Electronic Journal of Applied Statistical Analysis EJASA (2012), Electron. J. App. Stat. Anal., Vol. 5, Issue 3, 360 – 366 e-ISSN 2070-5948, DOI 10.1285/i20705948v5n3p360 © 2012 Università del Salento – http://siba-ese.unile.it/index.php/ejasa/index 360 COMPARISON OF TWO BIAS REDUCTION TECHNIQUES FOR THE RASCH MODEL Lucio Bertoli Barsotti *(1) , Antonio Punzo (2) (1) Dipartimento di Scienze Aziendali, Economiche e Metodi Quantitativi, University of Bergamo, Italy (2) Dipartimento di Impresa, Culture e Società,Università di Catania, Italy Received 20 July 2012; Accepted 07 October 2012 Available online 16 November 2012 Abstract: This study examines the effect of two different techniques of bias reduction in the case of the fixed persons-fixed items formulation of the Rasch model. A first approach can be considered “corrective”, because it consists simply in correcting ex-post the joint maximum likelihood estimates by a factor (m-1)/m, were m represents the number of items and/or persons. A second approach, which is an application of a quite general formula for reducing the maximum likelihood estimation bias, can be considered “preventive”, because it arises from a modification of the score function. A comparative study of these two techniques was done using simulated data. Keywords: Maximum likelihood estimation, Rasch model, bias, modified score. 1. Introduction For the Rasch Model (RM), the Joint Maximum Likelihood (JML) is an estimation procedure in which item and person parameters are estimated simultaneously. One of the major drawbacks of the JML approach is that item parameters cannot be estimated consistently if the number of subjects, n, approaches infinity and the number of items, k, is fixed. More specifically, it is known that the JML estimation of item parameters is biased (both for the case of finite samples, and asymptotically). Indeed the JML estimate of the item difficulty parameters have an approximate bias that is a function of the constant k/(k-1) ([1], p. 244). As a practical solution for reducing this bias, [1] proposed the use of a multiplicative bias correcting factor (k-1)/k. The main purpose of this study is to compare the properties of two possible bias-reducing procedures for the JML estimation of the RM parameters: i) the (m-1)/m bias correction (where m can be either n or k); ii) the procedure of bias reduction suggested by [6] and based on a * E-mail: lucio.bertoli-barsotti@unibg.it