TAM (version 1.6-0)

tam.se: Standard Error Estimation

Description

Standard error computation for objects of the classes tam and tam.mml.

Usage

tam.se(tamobj, ...)

tam.mml.se(tamobj, numdiff.parm = 0.001)

Arguments

tamobj

An object generated by tam.mml

numdiff.parm

Step width parameter for numerical differentiation

...

Further arguments to be passed

Value

• A list with following entries:
• xsi
  Data frame with $\xi$ parameters (est) and their corresponding standard errors (se)
• beta
  Data frame with $\beta$ regression parameters and their standard error estimates
• B
  Data frame with loading parameters and their corresponding standard errors

Details

Covariances between parameters estimates are ignored in this standard error calculation. The standard error is obtained by numerical differentiation.

Examples

#############################################################################
# EXAMPLE 1: 1PL model, sim.rasch data
#############################################################################
	
data(sim.rasch)
# estimate Rasch model
mod1 <- tam.mml(resp=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

#############################################################################
# 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')