Estimation of Person Parameters and calculation of Person Fit for the 1,2,3,4-PL model and the GPCM.

PP-package has been developed to easily compute ML, WL (Warm 1989), MAP, EAP and robust estimates of person parameters for a given response matrix and given item parameters of the 1,2,3,4-PL model (Birnbaum 1968, Barton & Lord 1981) and the GPCM (Muraki 1992). It provides c++ routines which makes estimation of parameters very fast. Additional some methods to calculate the person fit are provided like the infit-outfit-, lz- and lz*-idex. Read the vignettes for getting started with this package.

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 Lord, F.M. & Novick, M.R. (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, Eiji (1992). A Generalized Partial Credit Model: Application of an EM Algorithm. Applied Psychological Measurement, 16, 159-176.

Samejima, Fumiko (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, Thomas 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.

See also

PPass, PP_gpcm, PP_4pl, PPall, Pfit

Author

Manuel Reif and Jan Steinfeld

Examples

set.seed(1522)
# intercepts
diffpar <- seq(-3,3,length=12)
# slope parameters
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)

# response matrix
awm <- matrix(sample(0:1,10*12,replace=TRUE),ncol=12)
# MLE estimation
res3plmle <- PP_4pl(respm = awm,thres = diffpar, slopes = sl,lowerA = la,type = "mle")
#> Estimating:  3pl model ... 
#> type = mle 
#> Estimation finished!
# WLE estimation
res3plwle <- PP_4pl(respm = awm,thres = diffpar, slopes = sl,lowerA = la,type = "wle")
#> Estimating:  3pl model ... 
#> type = wle 
#> Estimation finished!
# MAP estimation
res3plmap <- PP_4pl(respm = awm,thres = diffpar, slopes = sl,lowerA = la,type = "map")
#> Warning: all mu's are set to 0! 
#> Warning: all sigma2's are set to 1! 
#> Estimating:  3pl model ... 
#> type = map 
#> Estimation finished!

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

# or estimate person parameter and calculate person fit in one step 
out <- PPass(respdf = data.frame(awm),thres = diffpar, items="all",
             mod=c("1PL"), fitindices= c("lz","lzstar","infit","outfit"))
#> Estimating:  1pl model ... 
#> type = wle 
#> Estimation finished!