PP-package: PP: Estimation of Person Parameters and Person Fit
In PP: Person Parameter Estimation

PP-package

R Documentation

PP: Estimation of Person Parameters and Person Fit

Description

The PP package provides functions for estimating person parameters for the 1PL, 2PL, 3PL, and 4PL models, as well as the generalized partial credit model (GPCM). Supported estimation methods include maximum likelihood (ML), weighted likelihood (WL; Warm, 1989), maximum a posteriori (MAP), expected a posteriori (EAP), and robust estimation.

Details

In addition, the package includes routines for person-fit analysis, including infit, outfit, lz, and lzstar statistics. The implementation is designed for efficient computation and includes compiled code for fast estimation.

For an introduction to the package workflow, see the package vignettes.

Author(s)

Jan Steinfeld and Manuel Reif

References

Barton, M. A., & Lord, F. M. (1981). An upper asymptote for the three-parameter logistic item-response model.

Birnbaum, A. (1968). Some latent trait models and their use in inferring an examinee's ability. In F. M. Lord & M. R. Novick (Eds.), Statistical theories of mental test scores. Reading, MA: Addison-Wesley.

Drasgow, F., Levine, M. V., & Williams, E. A. (1985). Appropriateness measurement with polychotomous item response models and standardized indices. British Journal of Mathematical and Statistical Psychology, 38(1), 67–86.

Muraki, E. (1992). A generalized partial credit model: Application of an EM algorithm. Applied Psychological Measurement, 16, 159–176.

Samejima, F. (1993). An approximation of the bias function of the maximum likelihood estimate of a latent variable for the general case where the item responses are discrete. Psychometrika, 58, 119–138.

Snijders, T. B. (2001). Asymptotic null distribution of person fit statistics with estimated person parameter. Psychometrika, 66(3), 331–342.

Warm, T. A. (1989). Weighted likelihood estimation of ability in item response theory. Psychometrika, 54, 427–450.

Wright, B. D., & Masters, G. N. (1990). Computation of OUTFIT and INFIT statistics. Rasch Measurement Transactions, 3(4), 84–85.

Yen, Y.-C., Ho, R.-G., Liao, W.-W., Chen, L.-J., & Kuo, C.-C. (2012). An empirical evaluation of the slip correction in the four parameter logistic models with computerized adaptive testing. Applied Psychological Measurement, 36, 75–87.

Examples

set.seed(1522)

diffpar <- seq(-3, 3, length = 12)
sl <- round(runif(12, 0.5, 1.5), 2)
la <- round(runif(12, 0, 0.25), 2)
ua <- round(runif(12, 0.8, 1), 2)

awm <- matrix(sample(0:1, 10 * 12, replace = TRUE), ncol = 12)

res3plmle <- PP_4pl(
  respm = awm,
  thres = diffpar,
  slopes = sl,
  lowerA = la,
  type = "mle"
)

res3plwle <- PP_4pl(
  respm = awm,
  thres = diffpar,
  slopes = sl,
  lowerA = la,
  type = "wle"
)

res3plmap <- PP_4pl(
  respm = awm,
  thres = diffpar,
  slopes = sl,
  lowerA = la,
  type = "map"
)

res3plmlepfit <- Pfit(
  respm = awm,
  pp = res3plmle,
  fitindices = c("infit", "outfit")
)

out <- PPass(
  respdf = data.frame(awm),
  thres = diffpar,
  items = "all",
  mod = c("1PL"),
  fitindices = c("lz", "lzstar", "infit", "outfit")
)

PP documentation built on April 21, 2026, 5:09 p.m.