Psychometrics.jl

This package is a playground I built for working on my research projects. It provides objects (Julia structs) and dedicated methods (functions) to deal with psychometric data under the item response theory (IRT) statistical paradigm.

The documentation is still in progress. Nevertheless, some functions have detailed descriptions that can be found in the documentation pages or using the Julia help ?.

Structs

• Item: an immutable containing information about an item (a question in a test), e.g. id::String the item identifier, and the field parameters::AbstractParameter which accepts a mutable item parameter object (see below).
• Examinee: an immutable containing the information about the examinee (the test taker). The field latent::AbstractLatent accepts a mutable latent variable (see below).
• AbstractParameters: an abstract type which, at the moment, has only the abstract AbstractParametersBinary as subtype. Thus, it works only with binary (dichotomous) responses. The available mutables for the latter are Parameters1PL, Parameters2PL, Parameters3PL. They contain the details about the item parameters under the 1-parameter logistic (1PL), 2-parameters logistic (2PL) and 3-parameter logistic (3PL) IRT models, respectively. For example, the object Parameters2PL has the fields difficulty b::Float64 and discrimination a::Float64. It is possible to define the Bayesian priors and posterior by assigning multivariate distributions from the package Distributions to the fields prior::Distributions.MultivariateDistribution and posterior::Distributions.MultivariateDistribution.
• Latent1D and LatentND: mutables describing an univariate or multivariate latent variable, respectively. For the univariate case, the field val::Float64 holds the estimate of the ability of the examinee, like the item parameters, also the latent variables can have a prior or a posterior, assigning them to the fields prior and posterior, respectively.
• Response: an immutable which holds the information about a binary (correct or incorrect) response, such as the identifier of the examinee who gave the response examinee_id::String, the identifier of the answered item item_idx::String, and the answer starting and ending times start_time::Dates.DateTime and end_time::Dates.DateTime.

Each of the mentioned structs has a random default factory, callable by using the name of the struct followed by ().

Example: Parameters2PL() generates a set of 2PL item parameters from the product distribution (independent bivariate)

Distributions.Product([
   Distributions.LogNormal(0, 0.25),
   Distributions.Normal(0, 1)
])

The immutable structs Item and Examinee need the identification fields id and idx to be randomly generated.

Example: Item(1, "item_1") generates an operational item with an empty content description, and a default 1PL item parameter.

Basic functions

• Item characteristic function (ICF): probability.
• Latent and item information function (IIF) (expected and observed are different for the 3PL model): item_expected_information, item_observed_information, latent_information.
• Likelihood function: likelihood, log_likelihood.