sirt (version 0.36-30)

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.

Examples

##################################
# Person fit for 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
##