| logL_gpcm {FedIRT} | R Documentation |
Log-Likelihood of the federated graded Model
Description
Computes the log-likelihood of the graded IRT model given item parameters and response data. The computation utilizes numerical integration and is optimized through memoization for repeated evaluations.
Usage
logL_gpcm(a, b, data, q = 21, lower_bound = -3, upper_bound = 3)
Arguments
a |
The vector of item discrimination parameters in the graded model. |
b |
The vector of item difficulty parameters in the graded model. |
data |
The matrix of observed responses, with individuals in rows and items in columns. |
q |
The number of Gaussian quadrature points to use for numerical integration (default is 21). Gaussian quadrature is a numerical integration technique to approximate the integral of a function, and is particularly useful for accurate and efficient computation. |
lower_bound |
The lower limit for the Gaussian quadrature integration (default is -3). |
upper_bound |
The upper limit for the Gaussian quadrature integration (default is 3). |
Details
The function performs numerical integration over a set of quadrature points to calculate the probabilities of the observed responses under the graded model, considering the item discrimination (a) and difficulty (b) parameters. Memoization is used to cache computed values of the probabilities, logits, and log-likelihoods to avoid redundant calculations and speed up the process.
Value
The computed log-likelihood of the graded model as a single numeric value.