Person Fit Statistics for the Rasch Model
This function collects some person fit statistics for the Rasch model (Karabatsos, 2003; Meijer & Sijtsma, 2001).
personfit.stat(dat, abil, b)
dat |
An N \times I data frame of dichotomous item responses |
abil |
An ability estimate, e.g. the WLE |
b |
Estimated item difficulty |
A data frame with following columns (see Meijer & Sijtsma 2001 for a review of different person fit statistics):
case |
Case index |
abil |
Ability estimate |
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 |
U3 |
Fit statistic U_3 |
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 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:
mirt::personfit,
eRm::personfit and
ltm::person.fit.
############################################################################# # 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) ## Not run: # 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 ## ## End(Not run)
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