fit.isop: Fitting the ISOP and ADISOP Model for Frequency Tables

In sirt: Supplementary Item Response Theory Models

Fitting the ISOP and ADISOP Model for Frequency Tables

Description

Fit the isotonic probabilistic model (ISOP; Scheiblechner, 1995) and the additive isotonic probabilistic model (ADISOP; Scheiblechner, 1999).

Usage

fit.isop(freq.correct, wgt, conv=1e-04, maxit=100,
      progress=TRUE, calc.ll=TRUE)

fit.adisop(freq.correct, wgt, conv=1e-04, maxit=100,
      epsilon=0.01, progress=TRUE, calc.ll=TRUE)

Arguments

freq.correct	Frequency table
wgt	Weights for frequency table (number of persons in each cell)
conv	Convergence criterion
maxit	Maximum number of iterations
epsilon	Additive constant to handle cell frequencies of 0 or 1 in fit.adisop
progress	Display progress?
calc.ll	Calculate log-likelihood values? The default is TRUE.

Details

See isop.dich for more details of the ISOP and ADISOP model.

Value

A list with following entries

fX	Fitted frequency table
ResX	Residual frequency table
fit	Fit statistic: weighted least squares of deviations between observed and expected frequencies
item.sc	Estimated item parameters
person.sc	Estimated person parameters
ll	Log-likelihood of the model
freq.fitted	Fitted frequencies in a long data frame

Note

For fitting the ADISOP model it is recommended to first fit the ISOP model and then proceed with the fitted frequency table from ISOP (see Examples).

References

Scheiblechner, H. (1995). Isotonic ordinal probabilistic models (ISOP). Psychometrika, 60, 281-304.

Scheiblechner, H. (1999). Additive conjoint isotonic probabilistic models (ADISOP). Psychometrika, 64, 295-316.

See Also

For fitting the ISOP model to dichotomous and polytomous data see isop.dich.

Examples

#############################################################################
# EXAMPLE 1: Dataset Reading
#############################################################################

data(data.read)
dat <- as.matrix( data.read)
dat.resp <- 1 - is.na(dat) # response indicator matrix
I <- ncol(dat)

#***
# (1) Data preparation
#     actually only freq.correct and wgt are needed
#     but these matrices must be computed in advance.

# different scores of students
stud.p <- rowMeans( dat, na.rm=TRUE )
# different item p values
item.p <- colMeans( dat, na.rm=TRUE )
item.ps <- sort( item.p, index.return=TRUE)
dat <- dat[,  item.ps$ix ]
# define score groups students
scores <- sort( unique( stud.p ) )
SC <- length(scores)
# create table
freq.correct <- matrix( NA, SC, I )
wgt <- freq.correct
# percent correct
a1 <- stats::aggregate( dat==1, list( stud.p ), mean, na.rm=TRUE )
freq.correct <- a1[,-1]
# weights
a1 <- stats::aggregate( dat.resp, list( stud.p ), sum, na.rm=TRUE )
wgt <- a1[,-1]

#***
# (2) Fit ISOP model
res.isop <- sirt::fit.isop( freq.correct, wgt )
# fitted frequency table
res.isop$fX

#***
# (3) Fit ADISOP model
# use monotonely smoothed frequency table from ISOP model
res.adisop <- sirt::fit.adisop( freq.correct=res.isop$fX, wgt )
# fitted frequency table
res.adisop$fX

sirt documentation built on May 29, 2024, 8:43 a.m.