pairwise (version 0.2.2)

pairSE: Item Parameter calculation with Standard Errors for polytomous Partial Credit Model

Description

Calculation of the item parameter for dichotomous (difficulty) or polytomous items (thurstonian thresholds) and their standard errors (SE) respectively. All parameters are calculatetd 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

pairSE(daten, m = NULL, nsample = 30, size = 0.5,
    seed = "no", pot = TRUE, zerocor = TRUE,
    verbose = TRUE, ...)

Arguments

daten

a data.frame or matrix with optionaly named colums (names of items), potentially with missing values, comprising polytomous or dichotomous (or mixted category numbers) responses of n respondents (rows) on k items (colums)

m

an integer (will be recycled to a vector of length k) or a vector giving the number of response categories for all items - by default m = NULL m is calculatetd from data, assuming that every response category is at least once present in d

nsample

numeric specifying the number of subsamples sampled from data, which is the number of replications of the parameter calculation.

WARNING! specifying high values for nsample ( > 100 ) may result in long computing time without leadig t

size

numeric with valid range between 0 and 1 (but not exactly 0 or 1) specifying the size of the subsample of data when bootstraping for SE estimation. As an alternative, size can be set to the character "jack" (

seed

numeric used for set.seed(seed).

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).

verbose

logical, if verbose = TRUE (default) a message about subsampling whe calculation standrderrors is sent to console.

...

additional parameters passed through.

Value

• A (list) object of class "pairSE" containing the item category thresholds, difficulties sigma and their standard errors.

A Note on Standard Errors

Estimation of standard errors is done by repeated calculation of item parameters for subsamples of the given data. This procedure is mainly controlled by the arguments nsample and size (see arguments). With regard to calculation time, the argument nsample is the 'time killer'. On the other hand, things (estimation of standard errors) will not necessarily get better when choosing large values for nsample. For example choosing nsample=400 will only result in minimal change for standard error estimation in comparison to (nsample=30) which is the default setting (see examples).

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.

Estimation of standard errors is done by repeated calculation of item parameters for subsamples of the given data.

To avoid numerical problems with off diagonal zeros when constructing the pairwise comparison matrix Mnicjc, 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.

Examples

data(bfiN) # loading example data set

# calculating itemparameters and their SE for 5 neuroticism items with 6 answer categories (0-5).
neuro_itempar<-pairSE(daten = bfiN, m = 6)
summary(neuro_itempar) # summary for result

# plotting item thresholds with with their CI = 95\%
plot(neuro_itempar)
plot(neuro_itempar,sortdif=TRUE)

###### example from details section 'Some Notes on Standard Errors' ########
neuro_itempar_400<-pairSE(daten = bfiN, m = 6,nsample=400)
plot(neuro_itempar)
plot(neuro_itempar_400)