`FittedItemBanks.FittedItemBanks`

— ModuleThis 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.BSplineItemBank`

— Type`struct BSplineItemBank <: AbstractItemBank`

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

**References:**

`FittedItemBanks.BooleanResponse`

— Type`struct BooleanResponse <: ResponseType`

A boolean/dichotomous response.

`FittedItemBanks.CdfMirtItemBank`

— TypeThis 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.ContinuousDomain`

— Type`abstract type ContinuousDomain <: DomainType`

A continuous domain.

`FittedItemBanks.DichotomousPointsItemBank`

— Type`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.DiscreteDomain`

— Type`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.DiscreteIndexableDomain`

— Type`struct DiscreteIndexableDomain <: DiscreteDomain`

An discrete domain which is efficiently indexable and iterable.

`FittedItemBanks.DiscreteIterableDomain`

— Type`struct DiscreteIterableDomain <: DiscreteDomain`

An discrete domain which is only efficiently iterable.

`FittedItemBanks.DomainType`

— Type`abstract type DomainType`

Domain type for a item banks' item response function.

`FittedItemBanks.ItemResponse`

— Type`struct ItemResponse{ItemBankT<:AbstractItemBank}`

`item_bank::AbstractItemBank`

`index::Int64`

An item response.

`FittedItemBanks.KernelSmoother`

— Type`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.MonopolyItemBank`

— Type`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.MultinomialResponse`

— Type`struct MultinomialResponse <: ResponseType`

A multinomial response, including ordinal responses.

`FittedItemBanks.NearestNeighborSmoother`

— Type`struct NearestNeighborSmoother <: Smoother`

Nearest neighbor/staircase smoother.

`FittedItemBanks.NominalItemBank`

— Type`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.OneDimContinuousDomain`

— Type`struct OneDimContinuousDomain <: ContinuousDomain`

A continuous domain that is scalar valued.

`FittedItemBanks.PointsItemBank`

— Type`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.ResponseType`

— Type`abstract type ResponseType`

A response type for an item bank.

`FittedItemBanks.Smoother`

— Type`abstract type Smoother`

`FittedItemBanks.VectorContinuousDomain`

— Type`struct VectorContinuousDomain <: ContinuousDomain`

A continuous domain that is vector valued.

`FittedItemBanks.ItemBank2PL`

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

`FittedItemBanks.ItemBank3PL`

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

`FittedItemBanks.ItemBank4PL`

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

`FittedItemBanks.ItemBankMirt2PL`

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

`FittedItemBanks.ItemBankMirt3PL`

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

`FittedItemBanks.ItemBankMirt4PL`

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

`FittedItemBanks._search`

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

`FittedItemBanks.gauss_kern`

— Method```
gauss_kern(u)
```

A guassian kernel for use with `KernelSmoother`

`FittedItemBanks.item_bank_domain`

— MethodGiven 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.

`FittedItemBanks.quad_kern`

— Method```
quad_kern(u)
```

A quadratic kernel for use with `KernelSmoother`

`FittedItemBanks.uni_kern`

— Method```
uni_kern(u)
```

A uniform kernel for use with `KernelSmoother`