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

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Description

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

Usage

1
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

1
2

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