pairwise (version 0.6.1-0)

deltapar: Compute delta parameters from thurstonian thresholds

Description

Calculation of delta parameters or rather item step parameters from thurstonian threshold parameters returned by the function pair.

Usage

deltapar(object, sigma = TRUE)

Value

If sigma=TRUE an object of class c("data.frame", "deltapar") containing delta parameters for items and their difficultie (first column). Otherwise a matrix containing only the delta parameters.

Arguments

object

an object of class "pair" as resulting from item parameter calculation using the function pair.

sigma

a logical whether to return item difficulties (sigma) or not

Details

The "Thurstone threshold" or rather thurstonian threshold for a category corresponds to a point on the latent variable at which the probability of being observed in that category or above equals that of being observed in the categories below. Thus these thurstonian threshold parameters can be interpreted in an strait forward and easy way. However, some other computer programs related to Rasch analysis don't return thurstonian threshold parameters from their estimation procedure, but rather so called delta parameters for the item steps. The later are also known as "step measures", "step calibrations", "step difficulties", "tau parameters", and "Rasch-Andrich thresholds". For a better comparability between different Rasch software and estimation procedures the thurstonian threshold parameters can be converted into delta or rather items step parameters.

References

Linacre J.M. (1992). Rasch-Andrich Thresholds and Rasch-Thurstone Thresholds. Rasch Measurement Transactions, 5:4, 191. https://www.rasch.org/rmt/rmt54r.htm

Linacre J.M. (2001). Category, Step and Threshold: Definitions & Disordering. Rasch Measurement Transactions, 15:1, 794. https://www.rasch.org/rmt/rmt151g.htm

Adams, R. J., Wu, M. L., & Wilson, M. (2012). The Rasch Rating Model and the Disordered Threshold Controversy. Educational and Psychological Measurement, 72(4), 547–573. https://doi.org/10.1177/0013164411432166

Linacre J.M. (2006). Item Discrimination and Rasch-Andrich Thresholds. Rasch Measurement Transactions, 20:1, 1054. https://www.rasch.org/rmt/rmt201k.htm

Examples

######################
data(sim200x3) # loading reponse data
ip <- pair(sim200x3,m = c(2,3,3)) # compute item parameters
summary(ip) # have a look at the results (thurstonian thresholds)
deltapar(ip) # compute delta parameters from these