API

Types

PersonParameters.EAP Type

struct EAP{T<:Distributions.Distribution{Distributions.Univariate, Distributions.Continuous}, U<:Real} <: PersonParameterAlgorithm

Expected posterior estimation of person parameters of item response models. Use prior to specify the prior distribution of ability values.

domain can be used to restrict the domain for numerical integration. Defaults to extrema(prior), c.f. the whole support of the prior distribution.

Fields

• prior: the prior distribution of person abilities

• domain: the integration domain

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PersonParameters.MAP Type

struct MAP{T<:Distributions.Distribution{Distributions.Univariate, Distributions.Continuous}, U<:Roots.AbstractSecantMethod} <: PersonParameterAlgorithm

Maximum posterior estimation of person parameters of item response models. Use prior to specify the prior distribution of ability values.

Fields

• prior: The prior distribution of person abilities

• root_finding_alg

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PersonParameters.MLE Type

struct MLE{T<:Roots.AbstractSecantMethod} <: PersonParameterAlgorithm

Maximum likelihood estimation for person parameters of item response models.

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PersonParameters.PersonParameter Type

struct PersonParameter{U<:Real}

A container holding a single estimated person parameter.

Fields

• value: the estimated ability value

• se: the estimated standard error

Methods

• value: Extract the person parameter estimate

• se: Extract the standard error of estimation

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PersonParameters.PersonParameterAlgorithm Type

abstract type PersonParameterAlgorithm

An abstract type representing an estimation algorithm for person parameters of an item response model.

Each algorithm must implement the following functions:

• optfun: The optimization function passed to the root finding algorithm

• se: Calculation of the standard error of estimation. Defaults to $1/\sqrt{I(\theta )}$, where $I$ is the test information at $\theta$.

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PersonParameters.PersonParameterResult Type

struct PersonParameterResult{T<:AbstractItemResponseModels.ItemResponseModel, U<:PersonParameter, V<:PersonParameterAlgorithm} <: AbstractArray{U<:PersonParameter, 1}

A collection of estimated person parameters.

Fields

• values: A vector of estimated person parameters

• algorithm: The algorithm used for estimation

Methods

• modeltype: Get the model type of the scaling model

• algorithm: Get the algorithm used for estimation

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PersonParameters.ResponsePatterns Type

struct ResponsePatterns{T<:(AbstractVector)}

A struct holding unique response patterns of a data matrix.

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PersonParameters.WLE Type

struct WLE{T<:Roots.AbstractSecantMethod} <: PersonParameterAlgorithm

Warm's weighted likelihood estimation for person parameters of item response models.

References

• Warm, T. A. (1989). Weighted likelihood estimation of ability in item response theory. Psychometrika, 54, 427-450. doi: 10.1007/BF02294627

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Functions

PersonParameters.algorithm Method

algorithm(pp)

Get the algorithm used to calculate the person parameters in pp.

Examples

julia> pp = person_parameters(OnePL, fill(zeros(3), 5), zeros(3), MLE());

julia> algorithm(pp)
MLE{Roots.Secant}(Roots.Secant())

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PersonParameters.ids Method

ids(p)

Get the id mapping for the response patterns in p

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PersonParameters.modeltype Method

modeltype(pp)

Get the scaling model used to calculate the person parameters in pp.

Examples

julia> pp = person_parameters(TwoPL, fill(zeros(3), 10), fill((a = 1.0, b = 0.0), 3), WLE());

julia> modeltype(pp)
TwoParameterLogisticModel

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PersonParameters.patterns Method

patterns(p)

Get the unique response patterns from p.

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PersonParameters.person_parameter Method

person_parameter(M, responses, betas, alg; init, kwargs...)

Estimate a single person parameter for an item response theory model M from a response vector (responses) given item parameters beta and an estimation algorithm alg.

Examples

1 Parameter Logistic Model

julia> responses = [0, 1, 1, 0, 0];

julia> betas = [0.2, -1.3, 0.4, 1.2, 0.0];

julia> person_parameter(OnePL, responses, betas, MLE())
PersonParameter{Float64}(-0.34640709530672537, 0.9812365857368596)

3 Parameter Logistic Model

julia> responses = [0, 1, 1];

julia> betas = [(a = 1.0, b = 0.3, c = 0.1), (a = 0.3, b = -0.5, c = 0.0), (a = 1.4, b = 1.1, c = 0.3)];

julia> person_parameter(ThreePL, responses, betas, WLE())
PersonParameter{Float64}(0.657715606325967, 1.5321777539977457)

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PersonParameters.person_parameters Method

person_parameters(M, responses, betas, alg)

Estimate person parameters for an item response theory model of type M given item parameters betas, an estimation algorithm alg and responses for each person.

responses can be a vector of responses where each entry corresponds to the responses for a person, or a response matrix with size(responses) == (n, length(betas)), i.e. each row of the response matrix corresponds to the responses of a single person.

Examples

1 Parameter Logistic Model

julia> responses = [1 1 0; 0 1 0; 1 1 0; 0 0 1]
4×3 Matrix{Int64}:
 1  1  0
 0  1  0
 1  1  0
 0  0  1

julia> betas = [-0.1, 0.0, 1.0];

julia> person_parameters(OnePL, responses, betas, MLE());

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PersonParameters.se Method

se(alg, M, theta, betas)

Calculate the standard error for a person parameter estimate theta given an estimation algorithm (alg), a model type (M), and item parameters (betas).

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PersonParameters.se Method

se(pp)

Extract the standard error from a PersonParameter estimate pp.

Examples

julia> pp = PersonParameter(0.5, 0.3);

julia> se(pp)
0.3

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PersonParameters.value Method

value(pp)

Extract the value from a PersonParameter estimate pp.

Examples

julia> pp = PersonParameter(0.0, 1.0);

julia> value(pp)
0.0

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