logLik-class: Extract Log-Likelihood from Fitted Models

In ForceChoice: Forced-Choice Modeling Based on Item Response Theory and Cognitive Diagnostic Models

Extract Log-Likelihood from Fitted Models

Description

Extracts the marginal log-likelihood from a fitted ForceChoice model object. For continuous-trait IRT models, the log-likelihood is computed by numerically integrating the joint likelihood of the observed responses over the latent trait distribution using Cartesian-product normal quadrature. For FCGDINA, the marginal likelihood is obtained by summing over the 2^D discrete attribute profiles.

For a sample of N independent persons with responses \mathbf{Y}_j, the marginal log-likelihood is:

\ell = \sum_{j=1}^{N} \log \int P(\mathbf{Y}_j \mid \boldsymbol{\theta})\, \phi_D(\boldsymbol{\theta}; \mathbf{0}, \boldsymbol{\Sigma})\, d\boldsymbol{\theta},

where \phi_D(\cdot) is the D-variate normal density with correlation matrix \boldsymbol{\Sigma}. The integral is approximated on a Cartesian-product quadrature grid over [-6, 6]^D.

The continuous-trait quadrature weights are normalized normal densities computed on the grid points, with the fitted correlation matrix used when available. FCGDINA instead uses the estimated class-proportion vector \boldsymbol{\pi} over attribute profiles.

S3 methods for extracting marginal log-likelihoods from fitted ForceChoice model objects.

Usage

## S3 method for class 'FCDCM'
logLik(object, theta.low = NULL, theta.up = NULL, L = NULL, ...)

## S3 method for class 'FCGDINA'
logLik(object, ...)

## S3 method for class 'FCGGUM'
logLik(object, theta.low = NULL, theta.up = NULL, L = NULL, ...)

## S3 method for class 'FCMIRT'
logLik(object, theta.low = NULL, theta.up = NULL, L = NULL, ...)

## S3 method for class 'MGGUM'
logLik(object, theta.low = NULL, theta.up = NULL, L = NULL, ...)

## S3 method for class 'MGPCM'
logLik(object, theta.low = NULL, theta.up = NULL, L = NULL, ...)

## S3 method for class 'MIRT'
logLik(object, theta.low = NULL, theta.up = NULL, L = NULL, ...)

## S3 method for class 'TIRT'
logLik(object, theta.low = NULL, theta.up = NULL, L = NULL, ...)

Arguments

object	A fitted model object of class "MIRT", "MGPCM", "MGGUM", "FCMIRT", "FCDCM", "FCGDINA", "FCGGUM", or "TIRT".
theta.low	Numeric; lower bound for the quadrature grid on the latent scale. Used by continuous-trait models; if NULL, the value stored in the fitted object's controls is used, falling back to -6.
theta.up	Numeric; upper bound for the quadrature grid on the latent scale. Used by continuous-trait models; if NULL, the value stored in the fitted object's controls is used, falling back to 6.
L	Integer; number of quadrature points per dimension. If NULL, the package chooses a dimension-dependent default.
...	Additional arguments passed to the method. Currently ignored by the implemented methods.

Details

For MIRT, MGPCM, MGGUM, FCMIRT, FCGGUM, TIRT, and FCDCM objects, the likelihood is evaluated by marginalizing over a normal quadrature grid (and, for FCDCM, over attribute profiles conditional on the higher-order trait). For FCGDINA objects, the likelihood is evaluated exactly over the 2^D latent attribute profiles.

Value

An object of class "logLik" with attributes:

• nobs: number of observations (N)

• df: number of free parameters

• theta.norm: continuous-trait quadrature grid points, when applicable

• prob: model-implied response probabilities at grid points, when applicable

• pi: quadrature weights or FCGDINA class probabilities

• L: quadrature grid size used, when applicable

• prob.class: FCGDINA class-conditional forced-choice probabilities, when applicable

An object of class "logLik": a length-one numeric vector containing the marginal log-likelihood, with at least attributes nobs (sample size) and df (number of free parameters). Continuous-trait methods also attach quadrature diagnostics such as theta.norm, prob, pi, and L; FCGDINA attaches latent-class probabilities and class-conditional response probabilities.

Functions

• logLik(FCDCM): FCDCM model: higher-order trait quadrature with exact marginalization over discrete attribute profiles.

• logLik(FCGDINA): FCGDINA model: marginal forced-choice probabilities over all 2^D attribute profiles.

• logLik(FCGGUM): FCGGUM model: forced-choice unfolding block probabilities with multivariate normal quadrature.

• logLik(FCMIRT): FCMIRT model: forced-choice block pattern probabilities with multivariate normal quadrature.

• logLik(MGGUM): MGGUM model: polytomous unfolding responses with per-item block-structured quadrature evaluation.

• logLik(MGPCM): MGPCM model: polytomous responses integrated over the fitted multivariate normal latent distribution.

• logLik(MIRT): MIRT model: multivariate normal quadrature over D-dimensional latent space with Gaussian correlation structure.

• logLik(TIRT): TIRT model: pairwise binary probit probabilities with multivariate normal quadrature over traits.

See Also

fit.MIRT, get.fit.index, good.of.fit

Examples

sim <- sim.data.MIRT(N = 20, I = 6, D = 2, model = "m2pl")
fit <- fit.MIRT(
  sim$response, model = "m2pl", D = 2, method = "iStEM",
  control.method = list(
    vis = FALSE, seed = 123,
    M = 2, B = 2, burnin.maxitr = 2,
    maxitr = 3, eps1 = 10, eps2 = 10,
    estimate.se = FALSE)
)
ll <- logLik(fit, L = 9)
as.numeric(ll)
attr(ll, "df")

ForceChoice documentation built on Sept. 13, 2026, 1:06 a.m.