pairwise (version 0.1.4)

itempar.poly: Item Parameter for polytomous Partial Credit Model

Description

Calculation of the item parameter for polytomous items according to the Partial Credit Model using a generalization of the pairwise comparison algorithm (Choppin, 1968, 1985). Missing values up to an high amount in data matrix are allowed, as long as items are proper linked together.

Usage

itempar.poly(daten, m = max(daten, na.rm = TRUE) + 1,
    sortdif = TRUE, pot = TRUE, zerocor = TRUE, ...)

Arguments

daten

a data matrix with optionaly named colums (names of items) or a data.frame, potentially with missing values, comprising polytomous responses of respondents (rows) on some items (colums) coded starting with 0 for lowest category to m-1 for

m

number of response categories for all items - by default m is defined as m = max(daten,na.rm=TRUE)+1.

sortdif

logical, if TRUE (default) items are sorted in an ascending order by difficulty for output.

pot

logical, if TRUE (default) a power of three of the pairwise comparison matrix is used for further calculations.

zerocor

logical, if TRUE (default) unobserved combinations (1-0, 0-1) in data for each pair of items are given a frequency of one conf. proposal by Alexandrowicz(2011, p.373).

...

additional parameters passed through.

Value

• A (list) object of class ippwpo containing the item category thresholds and difficulties sigma.

Details

Parameter calculation is based on the construction of a paired comparison matrix Mnicjc with entries ficjc representing 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. This algorithm is simply realized by matrix multiplication.

To avoid numerical problems with off diagonal zero's when constructing the pairwise comparison matrix Mnij, powers of the Mnicjc matrix, can be used (Choppin, 1968, 1985). Using powers k of Mnicjc - argument pot=TRUE (default), replaces the results of the direct comparisons between i and j with the sum of the indirect comparisons of i and j through an intermediate k.

In general, it is recommended to use the argument with default value pot=TRUE.

References

Choppin, B. (1968). Item Bank using Samplefree Calibration. Nature, 219(5156), 870-872.

Choppin, B. (1985). A fully conditional estimation procedure for Rasch model parameters. Evaluation in Education, 9(1), 29-42.

Alexandrowicz, R. W. (2011). 'GANZ RASCH': A Free Software for Categorical Data Analysis. Social Science Computer Review, 30(3), 369-379.

Examples

data(bfiN) # loading example data set
# calculating itemparameters for 5 neuroticism items with 6 answer categories (0-5).
neuro_itempar<-itempar.poly(daten = bfiN, m = 6)
neuro_itempar
################
# plotting threshold profiles for 5 neuroticism items.
# 6 categories - 5 thresholds
plot(neuro_itempar)