sirt (version 1.5-0)

fit.isop: 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.

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

Details

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

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 <- aggregate( dat == 1 , list( stud.p ) , mean , na.rm=TRUE )
freq.correct <- a1[,-1]
# weights
a1 <- aggregate( dat.resp , list( stud.p ) , sum , na.rm=TRUE )
wgt <- a1[,-1]

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