R: Compute accuracy estimates and maximum likelihood estimates...
cb.pd
R Documentation
Compute accuracy estimates and maximum likelihood estimates of precision for the
constant bias measurement error model using paired data.
Description
Compute accuracy estimates and maximum likelihood estimates of precision for the
constant bias measurement error model using paired data.
Usage
cb.pd(x, conf.level = 0.95, M = 40)
Arguments
x
n (no. of items) x N (no. of methods) matrix or data.frame containing the measurements. N must be >= 3 and n > N.
conf.level
Chosen onfidence level.
M
Maximum no.of iterations to reach convergence.
Details
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.
Value
conf.level
Confidence level used.
sigma.table
Table of accuracy and precision estimates and confidence
intervals.
n.items
No. of items.
N.methods
No. of methods
Grubbs.initial.sigma2
N vector of initial imprecision estimates using Grubbs' method
sigma2
N vector of variances that measure the method imprecision.
sigma2.se2
N vector of squared standard errors of the estimated imprecisions (variances).
alpha.cb
N vector of estimated alphas for constant bias model.
alpha.ncb
N vector of estimated alphas for nonconstant bias model
beta
N vector of hypothesized betas for the constant bias model - all ones.
df
N vector of estimated degrees of freedom.
chisq.low
N vector of chi-square values for the lower tail (used to compute the ci upper bound).
chisq.low
N vector of chi-square values for the upper tail (used to compute the ci lower bound).
lb
N vector of lower bounds for confidence intervals
ub
N vector of upper bounds for confidence intervals
Author(s)
Richard A. Bilonick
References
Jaech, J. L. (1985) Statistical Analysis of Measurement Errors. New York: Wiley.