Scoring Persons and Items in the ISOP Model
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).
isop.scoring(dat,score.itemcat=NULL)
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). |
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
s_{ik} for item i and category k
is calculated as
s_{ik}=∑_{j=0}^{k-1} f_{ij} - ∑_{j=k+1}^K f_{ij}=P( X_i < k ) - P( X_i > k )
where f_{ik} is the relative frequency of item i
in category k and K is the maximum category.
The modified percentile score ρ_p
for subject p (mpsc in person) is
defined by
ρ_p=\frac{1}{I} ∑_{i=1}^I ∑_{j=0}^K s_{ik} \mathbf{1}( X_{pi}=k )
Note that for dichotomous items, the sum score is a sufficient statistic for ρ_p but this is not the case for polytomous items. The modified percentile score ρ_p ranges between -1 and 1.
The modified item P-score ρ_i (Scheiblechner, 2007, p. 52) is defined by
ρ_i=\frac{1}{I-1} \cdot ∑_j ≤ft[ P( X_j < X_i ) - P( X_j > X_i ) \right ]
A list with following entries:
person |
A data frame with person parameters. The modified
percentile score ρ_p is denoted by |
item |
Item statistics and scoring parameters.
The item P-scores ρ_i
are labeled as |
p.itemcat |
Frequencies for every item category |
score.itemcat |
Scoring points for every item category |
distr.fct |
Empirical distribution function |
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.
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# EXAMPLE 1: Dataset Reading
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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 )
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# EXAMPLE 2: Dataset students from CDM package | polytomous items
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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 )Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.