ncb.od {merror} | R Documentation |
Compute accuracy estimates and maximum likelihood estimates of precision for the nonconstant bias measurement error model using original data.
ncb.od(x, beta = beta.bar(x), M = 40, conf.level = 0.95)
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. |
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.
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 |
Richard A. Bilonick rab@nauticom.net
Jaech, J. L. (1985) Statistical Analysis of Measurement Errors. New York: Wiley.
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