isop.scoring {sirt} | R Documentation |
Scoring Persons and Items in the ISOP Model
Description
This function does the scoring in the isotonic probabilistic model (Scheiblechner, 1995, 2003, 2007). Person parameters are ordinally scaled but the ISOP model also allows specific objective (ordinal) comparisons for persons (Scheiblechner, 1995).
Usage
isop.scoring(dat,score.itemcat=NULL)
Arguments
dat |
Data frame with dichotomous or polytomous item responses |
score.itemcat |
Optional data frame with scoring points for every item and every category (see Example 2). |
Details
This function extracts the scoring rule of the ISOP model
(if score.itemcat !=NULL
) and calculates the
modified percentile score for every person. The score
for item
and category
is calculated as
where is the relative frequency of item
in category
and
is the maximum category.
The modified percentile score
for subject
(
mpsc
in person
) is
defined by
Note that for dichotomous items, the sum score is a
sufficient statistic for but this is
not the case for polytomous items.
The modified percentile score
ranges between -1 and 1.
The modified item P-score (Scheiblechner, 2007, p. 52) is
defined by
Value
A list with following entries:
person |
A data frame with person parameters. The modified
percentile score |
item |
Item statistics and scoring parameters.
The item P-scores |
p.itemcat |
Frequencies for every item category |
score.itemcat |
Scoring points for every item category |
distr.fct |
Empirical distribution function |
References
Scheiblechner, H. (1995). Isotonic ordinal probabilistic models (ISOP). Psychometrika, 60, 281-304.
Scheiblechner, H. (2003). Nonparametric IRT: Scoring functions and ordinal parameter estimation of isotonic probabilistic models (ISOP). Technical Report, Philipps-Universitaet Marburg.
Scheiblechner, H. (2007). A unified nonparametric IRT model for d-dimensional psychological test data (d-ISOP). Psychometrika, 72, 43-67.
See Also
For fitting the ISOP and ADISOP model see
isop.dich
or fit.isop
.
Examples
#############################################################################
# EXAMPLE 1: Dataset Reading
#############################################################################
data( data.read )
dat <- data.read
# Scoring according to the ISOP model
msc <- sirt::isop.scoring( dat )
# plot student scores
boxplot( msc$person$mpsc ~ msc$person$score )
#############################################################################
# EXAMPLE 2: Dataset students from CDM package | polytomous items
#############################################################################
library("CDM")
data( data.Students, package="CDM")
dat <- stats::na.omit(data.Students[, -c(1:2) ])
# Scoring according to the ISOP model
msc <- sirt::isop.scoring( dat )
# plot student scores
boxplot( msc$person$mpsc ~ msc$person$score )
# scoring with known scoring rule for activity items
items <- paste0( "act", 1:5 )
score.itemcat <- msc$score.itemcat
score.itemcat <- score.itemcat[ items, ]
msc2 <- sirt::isop.scoring( dat[,items], score.itemcat=score.itemcat )