llike_score {irtQ}

Loglikelihood of Ability Parameters

Description

This function computes the loglikelihood of ability parameters given the item parameters and response data.

Usage

llike_score(
  x,
  data,
  theta,
  D = 1,
  method = "ML",
  norm.prior = c(0, 1),
  fence.a = 3,
  fence.b = NULL,
  missing = NA
)

Arguments

x

A data frame containing the item metadata (e.g., item parameters, number of score categories, models). This can be created easily using the shape_df function. See est_irt, irtfit, \codeinfo, or simdat for more details about the item metadata.

data

A matrix representing examinees' response data for the items in x. Each row and column corresponds to an examinee and an item, respectively.

theta

A numeric vector of ability parameters for which the loglikelihood values will be computed.

D

A scaling factor in IRT models that adjusts the logistic function to approximate the normal ogive function (set to 1.7). The default is 1.

method

A character string specifying the scoring method. Options include "ML" for maximum likelihood estimation, "MLF" for maximum likelihood estimation with fences, and "MAP" for maximum a posteriori estimation. The default method is "MLE".

norm.prior

A numeric vector of two elements indicating the mean and standard deviation of the normal prior distribution. These parameters are used to obtain the Gaussian quadrature points and corresponding weights from the normal distribution. Default is c(0,1). This parameter is ignored if method is "ML" or "MLF".

fence.a

A numeric value defining the item slope parameter (a-parameter) for the two imaginary items in the MLF method. Default is 3.0.

fence.b

A numeric vector of two elements specifying the lower and upper fences of item difficulty parameters (b-parameters) for the two imaginary items in the MLF method. If fence.b = NULL, the range values are used to set the fences. The default is NULL.

missing

A value used to denote missing values in the response data set. Default is NA.

Details

The function computes the loglikelihood value of the ability parameter given the item parameters and response data for each item. As an example, to assess the loglikelihoods of abilities for two examinees who have taken the same test items specified in x, supply their item response data matrix with two rows in data and a vector of ability values for which loglikelihood needs to be computed in theta.

Value

A data frame of loglikelihood values. Each row indicates the ability parameter for which the loglikelihood was computed, and each column represents a response pattern.

Examples

#'
## Import the "-prm.txt" output file from flexMIRT
flex_sam <- system.file("extdata", "flexmirt_sample-prm.txt", package = "irtQ")

# Read item parameters and transform them into item metadata
x <- bring.flexmirt(file=flex_sam, "par")$Group1$full_df

# Generate examinees' abilities from N(0, 1)
set.seed(10)
score <- rnorm(5, mean=0, sd=1)

# Simulate the response data
data <- simdat(x=x, theta=score, D=1)

# Specify the ability values for which the loglikelihood values will be computed
theta <- seq(-3, 3, 0.5)

# Compute the loglikelihood values (using the MLE method)
llike_score(x=x, data=data, theta=theta, D=1, method="ML")