B1696
Title: Speeding up the Laplace approximation method for a high-dimensional Rasch model
Authors: Shuhrah Alghamdi - University of Glasgow (United Kingdom) [presenting]
Abstract: The Laplace approximation (LA) method can be a valuable tool for researchers interested in estimating students' abilities using item response theory models. Computational time is an essential criterion for assessing the efficiency of the LA for online inference or massive datasets. The performance of the LA depends on obtaining the covariance matrix $\Sigma$ by inverting the Hessian matrix $H$. However, computing the inverse of the $H$ matrix is computationally expensive for high-dimensional problems (i.e. when there are many students). Two methods are discussed for reducing the computational costs of estimating students' abilities using the Rasch model. The first method is to use the idea of the block matrix, according to which the $H$ matrix can be divided into sub-matrices, and linear algebra strategies can subsequently be used to simplify the calculations for inverting the $H$ matrix. The second method approximates the posterior distribution using only the diagonal of the $H$ matrix. These methods do not affect the point estimates, and as the number of students increases, the difference between the full $H$ matrix and the diagonal $H$ matrix becomes negligible. Compared with the standard LA method, our two proposed strategies can reduce the computational time 3- to 15-fold.
