# Concordance correlation coefficient

## Description

The concordance correlation coefficient *ρ*_{c} (Lin, 1989 & 2000) evaluates the degree to which pairs of observations fall on the 45° line through the origin.
It contains a measurement of precision *ρ* and accuracy *C*_{b}:

*ρ*_{c} = *ρ* *C*_{b}

where

*ρ*is the Pearson correlation coefficient, which measures how far each observation deviates from the best-fit line, and is a**measure of precision**, and*C*_{b}is a bias correction factor that measures how far the best-fit line deviates from the 45° line through the origin, and is a**measure of accuracy**.

## Required input

- Select the variables of interest. If one or both variables needs Logarithmic transformation, select the corresponding option(s).
- Optionally select a filter to include a subset of cases.

## Results

The concordance correlation coefficient *ρ*_{c} (Lin, 1989 & 2000) evaluates the degree to which pairs of observations fall on the 45° line through the origin.
It contains a measurement of precision *ρ* and accuracy *C*_{b}:

*ρ*_{c} = *ρ* *C*_{b}

where

*ρ*is the Pearson correlation coefficient, which measures how far each observation deviates from the best-fit line, and is a**measure of precision**, and*C*_{b}is a bias correction factor that measures how far the best-fit line deviates from the 45° line through the origin, and is a**measure of accuracy**.

## Descriptive scale

McBride (2005) suggests the following descriptive scale for values of the concordance correlation coefficient (for continuous variables):

Value of ρ_{c} | Strength of agreement |

< 0.90 | Poor |

0.90 - 0.95 | Moderate |

0.95 - 0.99 | Substantial |

>0.99 | Almost perfect |

## Literature

- Lin L.I-K (1989) A concordance correlation coefficient to evaluate reproducibility. Biometrics 45:255-268.
- Lin L.I-K (2000) A note on the concordance correlation coefficient. Biometrics 56:324-325.
- McBride GB (2005) A proposal for strength-of-agreement criteria for Lin's Concordance Correlation Coefficient. NIWA Client Report: HAM2005-062.