Information (Item Information Function) (Internals)

_latent_information(latent::Latent1D, parameters::Parameters1PL)

Description

It computes the information (second derivative of the likelihood) with respect to the 1-dimensional latent variable under the 1PL model. It follows the parametrization $a(θ - b)$.

Arguments

• latent::Latent1D : Required. A 1-dimensional Latent1D latent variable.
• parameters::Parameters1PL : Required. A 1-parameter logistic parameters object.

Output

A Float64 scalar.

_latent_information(latent::Latent1D, parameters::Parameters2PL)

Description

It computes the information (-second derivative of the likelihood) with respect to the 1-dimensional latent variable under the 2PL model. It follows the parametrization $a(θ - b)$.

Arguments

• latent::Latent1D : Required. A 1-dimensional Latent1D latent variable.
• parameters::Parameters2PL : Required. A 2-parameter logistic parameters object.

Output

A Float64 scalar.

_latent_information(latent::Latent1D, parameters::Parameters3PL)

Description

It computes the information (-second derivative of the likelihood) with respect to the 1-dimensional latent variable under the 3PL model. It follows the parametrization $a(θ - b)$.

Arguments

• latent::Latent1D : Required. A 1-dimensional Latent1D latent variable.
• parameters::Parameters3PL : Required. A 3-parameter logistic parameters object.

Output

A Float64 scalar.

_item_expected_information(parameters::Parameters1PL, latent::Latent1D)

Description

It computes the expected information (-second derivative of the likelihood) with respect to the difficulty parameter of the 1PL model. It follows the parametrization $a(θ - b)$.

Arguments

• parameters::Parameters1PL : Required. A 1-parameter logistic parameters object.
• latent::Latent1D : Required. A 1-dimensional Latent1D latent variable.

Output

A Float64 scalar.

_item_expected_information(parameters::Parameters2PL, latent::Latent1D)

Description

It computes the expected information (-second derivative of the likelihood) with respect to the 2 parameters of the 2PL model. It follows the parametrization $a(θ - b)$.

Arguments

• parameters::Parameters1PL : Required. A 2-parameter logistic parameters object.
• latent::Latent1D : Required. A 1-dimensional Latent1D latent variable.

Output

A $2 imes 2$ matrix of the expected informations.

_item_expected_information(parameters::Parameters3PL, latent::Latent1D)

Description

It computes the expected information (-second derivative of the likelihood) with respect to the 3 parameters of the 3PL model. It follows the parametrization $a(θ - b)$. It should be always positive.

Arguments

• parameters::Parameters1PL : Required. A 3-parameter logistic parameters object.
• latent::Latent1D : Required. A 1-dimensional Latent1D latent variable.

Output

A $3 imes 3$ matrix of the expected informations.

_item_observed_information(
    parameters::Parameters3PL,
    latent::Latent1D,
    response_val::Float64,
)

Description

It computes the observed information (-second derivative of the likelihood) with respect to the 3 parameters of the 3PL model. It follows the parametrization $a(θ - b)$.

Arguments

• parameters::Parameters3PL : Required. A 3-parameter logistic parameters object.
• latent::Latent1D : Required. A 1-dimensional Latent1D latent variable.
• response_val::Float64 : Required. A scalar response.

Output

A $3 imes 3$ matrix of the observed informations.