personfit.stat.Rd
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 index
Ability estimate abil
Person mean of correctly solved items
Caution index
Dependability index
\(ECI1\)
\(ECI2\)
\(ECI3\)
\(ECI4\)
\(ECI5\)
\(ECI6\)
Fit statistic \(l_0\)
Fit statistic \(l_z\)
Person outfit statistic
Person infit statistic
Point biserial correlation of item responses and item \(p\) values
Point biserial correlation of item responses
and item difficulties b
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) 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 ## }