sirt (version 1.5-0)

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

b

Estimated item difficulty

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 $U_3$

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.

See Also

See pcm.fit for person fit in the partial credit model. See the irtProb and PerFit packages for person fit statistics and person response curves and functions included in other packages: personfit (mirt), personfit (eRm) and person.fit (ltm).

Examples

#############################################################################
# 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
  ##