Longitudinal concordance correlation function based on variance components: an application in fruit color analysis

The maturity stages of papaya fruit based on peel color are frequently characterized from a sample of four points on the equatorial region measured by a colorimeter. However, this procedure may not be suitable for assessing the papaya's overall mean color and an alternative proposal is to use image acquisition of the whole fruit’s peel. Questions of interest are whether a sample on the equatorial region can reproduce a sample over the whole peel region and if the colorimeter can compete with a scanner, or digital camera, in measuring the mean hue over time. The reproducibility can be verified by using the concordance correlation for responses measured on a continuous scale. Thus, in this work we propose a longitudinal concordance correlation (LCC), based on a mixed-effects regression model, to estimate agreement over time among pairs of observations obtained from different combinations between measurement method and sampled peel region. The results show that the papaya's equatorial region is not representative of the whole peel region, suggesting the use of image analysis rather than a colorimeter to measure the mean hue.