, Volume 46, Issue 1, pp 101–119 | Cite as

Comparing two maximum likelihood algorithms for mixture Rasch models

  • Yevgeniy PtukhinEmail author
  • Yanyan Sheng
Original Paper


The mixture Rasch model is gaining popularity as it allows items to perform differently across subpopulations and hence addresses the violation of the unidimensionality assumption with traditional Rasch models. This study focuses on comparing two common maximum likelihood methods for estimating such models using Monte Carlo simulations. The conditional maximum likelihood (CML) and joint maximum likelihood (JML) estimations, as implemented in three popular R packages are compared by evaluating parameter recovery and class accuracy. The results suggest that in general, CML is preferred in parameter recovery and JML is preferred in identifying the correct number of classes. A set of guidelines is also provided regarding how sample sizes, test lengths or actual class probabilities affect the accuracy of estimation and number of classes, as well as how different information criteria compare in achieving class accuracy. Specific issues regarding the performance of particular R packages are highlighted in the study as well.


Mixture models Rasch model Conditional maximum likelihood Joint maximum likelihood 


Compliance with ethical standards

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.


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Copyright information

© The Behaviormetric Society 2019

Authors and Affiliations

  1. 1.Mathematical Sciences DepartmentWorcester Polytechnic InstituteWorcesterUSA
  2. 2.Southern Illinois University – CarbondaleCarbondaleUSA

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