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This study compared the joint, conditional, marginal and penalized maximum likelihood estimations (JML, CML, MML, PML) and their computer programs in estimating the Rasch model, i.e., WINSTEPS, R-packages eRm and ltm, BILOG-MG, and SAS code using PML. A simulation study showed that PML generated less biased estimates than JML but did not perform as well as CML and MML; those ML methods and computer programs are acceptable practically; R-package ltm performed best.