FittedItemBanks.FittedItemBanksModule

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.

FittedItemBanks.CdfMirtItemBankType

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.

FittedItemBanks.DichotomousPointsItemBankType
struct DichotomousPointsItemBank <: AbstractItemBank
  • xs::Vector{Float64}

  • 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.

FittedItemBanks.DiscreteDomainType
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.

FittedItemBanks.ItemResponseType
struct ItemResponse{ItemBankT<:AbstractItemBank}
  • item_bank::AbstractItemBank

  • index::Int64

An item response.

FittedItemBanks.KernelSmootherType
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.

FittedItemBanks.MonopolyItemBankType
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:

FittedItemBanks.NominalItemBankType
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:

FittedItemBanks.PointsItemBankType
struct PointsItemBank <: AbstractItemBank
  • xs::Vector{Float64}

  • ys::ArraysOfArrays.VectorOfArrays{Float64, 2, M, VT} where {M, VT<:AbstractVector{Float64}}

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

FittedItemBanks.ItemBank2PLMethod

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

FittedItemBanks.ItemBank3PLMethod

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

FittedItemBanks.ItemBank4PLMethod

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

FittedItemBanks._searchMethod

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

FittedItemBanks.item_bank_domainMethod

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.