| fedirt_gpcm {FedIRT} | R Documentation |
Federated Graded Response Model Estimation Function
Description
Implements a federated learning approach for the estimation of the graded response model parameters, enabling collaborative parameter estimation across distributed datasets while ensuring individual data source privacy.
Usage
fedirt_gpcm(J, M, logL_entry, g_logL_entry)
Arguments
J |
An integer indicating the number of items in the IRT model across all sites. This number should be consistent for all response matrices provided. |
M |
An integer vector indicating the maximum level (number of categories minus one) for each item across all sites, which determines the total number of step difficulties to estimate for the graded response model. |
logL_entry |
A function that calculates the sum of log-likelihoods for the response matrices across all sites. This function is crucial for evaluating the fit of the model at each iteration. |
g_logL_entry |
A function that computes the aggregated gradient of the log-likelihood across all participating entities. |
Details
The function adopts a federated learning framework to perform estimation of item step difficulties and individual ability levels in an IRT graded response model without needing to pool the data into one centralized dataset. The estimator follows an iterative optimization procedure consisisting of local computations, information sharing with a central aggregator, and updating of the global parameters.
Value
A list containing the following components from the federated graded model estimation:
-
par: Numeric vector of model's fitted parameters including item discrimination (a) and item difficulty (b) parameters. -
value: The optimization objective function's value at the found solution, typically the log-likelihood. -
counts: Named integer vector with counts of function evaluations and gradient evaluations during optimization. -
convergence: Integer code indicating the optimization's convergence status (0 indicates successful convergence). -
message: Message from optimizer about optimization process, NULL if no message is available. -
loglik: The calculated log-likelihood of the fitted model, identical to the 'value' element when the objective function is log-likelihood. -
a: Numeric vector of estimated item discrimination parameters. -
b: Numeric vector of estimated item difficulty parameters.
#' @references Muraki, E. (1992). "A generalized partial credit model: Application of an EM algorithm." Applied Psychological Measurement, 16(2), 159–176. doi:10.1177/014662169201600206