Standard Error Estimation
Standard error computation for objects of the classes tam
and tam.mml.
tam.se(tamobj, item_pars=TRUE, ...) tam_mml_se_quick(tamobj, numdiff.parm=0.001, item_pars=TRUE ) tam_latreg_se_quick(tamobj, numdiff.parm=0.001 )
tamobj |
An object generated by |
item_pars |
Logical indicating whether standard errors should also be computed for item parameters |
numdiff.parm |
Step width parameter for numerical differentiation |
... |
Further arguments to be passed |
Covariances between parameters estimates are ignored in this standard error calculation. The standard error is obtained by numerical differentiation.
A list with following entries:
xsi |
Data frame with ξ parameters ( |
beta |
Data frame with β regression parameters and their standard error estimates |
B |
Data frame with loading parameters and their corresponding standard errors |
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.
#############################################################################
# EXAMPLE 1: 1PL model, data.sim.rasch
#############################################################################
data(data.sim.rasch)
# estimate Rasch model
mod1 <- TAM::tam.mml(resp=data.sim.rasch[1:500,1:10])
# standard error estimation
se1 <- TAM::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::tam.mml.mfr( resp=resp, facets=facets, formulaA=formulaA )
summary(mod)
# estimate standard errors
semod <- TAM::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)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.