ncb.od {merror}R Documentation

Compute accuracy estimates and maximum likelihood estimates of precision for the nonconstant bias measurement error model using original data.

Description

Compute accuracy estimates and maximum likelihood estimates of precision for the nonconstant bias measurement error model using original data.

Usage

ncb.od(x, beta = beta.bar(x), M = 40, conf.level = 0.95)

Arguments

x n (no. of items) x N (no. of methods) matrix or data.frame containing the measurements. N must be greater than 3 and n > N.
beta N vector of betas, either estimated by beta.bar function or hypothesized.
M Maximum no. of iterations for convergence.
conf.level Chosen confidence level.

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.

By using the original data values, the betas can be estimated and also the process variance.

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
sigma2 N vector of variances that measure the method imprecision.
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 estimated or hypothesized betas.
df N vector of estimated degrees of freedom.
lb N vector of lower bounds for confidence intervals.
ub N vector of upper bounds for confidence intervals.
H N+1 symmetric H matrix (see p. 201, Jaech).
errors.nb n x N matrix of estimated measurement errors for no bias model.
errors.cb n x N matrix of estimated measurement errors for constant bias model.
errors.ncb n x N matrix of estimated measurement errors for nonconstant bias model

Author(s)

Richard A. Bilonick rab@nauticom.net

References

Jaech, J. L. (1985) Statistical Analysis of Measurement Errors. New York: Wiley.

See Also

cb.pd,lrt

Examples


data(pm2.5)
ncb.od(pm2.5)               # nonconstant bias model using original data values
ncb.od(pm2.5,beta=rep(1,5)) # constant bias model using original data values


[Package merror version 1.0 Index]