# 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

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 |