PP

PP estimates person parameters (abilities) in item response theory when the item parameters are known, e.g. for items from an item bank given to a new sample.

• Models: 1PL (Rasch), 2PL, 3PL and 4PL model, partial credit and generalized partial credit model, and tests that mix dichotomous and polytomous items.
• Estimates: maximum likelihood, weighted likelihood (Warm), maximum a posteriori, expected a posteriori and a robust Huber-type estimate, each with standard error and a status per person.
• More: jackknife estimates, plausible values, the person fit statistics lz, lz*, infit and outfit, and simulation of response data.
• eRm: PPass() takes models fitted with the eRm package (RM, LLTM, RSM, PCM, LRSM, LPCM, also with time points and groups) and adds WLE/MAP/EAP estimates, person fit, jackknife and plausible values.

The numerical core is written in C++ and estimates the abilities of thousands of persons in milliseconds.

Installation

# from CRAN
install.packages("PP")

# development version from GitHub
# install.packages("remotes")
remotes::install_github("manuelreif/PP", build_vignettes = TRUE)

Example

fourpl_df contains an id, the sex and the responses of 60 persons to 12 items of a 3PL test, with the item parameters as attributes. PPass() estimates the abilities (WLE by default), computes the person fit in the same step and keeps the other variables:

library(PP)
data(fourpl_df)

res <- PPass(fourpl_df, items = 3:14,
             thres = attr(fourpl_df, "diffpar"), slopes = attr(fourpl_df, "slopes"),
             lowerA = attr(fourpl_df, "lowerA"))
print(res, n = 6)
#> Person assessment: 60 persons, 12 items
#> Model: 3PL model | WLE estimates
#> Status: 60 ok
#> Person fit: lz, lzstar, infit, outfit
#> Flagged (|lzstar| > 1.96): 4 persons
#>
#>        id sex estimate    SE status     lz lzstar infit   in_t outfit   ou_t
#> 1 LVL0694   w   -0.936 0.767     ok  1.019  1.026 0.692 -1.091 0.5342 -0.866
#> 2 BBU1225   w    1.811 1.022     ok  1.101  1.149 0.377 -1.537 0.2061 -0.526
#> 3 MJN2028   w    0.969 0.987     ok  1.270  1.324 0.288 -1.757 0.2011 -1.204
#> 4 TSU0771   m    1.224 1.008     ok -1.039 -1.157 1.487  0.978 1.9539  1.107
#> 5 XDS0698   w    0.252 0.925     ok  1.187  1.224 0.436 -1.392 0.3219 -1.257
#> 6 BOS1292   w   -4.730 2.118     ok  0.998  0.637 0.108 -1.505 0.0884 -1.196
#> ... 54 more persons
#> Not shown: lz_unst, in_chisq, in_df, in_pv, ou_chisq, ou_df, ou_pv

The result is a data.frame. summary(res) lists the flagged persons, and JKpp(res) works on it directly (as does PV() for EAP and MAP estimates). The estimation functions themselves are PP_4pl(), PP_gpcm() and PPall():

res_eap <- PP_4pl(respm = as.matrix(fourpl_df[, 3:14]),
                  thres = attr(fourpl_df, "diffpar"), slopes = attr(fourpl_df, "slopes"),
                  lowerA = attr(fourpl_df, "lowerA"), type = "eap")
head(res_eap$estimates)

Citation

If you use PP in your work, please cite it. citation("PP") prints the reference:

Reif, M. and Steinfeld, J. (2026). PP: Person Parameter Estimation. R package version 1.0.0. https://doi.org/10.32614/CRAN.package.PP

@Manual{PP,
  title  = {{PP}: Person Parameter Estimation},
  author = {Manuel Reif and Jan Steinfeld},
  year   = {2026},
  note   = {R package version 1.0.0},
  doi    = {10.32614/CRAN.package.PP},
  url    = {https://github.com/manuelreif/PP},
}

Learn more

• Vignettes: vignette("intro_pp", package = "PP"), vignette("intro_pfit", package = "PP") and vignette("ppass_erm", package = "PP")
• Website: https://manuelreif.github.io/PP/
• Changes: NEWS.md. Version 1.0.0 corrects several results of earlier versions (jackknife standard errors, MAP standard errors, plausible values, person fit with missing responses).
• Bugs and questions: https://github.com/manuelreif/PP/issues