Reliability Estimation in TAM

Functions for computing reliability estimates.

WLErel(theta, error, w=rep(1, length(theta)), select=NULL)

EAPrel(theta, error, w=rep(1, length(theta)), select=NULL)

Arguments

theta

Vector with theta estimates

error

Vector with standard errors of theta estimates

w

Optional vector of person weights

select

Optional vector for selecting cases

Details

The reliability formulas follow Adams (2005). Let \(v\) denote the variance of theta estimates and let \(s\) denote the average of the squared error. Then, the WLE reliability is defined as \(1-s/v=(v-s)/v\) while the EAP reliability is defined as \(1 - s/(s+v)=v/(s+v)\).

Value

Numeric value

References

Adams, R. J. (2005). Reliability as a measurement design effect. Studies in Educational Evaluation, 31(2), 162-172. doi:10.1016/j.stueduc.2005.05.008

Examples

#############################################################################
# EXAMPLE 1: Toy example for reliability functions
#############################################################################

set.seed(9897)
N <- 100
# simulate theta and error SDs
x <- stats::rnorm(N,sd=2)
error <- stats::runif(N, .7, 1.3)
# compute WLE reliability
WLErel(x,error)
# compute EAP reliaility
EAPrel(x,error)