Abstract
The Rasch model is one of the most prominent item response models. In this article, different item parameter estimation methods for the Rasch model are systematically compared through a comprehensive simulation study: Different alternatives of joint maximum likelihood (JML) estimation, different alternatives of marginal maximum likelihood (MML) estimation, conditional maximum likelihood (CML) estimation, and several limited information methods (LIM). The type of ability distribution (i.e., nonnormality), the number of items, sample size, and the distribution of item difficulties were systematically varied. Across different simulation conditions, MML methods with flexible distributional specifications can be at least as efficient as CML. Moreover, in many situations (i.e., for long tests), penalized JML and JML with ε adjustment resulted in very efficient estimates and might be considered alternatives to JML implementations currently used in statistical software. Moreover, minimum chi-square (MINCHI) estimation was the best-performing LIM method. These findings demonstrate that JML estimation and LIM can still prove helpful in applied research.
Highlights
Chi-square (MINCHI)Regular univariate sample median defined minimum as the innermost point of estimation a data set iswas the best-performing limited information methods (LIM) method
Regular univariate sample median defined minimum as the innermost point of estimation a data set iswas the best-performing LIM method. These findings demonstrate that joint maximum likelihood (JML) estimation and LIM can unique
We provide a comprehensive comparative simulation study that compares the performance of a large number of estimation methods under a wide range of θ distribution
Summary
Chi-square (MINCHI)Regular univariate sample median defined minimum as the innermost (deepest) point of estimation a data set iswas the best-performing LIM method. Sample points (i.e., θ = arg minθ ∈R1 ∑in=1 |θ − xi |, where xi , i = 1, · · · , n are the given n sample points in R1 ), it is not unique To overcome this drawback, conventionally it is defined as Keywords: Rasch model; estimation methods; nonnormality θ = Median{ xi } := x(b n+1 c) + x(b n+2 c) 2, where x(1) ≤ x(2) ≤ · · · ≤ x(n) are ordered values of xi ’s and b·c is the floor function. It is the innermost point (from both left and right direction) or the average of two deepest sample points.
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