pairwise (version 0.1.4)

itempar.dicho: Item Parameter dichotomous 1PL

Description

Calculation of the item parameter for dichotomous items according the 1PL Rasch Model using a 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.dicho(daten, sortdif = TRUE, pot = TRUE,
    zerocor = TRUE, ...)

Arguments

daten

a data matrix, potentially with missing values, comprising dichotomous responses of respondents (rows) on some items (colums) coded in the 0 1 manner.

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

• An object of class ippw containing item difficulties sigma.

Details

Parameter calculation is based on the construction of a paired comparison matrix Mnij with entries fij representing the number of respondents who got item i right and item j wrong according to Choppin's (1968, 1985) conditional pairwise algorithm. 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 Mnij matrix, can be used (Choppin, 1968, 1985). Using powers k of Mnij 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(cog) # loading example data set
sigma<-itempar.dicho(daten=cog[,4:34], pot=TRUE) # calculating itemparameters for 31 math items
sigma
#######
plot(sigma) # plotting item difficulties