empirical_rxx {mirt}

R Documentation

Function to calculate the empirical (marginal) reliability

Description

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

Author(s)

Phil Chalmers rphilip.chalmers@gmail.com

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

Examples

## No test: 

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

## End(No test)

---