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)

Arguments

dat

An $N \times I$ data frame of dichotomous item responses

abil

An ability estimate, e.g. the WLE

Estimated item difficulty

Value

A data frame with following columns (see Meijer & Sijtsma 2001 for a review of different person fit statistics):
caseCase index
abilAbility estimate abil
meanPerson mean of correctly solved items
cautionCaution index
dependDependability index
ECI1$ECI1$
ECI2$ECI2$
ECI3$ECI3$
ECI4$ECI4$
ECI5$ECI5$
ECI6$ECI6$
l0Fit statistic $l_0$
lzFit statistic $l_z$
outfitPerson outfit statistic
infitPerson infit statistic
rpbisPoint biserial correlation of item responses and item $p$ values
rpbis.itemdiffPoint biserial correlation of item responses and item difficulties b
U3Fit statistic $U_3$

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

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

# dimensional analysis of person fit statistics
x0 <- na.omit(pf1[ , -c(1:3) ] )
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
  ##

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