| deltapar {pairwise} | R Documentation |
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)
Arguments
object |
an object of class |
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.
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.
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