Utilities

fs_to_items(xₜ, n_items, fs_items)

Description

Ungroup items grouped by friend sets.

Arguments

• xₜ::Vector{Float64} : Required. grouped items 0-1 vector.
• n_items::Int64 : Required. Number if items.
• fs_items::Vector{Vector{Int64}} : Required. vector of items included in the friend sets.

Output

• x_Iₜ::Vector{Float64} Returns a 0-1 vector at item level.

item_char(pars::DataFrames.DataFrame, theta::Float64; model = "2PL", parametrization = "at-b", D = 1, derivatives = false)

Description

Compute the item characteristic function (probability of correct answer).

Arguments

• pars::DataFrames.DataFrame : Required. DataFrame with item parameters (difficulty: b or d, discrimination: a or a1, guessing: c or g).
• theta::Float64 : Required. Ability point.
• model : Optional. Default: "2PL". Values: "1PL", "2PL", "3PL". IRT model.
• parametrization : Optional. Default: "at-b". Values: "at-b", "at-ab", "at+b", "at+ab". IRT model parametrization. Ex: at-b is $Da(\theta-b)$.
• D : Optional. Default: 1.
• derivatives : Optional. Default: false. If it's true compute the derivatives. Ow a zeros(0,0) matrix is returned.

Output

• p::Matrix{Float64}: Matrix of probabilites.
• pder::Matrix{Float64}: Matrix of derivatives.

item_char(pars::DataFrames.DataFrame, theta::Vector{Float64}; model = "2PL", parametrization = "at-b", D = 1, derivatives = false)

Description

Compute the item characteristic function (probability of correct answer).

Arguments

• pars::DataFrames.DataFrame : Required. DataFrame with item parameters (difficulty: b or d, discrimination: a or a1, guessing: c or g).
• theta::Vector{Float64} : Required. Vector of ability points.
• model : Optional. Default: "2PL". Values: "1PL", "2PL", "3PL". IRT model.
• parametrization : Optional. Default: "at-b". Values: "at-b", "at-ab", "at+b", "at+ab". IRT model parametrization. Ex: at-b is $Da(\theta-b)$.
• D : Optional. Default: 1.
• derivatives : Optional. Default: false. If it's true compute the derivatives. Ow a zeros(0,0) matrix is returned.

Output

• p::Matrix{Float64}: Matrix of probabilites.
• pder::Matrix{Float64}: Matrix of derivatives.

item_info(
    pars::DataFrames.DataFrame,
    theta::Float64;
    model = "2PL", #1PL, 2PL, 3PL, grm
    parametrization = "at-b", #"at-b, at-ab, at+b, at+ab"
    D = 1,
)

Description

Compute the item Fisher information function.

Arguments

• pars::DataFrames.DataFrame : Required. DataFrame with item parameters (difficulty: b or d, discrimination: a or a1, guessing: c or g).
• theta::Float64 : Required. Vector of ability points.
• model : Optional. Default: "2PL". Values: "1PL", "2PL", "3PL". IRT model.
• parametrization : Optional. Default: "at-b". Values: "at-b", "at-ab", "at+b", "at+ab". IRT model parametrization. Ex: at-b is $Da(\theta-b)$.
• D : Optional. Default: 1.

Output

• i::Matrix{Float64}: Matrix of the item information.

item_info(
    pars::DataFrames.DataFrame,
    theta::Vector{Float64};
    model = "2PL", #1PL, 2PL, 3PL, grm
    parametrization = "at-b", #"at-b, at-ab, at+b, at+ab"
    D = 1,
)

Description

Compute the item Fisher information function.

Arguments

• pars::DataFrames.DataFrame : Required. DataFrame with item parameters (difficulty: b or d, discrimination: a or a1, guessing: c or g).
• theta::Vector{Float64} : Required. Vector of ability points.
• model : Optional. Default: "2PL". Values: "1PL", "2PL", "3PL". IRT model.
• parametrization : Optional. Default: "at-b". Values: "at-b", "at-ab", "at+b", "at+ab". IRT model parametrization. Ex: at-b is $Da(\theta-b)$.
• D : Optional. Default: 1.

Output

• i::Matrix{Float64}: Matrix of the item information.