Abstract
This research was conducted to address the paucity of comparative studies on different methods for estimating standard errors with Laplace approximated maximum likelihood in multidimensional item response theory models. We considered standard errors associated with the observed information matrix, a fast version of the observed information matrix and the empirical cross product matrix, along with the Sandwich estimators derived from the observed information matrix and the fast observed information matrix. This study compares the accuracy, precision, computational efficiency and the average coverage rate of the 95% confidence interval of the different standard error methods. A Monte-Carlo simulation was conducted to investigate the effect of samples size, test length, number of categories and model complexity. The simulation was based on a fully crossed design with two test lengths (4/8), three sample sizes (250/1,000/4,000), two model types (independent cluster and cross-loadings), and 2/5 number of categories (binary response and polytomous ) resulting in 24 data generating conditions which all used a three-dimensional latent variable vector. The standard error estimators were evaluated in terms of accuracy, precision and computation efficiency using the coverage rates of the 95% confidence intervals, average root mean squared and the average absolute bias. In terms of average absolute bias, and average root mean squared error no method was found unacceptable, they all had close to zero values. The empirical cross product matrix was found to be more computationally efficient compared to other methods. In relation to 95% confidence interval, the average coverage rate for methods using first order Laplace were lower than the nominal level hence biased and imprecise estimates across all conditions. Standard error methods estimated using second order Laplace produced precise and accurate estimates with the correct coverage rates. This study adds knowledge to the literature on standard error estimators with Laplace approximations.