fit.isop {sirt}

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