personfit.stat: Person Fit Statistics for the Rasch Model

Description

This function collects some person fit statistics for the Rasch model (Karabatsos, 2003; Meijer & Sijtsma, 2001).

Usage

personfit.stat(dat, abil, b)

Value

A data frame with following columns (see Meijer & Sijtsma 2001 for a review of different person fit statistics):

case: Case index
abil: Ability estimate abil
mean: Person mean of correctly solved items
caution: Caution index
depend: Dependability index
ECI1: \(ECI1\)
ECI2: \(ECI2\)
ECI3: \(ECI3\)
ECI4: \(ECI4\)
ECI5: \(ECI5\)
ECI6: \(ECI6\)
l0: Fit statistic \(l_0\)
lz: Fit statistic \(l_z\)
outfit: Person outfit statistic
infit: Person infit statistic
rpbis: Point biserial correlation of item responses and item \(p\) values
rpbis.itemdiff: Point biserial correlation of item responses and item difficulties b
U3: Fit statistic \(U_3\)

Arguments

dat: An \(N \times I\) data frame of dichotomous item responses
abil: An ability estimate, e.g. the WLE
b: Estimated item difficulty

References

Karabatsos, G. (2003). Comparing the aberrant response detection performance of thirty-six person-fit statistics. Applied Measurement in Education, 16, 277-298.

Meijer, R. R., & Sijtsma, K. (2001). Methodology review: Evaluating person fit. Applied Psychological Measurement, 25, 107-135.

Examples

Run this code

#############################################################################
# EXAMPLE 1: Person fit Reading Data
#############################################################################

data(data.read)
dat <- data.read

# estimate Rasch model
mod <- sirt::rasch.mml2( dat )
# WLE
wle1 <- sirt::wle.rasch( dat,b=mod$item$b )$theta
b <- mod$item$b # item difficulty

# evaluate person fit
pf1 <- sirt::personfit.stat( dat=dat, abil=wle1, b=b)

if (FALSE) {
# dimensional analysis of person fit statistics
x0 <- stats::na.omit(pf1[, -c(1:3) ] )
stats::factanal( x=x0, factors=2, rotation="promax" )
  ## Loadings:
  ##                Factor1 Factor2
  ## caution         0.914
  ## depend          0.293   0.750
  ## ECI1            0.869   0.160
  ## ECI2            0.869   0.162
  ## ECI3            1.011
  ## ECI4            1.159  -0.269
  ## ECI5            1.012
  ## ECI6            0.879   0.130
  ## l0              0.409  -1.255
  ## lz             -0.504  -0.529
  ## outfit          0.297   0.702
  ## infit           0.362   0.695
  ## rpbis          -1.014
  ## rpbis.itemdiff  1.032
  ## U3              0.735   0.309
  ##
  ## Factor Correlations:
  ##         Factor1 Factor2
  ## Factor1   1.000  -0.727
  ## Factor2  -0.727   1.000
  ##
}