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)
#> 
Iteration: 1, Log-Lik: -56256.669, Max-Change: 0.33820
Iteration: 2, Log-Lik: -55598.944, Max-Change: 0.25622
Iteration: 3, Log-Lik: -55344.183, Max-Change: 0.17901
Iteration: 4, Log-Lik: -55252.392, Max-Change: 0.12170
Iteration: 5, Log-Lik: -55219.175, Max-Change: 0.08221
Iteration: 6, Log-Lik: -55206.845, Max-Change: 0.05582
Iteration: 7, Log-Lik: -55202.096, Max-Change: 0.03866
Iteration: 8, Log-Lik: -55200.153, Max-Change: 0.02623
Iteration: 9, Log-Lik: -55199.330, Max-Change: 0.01879
Iteration: 10, Log-Lik: -55198.648, Max-Change: 0.00688
Iteration: 11, Log-Lik: -55198.588, Max-Change: 0.00523
Iteration: 12, Log-Lik: -55198.554, Max-Change: 0.00418
Iteration: 13, Log-Lik: -55198.501, Max-Change: 0.00094
Iteration: 14, Log-Lik: -55198.498, Max-Change: 0.00025
Iteration: 15, Log-Lik: -55198.497, Max-Change: 0.00024
Iteration: 16, Log-Lik: -55198.497, Max-Change: 0.00021
Iteration: 17, Log-Lik: -55198.497, Max-Change: 0.00096
Iteration: 18, Log-Lik: -55198.496, Max-Change: 0.00057
Iteration: 19, Log-Lik: -55198.496, Max-Change: 0.00015
Iteration: 20, Log-Lik: -55198.496, Max-Change: 0.00007

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

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

if (FALSE) { # \dontrun{

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

# empirical rxx the alternative way, given theta scores and SEs
fs <- fscores(mod, full.scores.SE=TRUE)
head(fs)
empirical_rxx(fs)

} # }