Project Details

Project Title: Choice Item Response Theory (cIRT)

Project URL:

Code Repository:

Project Paper:

Project Version: 1.1.0

Project Status: Frozen

Project Description: Jointly model the accuracy of cognitive responses and item choices within a bayesian hierarchical framework as described by Culpepper and Balamuta (2015) doi:10.1007/s11336-015-9484-7. In addition, the package contains the datasets used within the analysis of the paper.



  • C++ Implementation of the hierarchial modeling framework for choice
  • Three data sets containing information on how students did on the Revised Purdue Spatial Visualization Test (Revised PSVT:R) by Yoon, 2011.

Modeling Framework

  • Implementation of the hiercharical framework described in “A Hierarchical Model for Accuracy and Choice on Standardized Tests”
  • Specifically, a choice inclusive Probit HLM and a Two Parameter Ogive Model.

C++ Functions

  • Random Number Generation for the following distributions: Wishart, Inverse Wishart, and Multivariate Normal
  • Matrix Centering
  • Direct Sum calculation


  • Student Performance on Revised Purdue Spatial Visualization Test (Revised PSVT:R) by Yoon, 2011 in trial_matrix
  • The choices students made among items presented to them in choice_matrix
  • The end payout results for students based on their choices in payout_matrix
  • One additional data set exists containing the student’s sex response in survey_data
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