Parametric item banks

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.

struct SlopeInterceptTransferItemBank <: AbstractItemBank
SlopeInterceptTransferItemBank(distribution, difficulties, discriminations) -> SlopeInterceptTransferItemBank
DomainType(::SlopeInterceptTransferItemBank) = OneDimContinuousDomain()
ResponseType(::SlopeInterceptTransferItemBank) = BooleanResponse()

This item bank corresponds the slope-intercept form of teh 2 parameter, single dimensional IRT model.

struct TransferItemBank <: AbstractItemBank
TransferItemBank(distribution, difficulties, discriminations) -> TransferItemBank
DomainType(::TransferItemBank) = OneDimContinuousDomain()
ResponseType(::TransferItemBank) = BooleanResponse()

This item bank corresponds to a 2 parameter, single dimensional IRT model.

struct CdfMirtItemBank <: AbstractItemBank
CdfMirtItemBank(distribution, difficulties, discriminations) -> CdfMirtItemBank
DomainType(::CdfMirtItemBank) = VectorContinuousDomain()
ResponseType(::CdfMirtItemBank) = BooleanResponse()

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.

struct SlopeInterceptMirtItemBank <: AbstractItemBank
SlopeInterceptMirtItemBank(distribution, difficulties, discriminations) -> SlopeInterceptMirtItemBank
DomainType(::SlopeInterceptMirtItemBank) = VectorContinuousDomain()
ResponseType(::SlopeInterceptMirtItemBank) = BooleanResponse()

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

struct NominalItemBank <: AbstractItemBank
NominalItemBank(ranks, discriminations, cut_points) -> NominalItemBank
DomainType(::NominalItemBank) = VectorContinuousDomain()
ResponseType(::NominalItemBank) = MultinomialResponse()

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

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

See also: GPCMItemBank (psuedo-constructor)

References:

• Estimating item parameters and latent ability when responses are scored in two or more nominal categories, Bock, D. R., (1972). Psychometrika.

GPCMItemBank(discriminations, cut_points) -> NominalItemBank

This psuedo-constructor creates a NominalItemBank implementing the Graded Partial Credit Model (GPCM).

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 MonopolyItemBank <: AbstractItemBank

DomainType(::MonopolyItemBank) = OneDimContinuousDomain()
ResponseType(::MonopolyItemBank) = BooleanResponse()

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 BSplineItemBank <: AbstractItemBank

DomainType(::BSplineItemBank) = OneDimContinuousDomain()
ResponseType(::BSplineItemBank) = BooleanResponse()

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.