed at a fixed grid across the latent/ability dimension specified as xs. The responses are stored in ys. In most cases this item banks will be coupled with a Smoother and wrapped in a DichotomousSmoothedItemBank.

abstract type DiscreteDomain <: DomainType

A discrete domain. Typically this is a sampled version of a continuous domain item bank.

Item response functions with discrete domains tend to support less operations than those with continuous domains.

struct DiscreteIndexableDomain <: DiscreteDomain

An discrete domain which is efficiently indexable and iterable.

struct DiscreteIterableDomain <: DiscreteDomain

An discrete domain which is only efficiently iterable.

abstract type DomainType

Domain type for a item banks' item response function.

struct ItemResponse{ItemBankT<:AbstractItemBank}

• item_bank::AbstractItemBank

• index::Int64

An item response.

struct KernelSmoother <: Smoother

• kernel::Function

• bandwidths::Vector{Float64}

A smoother that uses a kernel to smooth the IRF. The bandwidths field stores the kernel bandwidth for each item.

struct MonopolyItemBank <: AbstractItemBank

This item bank implements the monotonic polynomial model with dichotomous responses.

\[\mathrm{irf}(\theta|\xi,{\bf b})=\xi+b_{1}\theta+b_{2}\theta^{2}+\dots+b_{2k+1}\theta^{2k+1}\]

\[\mathrm{irf}^{\prime}(\theta|\mathbf{a})=a_{0}+a_{1}\theta+a_{2}\theta^{2}+\cdot\cdot\cdot+a_{2k}\theta^{2k}\]

References:

• Maximum Marginal Likelihood Estimation of a Monotonic Polynomial Generalized Partial Credit Model with Applications to Multiple Group Analysis, Falk, C.F., Cai, L. (2016). Psychometrika.

struct MultiGridDichotomousPointsItemBank <: PointsItemBank

• xs::ArraysOfArrays.VectorOfVectors{Float64, VT} where VT<:AbstractVector{Float64}

• ys::ArraysOfArrays.VectorOfVectors{Float64, VT} where VT<:AbstractVector{Float64}

An item bank where all items each IRF has been computed on a potentially distrinct grid across the latent/ability dimension specified as xs. The responses are stored in ys. In most cases this item banks will be coupled with a Smoother and wrapped in a DichotomousSmoothedItemBank.

struct MultinomialResponse <: ResponseType

A multinomial response, including ordinal responses.

struct NearestNeighborSmoother <: Smoother

Nearest neighbor/staircase smoother.

struct NominalItemBank{RankStorageT<:(AbstractVector{<:AbstractArray{<:Real}}), CategoryStorageT<:(AbstractVector{<:AbstractArray{Float64}})} <: AbstractItemBank

This item bank implements the nominal model. The Graded Partial Credit Model (GPCM) is implemented in terms of this one.

Currently, this item bank only supports the normal scaled logistic as the characteristic/transfer function.

References:

• A Generalized Partial Credit Model: Application of an EM Algorithm, Muraki, E., (1992). Applied Psychological Measurement.
• A Generalized Partial Credit Model, Muraki, E. (1997). In Handbook of Modern Item Response Theory.

struct OneDimContinuousDomain <: ContinuousDomain

A continuous domain that is scalar valued.

abstract type ResponseType

A response type for an item bank.

abstract type Smoother

struct VectorContinuousDomain <: ContinuousDomain

A continuous domain that is vector valued.

Convenience function to construct an item bank of the standard 2-parameter logistic single-dimensional IRT model.

Convenience function to construct an item bank of the standard 3-parameter logistic single-dimensional IRT model.

Convenience function to construct an item bank of the standard 4-parameter logistic single-dimensional IRT model.

Convenience function to construct an item bank of the standard 2-parameter logistic MIRT model.

Convenience function to construct an item bank of the standard 3-parameter logistic MIRT model.

Convenience function to construct an item bank of the standard 4-parameter logistic MIRT model.

Binary search for the point x where f(x) = target += precis given f is assumed as monotonically increasing.

gauss_kern(u)

A guassian kernel for use with KernelSmoother

gridify(item_bank, xs)

Converts a dichotomous item bank item_bank into a gridded item bank by evaluating the items at points xs.

Given an item bank, this function returns the domain of the item bank, i.e. the range (lo, hi) which includes for each item the range in which the the item response function is changing.

quad_kern(u)

A quadratic kernel for use with KernelSmoother

uni_kern(u)

A uniform kernel for use with KernelSmoother