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Function to calculate the empirical (marginal) reliability

Source: R/empirical_rxx.R
empirical_rxx.Rd

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

See also

fscores, marginal_rxx

Author

Phil Chalmers rphilip.chalmers@gmail.com

Examples


# \donttest{

dat <- expand.table(deAyala)
itemstats(dat)
#> $overall
#>      N mean_total.score sd_total.score ave.r  sd.r alpha SEM.alpha
#>  19601            2.912          1.434 0.233 0.074 0.608     0.898
#> 
#> $itemstats
#>            N  mean    sd total.r total.r_if_rm alpha_if_rm
#> Item.1 19601 0.887 0.316   0.447         0.246       0.605
#> Item.2 19601 0.644 0.479   0.688         0.439       0.510
#> Item.3 19601 0.566 0.496   0.680         0.416       0.523
#> Item.4 19601 0.427 0.495   0.673         0.405       0.529
#> Item.5 19601 0.387 0.487   0.602         0.312       0.581
#> 
#> $proportions
#>            0     1
#> Item.1 0.113 0.887
#> Item.2 0.356 0.644
#> Item.3 0.434 0.566
#> Item.4 0.573 0.427
#> Item.5 0.613 0.387
#> 
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 

# }