Bayesian 4 Parameter Item Response Model

Estimate Barton & Lord's (1981) four parameter IRT model with lower and upper asymptotes using Bayesian formulation described by Culpepper (2016) .

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Estimate Barton & Lord’s (1981) four parameter IRT model with lower and upper asymptotes using Bayesian formulation described by Culpepper (2016)


You can install fourPNO from CRAN using:


Or, you can be on the cutting-edge development version on GitHub using:

if(!requireNamespace("devtools")) install.packages("devtools")


To use the fourPNO package, load it into R using:


Inside the package, the estimation routines can be viewed as:

  • Gibbs_2PNO()
  • Gibbs_4PNO()


Steven Andrew Culpepper

Citing the fourPNO package

To ensure future development of the package, please cite fourPNO package if used during an analysis or simulation study. Citation information for the package may be acquired by using in R:



GPL (>= 2)


fourPNO 1.0.5


  • Increased R dependency to 3.5.0.
  • Autogenerate native registration with Rcpp 1.0.0.
  • Suppressed internal functions from being exported.


  • Enabled markdown in documentation.
  • Cleaned up documentation entries.


  • Enabled TMSA Lab's travis-ci configuration.

fourPNO 1.0.4

  • Added src/init.c to meet R 3.4 standards.
  • Added URL to project on GitHub.

fourPNO 1.0.3

  • Changed default chain_length to be burnin-2 in examples.

fourPNO 1.0.2

  • Variable name change for guessing and slipping matrices.

fourPNO 1.0.1

  • Corrected guessing parameter notation from cs to gs.

fourPNO 1.0.0

  • Initial release of fourPNO

Reference manual

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1.1.0 by Steven Andrew Culpepper, a year ago

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Browse source code at

Authors: Steven Andrew Culpepper [aut, cre, cph]

Documentation:   PDF Manual  

Task views: Psychometric Models and Methods

GPL (>= 2) license

Imports Rcpp

Linking to Rcpp, RcppArmadillo

See at CRAN