Probability (Item Characteristic Function)

probability(parameters_matrix::Matrix{Float64}, latent_matrix::Matrix{Float64})

Description

It computes the probability (ICF) of a correct response for item parameters and latents values provided in matrix form. Not suitable for 3PL models, for such a kind of model use probability_3PL(). It follows the parametrization $a heta - b$.

Arguments

• parameters_matrix::Matrix{Float64} : Required. A $I x ( ext{n_latents}+ 1)$ matrix with item parameters. intercept (b) must be in first column, latents coefficients ($a_j$) in next columns $(2, ..., ext{n_latents} + 1)$.
• latent_matrix::Matrix{Float64} : Required. A $ext{n_latents} imes N$ or $( ext{n_latents} + 1) x N$ matrix with latents values.

Outputs

A $I x N$ Float64 matrix.

probability_3PL(parameters_matrix::Matrix{Float64}, latent_matrix::Matrix{Float64})

Description

Only for models which has guessing parameter (c) in last row of parameters_matrix. It computes the probability (ICF) of a correct response for item parameters and latents values provided in matrix form. It follows the parametrization $a heta - b$.

Arguments

• parameters_matrix::Matrix{Float64} : Required. A $I x ( ext{n_latents}+ 1)$ matrix with item parameters. intercept (b) must be in first column, latents coefficients ($a_j$) in next columns $(2, ..., ext{n_latents} + 1)$.
• latent_matrix::Matrix{Float64} : Required. A $ext{n_latents} imes N$ matrix with latents values.

Output

A $I x N$ Float64 matrix.

probability(examinee::AbstractExaminee, item::AbstractItem)

Description

It computes the probability (ICF) that an examinee answers correctly at item.

Arguments

• examinee::AbstractExaminee : Required. An Examinee.
• item::AbstractItem : Required. An Item.

Output

A Float64 scalar.

probability(items::Vector{<:AbstractItem}, examinees::Vector{<:AbstractExaminee})

Description

It computes the probability (ICF) that a vector of examinees answers correctly at a vector of items.

Arguments

• examinees::Vector{<:AbstractExaminee} : Required. A vector of Examinees.
• items::Vector{<:AbstractItem} : Required. A vector of Items.

Output

A I x N Float64 matrix.

probability(examinees::Vector{<:AbstractExaminee}, items::Vector{<:AbstractItem})

Description

It computes the probability (ICF) that a vector of examinees answers correctly at a vector of items.

Arguments

• examinees::Vector{<:AbstractExaminee} : Required. A vector of Examinees.
• items::Vector{<:AbstractItem} : Required. A vector of Items.

Output

A I x N Float64 matrix.