Step width parameter for numerical
differentiation
...
Further arguments to be passed
Details
Covariances between parameters estimates are ignored in this standard
error calculation. The standard error is obtained by numerical
differentiation.
Value
A list with following entries:
xsi
Data frame with ξ parameters (est)
and their corresponding standard errors (se)
beta
Data frame with β regression parameters and
their standard error estimates
B
Data frame with loading parameters and their
corresponding standard errors
Note
Standard error estimation for variances and covariances is not yet
implemented.
Standard error estimation for loading parameters in case of
irtmodel='GPCM.design' is highly experimental.
Examples
#############################################################################
# EXAMPLE 1: 1PL model, data.sim.rasch
#############################################################################
data(data.sim.rasch)
# estimate Rasch model
mod1 <- tam.mml(resp=data.sim.rasch[1:500,1:10])
# standard error estimation
se1 <- tam.se( mod1 )
# proportion of standard errors estimated by 'tam.se' and 'tam.mml'
prop1 <- se1$xsi$se / mod1$xsi$se
## > summary( prop1 )
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1.030 1.034 1.035 1.036 1.039 1.042
## => standard errors estimated by tam.se are a bit larger
## Not run:
#############################################################################
# EXAMPLE 2: Standard errors differential item functioning
#############################################################################
data(data.ex08)
formulaA <- ~ item*female
resp <- data.ex08[["resp"]]
facets <- as.data.frame( data.ex08[["facets"]] )
# investigate DIF
mod <- tam.mml.mfr( resp= resp , facets= facets , formulaA = formulaA )
summary(mod)
# estimate standard errors
semod <- tam.se(mod)
prop1 <- semod$xsi$se / mod$xsi$se
summary(prop1)
# plot differences in standard errors
plot( mod$xsi$se , semod$xsi$se , pch=16 , xlim=c(0,.15) , ylim=c(0,.15) ,
xlab="Standard error 'tam.mml'" , ylab="Standard error 'tam.se'" )
lines( c(-6,6) , c(-6,6) , col="gray")
round( cbind( mod$xsi , semod$xsi[,-1] ) , 3 )
## xsi se.xsi N est se
## I0001 -1.956 0.092 500 -1.956 0.095
## I0002 -1.669 0.085 500 -1.669 0.088
## [...]
## I0010 2.515 0.108 500 2.515 0.110
## female1 -0.091 0.025 500 -0.091 0.041
## I0001:female1 -0.051 0.070 500 -0.051 0.071
## I0002:female1 0.085 0.067 500 0.085 0.068
## [...]
## I0009:female1 -0.019 0.068 500 -0.019 0.068
##
# => The largest discrepancy in standard errors is observed for the
# main female effect (.041 in 'tam.se' instead of .025 in 'tam.mml')
## End(Not run)