Function to calculate the empirical (marginal) reliability

Given secondary latent trait estimates and their associated standard errors returned from fscores, compute the empirical reliability.

Usage

empirical_rxx(Theta_SE, T_as_X = FALSE)

Arguments

Theta_SE: a matrix of latent trait estimates returned from fscores with the options full.scores = TRUE and full.scores.SE = TRUE
T_as_X: logical; should the observed variance be equal to var(X) = var(T) + E(E^2) or var(X) = var(T) when computing empirical reliability estimates? Default (FALSE) uses the former

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

Author

Phil Chalmers rphilip.chalmers@gmail.com

Examples


# \donttest{

dat <- expand.table(deAyala)
itemstats(dat)
#> $overall
#>      N mean.total sd.total std.alpha alpha SEM.alpha mean.r  sd.r
#>  19601      2.912    1.434     0.603 0.608     0.898  0.233 0.074
#> 
#> $itemstats
#>            N K  mean    sd cor_if_rm   smc alpha_if_rm
#> Item.1 19601 2 0.887 0.316     0.246 0.070       0.605
#> Item.2 19601 2 0.644 0.479     0.439 0.199       0.510
#> Item.3 19601 2 0.566 0.496     0.416 0.177       0.523
#> Item.4 19601 2 0.427 0.495     0.405 0.171       0.529
#> Item.5 19601 2 0.387 0.487     0.312 0.100       0.581
#> 
mod <- mirt(dat)

theta_se <- fscores(mod, full.scores.SE = TRUE)
empirical_rxx(theta_se)
#>        F1 
#> 0.6200703 

theta_se <- fscores(mod, full.scores.SE = TRUE, method = 'ML')
empirical_rxx(theta_se)
#>        F1 
#> 0.5636644 
empirical_rxx(theta_se, T_as_X = TRUE)
#>        F1 
#> 0.2258948 

# }