personfit.appropriateness function

Appropriateness Statistic for Person Fit Assessment

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).

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 $\theta$)
• 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

Returns

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)