personfit.appropriateness: Appropriateness Statistic for Person Fit Assessment

In CDM: Cognitive Diagnosis Modeling

Appropriateness Statistic for Person Fit Assessment

Description

This function computes the person fit appropriateness statistics (Levine & Drasgow, 1988) as proposed for cognitive diagnostic models by Liu, Douglas and Henson (2009). The appropriateness statistic assesses spuriously high scorers (attr.type=1) and spuriously low scorers (attr.type=0).

Usage

personfit.appropriateness(data, probs, skillclassprobs, h=0.001, eps=1e-10,
    maxiter=30, conv=1e-05, max.increment=0.1, progress=TRUE)

## S3 method for class 'personfit.appropriateness'
summary(object, digits=3,  ...)

## S3 method for class 'personfit.appropriateness'
plot(x, cexpch=.65,  ...)

Arguments

data	Data frame of dichotomous item responses
probs	Probabilities evaluated at skill space (abilities θ)
skillclassprobs	Probabilities of skill classes
h	Numerical differentiation parameter
eps	Constant which is added to probabilities avoiding zero probability
maxiter	Maximum number of iterations
conv	Convergence criterion
max.increment	Maximum increment in iteration
progress	Optional logical indicating whether iteration progress should be displayed.
object	Object of class personfit.appropriateness
digits	Number of digits for rounding
x	Object of class personfit.appropriateness
cexpch	Point size in plot
...	Further arguments to be passed

Value

List with following entries

summary	Summaries of person fit statistic
personfit.appr.type1	Statistic for spuriously high scorers (appr.type=1) evaluated for every person.
personfit.appr.type0	Statistic for spuriously low scorers (appr.type=0) evaluated for every person.

References

Levine, M. V., & Drasgow, F. (1988). Optimal appropriateness measurement. Psychometrika, 53, 161-176.

Liu, Y., Douglas, J. A., & Henson, R. A. (2009). Testing person fit in cognitive diagnosis. Applied Psychological Measurement, 33(8), 579-598.

Examples

#############################################################################
# EXAMPLE 1: DINA model data.ecpe
#############################################################################

data(data.ecpe, package="CDM")

# fit DINA model
mod1 <- CDM::din( CDM::data.ecpe$data[,-1], q.matrix=CDM::data.ecpe$q.matrix )
summary(mod1)

# person fit appropriateness statistic
data <- mod1$data
probs <- mod1$pjk
skillclassprobs <- mod1$attribute.patt[,1]
res <- CDM::personfit.appropriateness( data, probs, skillclassprobs, maxiter=8)
                 # only few iterations
summary(res)
plot(res)

## Not run: 
#############################################################################
# EXAMPLE 2: Person fit 2PL model
#############################################################################

data(data.read, package="sirt")
dat <- data.read
I <- ncol(dat)

# fit 2PL model
mod1 <- sirt::rasch.mml2( dat, est.a=1:I)
# person fit statistic
data <- mod1$dat
probs0 <- t(mod1$pjk)
probs <- array( 0, dim=c( I, 2, dim(probs0)[2] ) )
probs[,2,] <- probs0
probs[,1,] <- 1 - probs0
skillclassprobs <- mod1$trait.distr$pi.k
res <- CDM::personfit.appropriateness( data, probs, skillclassprobs )
summary(res)
plot(res)

## End(Not run)

CDM documentation built on Aug. 25, 2022, 5:08 p.m.