Function to calculate the marginal reliability

Given an estimated model and a prior density function, compute the marginal reliability (Thissen and Wainer, 2001). This is only available for unidimensional tests.

Usage

marginal_rxx(mod, density = dnorm, ...)

Arguments

mod: an object of class 'SingleGroupClass'
density: a density function to use for integration. Default assumes the latent traits are from a normal (Gaussian) distribution
...: additional arguments passed to the density function

References

Chalmers, R., P. (2012). mirt: A Multidimensional Item Response Theory Package for the R Environment. Journal of Statistical Software, 48(6), 1-29. doi:10.18637/jss.v048.i06

Thissen, D. and Wainer, H. (2001). Test Scoring. Lawrence Erlbaum Associates.

Author

Phil Chalmers rphilip.chalmers@gmail.com

Examples



dat <- expand.table(deAyala)
mod <- mirt(dat)

# marginal estimate treating item parameters as known
marginal_rxx(mod)
#> [1] 0.6092894

# compare to alpha
itemstats(dat)$overall$alpha
#> [1] 0.6077281

# \donttest{

# empirical estimate (assuming the same prior)
fscores(mod, returnER = TRUE)
#>        F1 
#> 0.6200703 

# empirical rxx the alternative way, given theta scores and SEs
fs <- fscores(mod, full.scores.SE=TRUE)
head(fs)
#>             F1     SE_F1
#> [1,] -1.580133 0.6699424
#> [2,] -1.580133 0.6699424
#> [3,] -1.580133 0.6699424
#> [4,] -1.580133 0.6699424
#> [5,] -1.580133 0.6699424
#> [6,] -1.580133 0.6699424
empirical_rxx(fs)
#>        F1 
#> 0.6200703 

# }