Table V.

Function in R for calculating the two-rater model-based kappa statistic and its variance.

twokappafn = function(sigma2u, beta1)

{

integrand1 = function(z)

{

term1=pnorm(sqrt(sigma2u)*z − beta1)

term2= pnorm(sqrt(sigma2u)*z + beta1)

fullintegrand= term1*term2*dnorm(z)

}

result1 = integrate (integrand1, lower=−100, upper=100)

integrand2=function(z)

{

term3=(1-pnorm(sqrt(sigma2u)*z − beta1))

term4=(1-pnorm(sqrt(sigma2u)*z + beta1))

fullintegrand2=term3*term4*dnorm(z)

}

result2= integrate(integrand2, lower=−100, upper=100)

res2=result2 $value

# two-rater model-based kappa

2*(res1 + res2)−1

}

# Calculation of variance: need to enter values for varbeta1, varsigmasqu, sigmasqu and beta1.

integrand1a = function(z)

{term=(0.5*(1/sqrt(sigmasqu))*dnorm(sqrt(sigmasqu)*z + beta1/2)*pnorm(sqrt(sigmasqu)*z − beta1/2)

+ 0.5*(1/sqrt (sigmasqu))*pnorm(sqrt(sigmasqu)*z + beta1/2)*dnorm(sqrt(sigmasqu)*z − beta1/2))

*dnorm(z)*z }

result1a=integrate(integrand1a, lower=−100, upper=100)

integrand1b = function(z)

{term=(−0.5*(1/sqrt(sigmasqu))*dnorm(sqrt(sigmasqu)*z + beta1/2)*(1-pnorm(sqrt(sigmasqu)*z − beta1/2))*z

−0.5*(1/sqrt(sigmasqu))*pnorm(sqrt(sigmasqu)*z + beta1/2)*dnorm(sqrt(sigmasqu)*z − beta1/2))

*dnorm(z)*z}

result1b=integrate(integrand1b, lower=−100, upper=100)

vectorh1=result1a$value+result1b$value

integrand1b = function(z)

{term=(0.5*dnorm(sqrt(sigmasqu)*z + beta1/2)*pnorm(sqrt(sigmasqu)*z − beta1/2) − 0.5*pnorm(sqrt(sigmasqu)*z

+ beta1/2)*dnorm(sqrt(sigmasqu)*z − beta1/2))*dnorm(z)}

result2a=integrate(integrand2a, lower=−100, upper=100)

integrand2b = function(z)

{term=(−0.5*dnorm(sqrt(sigmasqu)*z + beta1/2)*(1-pnorm(sqrt(sigmasqu)*z − beta1/2))

+ 0.5*(1-pnorm(sqrt(sigmasqu)*z + beta1/2))*dnorm(sqrt(sigmasqu)*z − beta1/2))*dnorm(z)}

result2b=integrate(integrand2b, lower=−100, upper=100)

vectorh2=result2a$value+result2b$value

covarmat = matrix(c(varsigmasqu,0,0,varbeta1), ncol=2)

vectorh = c(vectorh1, vectorh2)

varkappam = 4*(vectorh %*% covarmat %*% vectorh)

}