cb.pd {merror}

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.

See Also

ncb.od, lrt

Examples

data(pm2.5)
cb.pd(pm2.5)