pairwise performs the explicit
calculation, not estimation!, of the Rasch item
parameters for dichotomous an polytomous response formats
using a pairwise comparison approach (Choppin, 1968,
1985).For the calculation of the item thresholds and difficulty in case of polytomous answer formats, according to the Partial Credit Model (Masters, 1982), a generalization of the pairwise comparison algorithm is used. The construction of the pairwise comparison matrix is therefore extended to the comparison of answer frequencies for each category of each item. In this case, the pairwise comparison matrix Mnicjc with entries ficjc represents the number of respondents who answered to item i in category c and to item j in category c-1 widening Choppin's (1968, 1985) conditional pairwise algorithm to polytomous item response formats. Within R this algorithm is simply realized by matrix multiplication.
In general, for both polytomous and dichotomous response formats, the benefit in applying this algorithm lies in it's capability to return stabel item parameter 'estimates' even when using data with a relative high amount of missing values, as long as the items are still proper linked together.
Based on the explicit calculated item parameters for a
dataset, the person parameters may thereupon be estimated
using an mle or wle approach, for example implementetd in
the R-package {PP} by Manuel Reif.
The recent version of the package 'pairwise' (0.1.4)
computes item parameters for dichotomous and polytomous
item responses according the 1PL (when using the function
itempar.dicho) and the partial credit model
(when using the function itempar.poly).
The calculation of standard errors, when using functions
ipSE.dicho or ipSE.poly is
realized by bootstrap or jack-knife technique.
Splitting the data (e.g. by rawscore or by random) and
calculating model parameter for each subsample can be
done with the functions grmSE.dicho and
grmSE.poly
Choppin, B. (1985). A fully conditional estimation procedure for Rasch model parameters. Evaluation in Education, 9(1), 29-42.
Heine, J. H. & Tarnai, Ch. (2011). Item-Parameter Bestimmung im Rasch-Modell bei unterschiedlichen Datenausfallmechanismen. Referat im 17. Workshop 'Angewandte Klassifikationsanalyse' [Item parameter determination in the Rasch model for different missing data mechanisms. Talk at 17. workshop 'Applied classification analysis'], Landhaus Rothenberge, Muenster, Germany 09.-11.11.2011
Heine, J. H., Tarnai, Ch. & Hartmann, F. G. (2011). Eine Methode zur Parameterbestimmung im Rasch-Modell bei fehlenden Werten. Vortrag auf der 10. Tagung der Fachgruppe Methoden & Evaluation der DGPs. [A method for parameter estimation in the Rasch model for missing values. Paper presented at the 10th Meeting of the Section Methods & Evaluation of DGPs.] Bamberg, Germany, 21.09.2011 - 23.09. 2011.
Masters, G. N. (1982). A Rasch model for partial credit scoring. Psychometrika, 47(2), 149-174.
Reif, M. (2012). PP: Person Parameter estimation. R package version 0.2, Abgerufen von http://CRAN.R-project.org/package=PP