Compute accuracy estimates and maximum likelihood estimates of precision for the constant bias measurement error model using paired data.
cb.pd(x, conf.level = 0.95, M = 40)
Confidence level used.
Table of accuracy and precision estimates and confidence intervals.
No. of items.
No. of methods
N vector of initial imprecision estimates using Grubbs' method
N vector of variances that measure the method imprecision.
N vector of squared standard errors of the estimated imprecisions (variances).
N vector of estimated alphas for constant bias model.
N vector of estimated alphas for nonconstant bias model
N vector of hypothesized betas for the constant bias model - all ones.
N vector of estimated degrees of freedom.
N vector of chi-square values for the lower tail (used to compute the ci upper bound).
N vector of chi-square values for the upper tail (used to compute the ci lower bound).
N vector of lower bounds for confidence intervals
N vector of upper bounds for confidence intervals
n (no. of items) x N (no. of methods) matrix or data.frame containing the measurements. N must be >= 3 and n > N.
Chosen onfidence level.
Maximum no.of iterations to reach convergence.
Richard A. Bilonick
Measurement Error Model:
x[i,k] = alpha[i] + beta[i]*mu[k] + epsilon[i,k]
where x[i,k] is the measurement by the ith method for the kth item, i = 1 to N, k = 1 to n, mu[k] is the true value for the kth item, epsilon[i,k] is the Normally distributed random error with variance sigma[i] squared for the ith method and the kth item, and alpha[i] and beta[i] are the accuracy parameters for the ith method.
The imprecision for the ith method is sigma[i]. If all alphas are zeroes and all betas are ones, there is no bias. If all betas equal 1, then there is a constant bias. Otherwise there is a nonconstant bias.
ME (method of moments estimator) and MLE are the same for N=3 instruments except for a factor of (n-1)/n: MLE = (n-1)/n * ME
Using paired differences forces Constant Bias model (beta[1] = beta[2] = ... = beta[N]). Also, the process variance CANNOT be estimated.
Jaech, J. L. (1985) Statistical Analysis of Measurement Errors. New York: Wiley.
ncb.od,
lrt