Longitudinal Concordance Correlation Function Based on Variance Components: An Application in Fruit Color Analysis

  • Thiago de Paula Oliveira
  • John Hinde
  • Silvio Sandoval Zocchi


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. Moreover, in longitudinal studies the LCC can suggest over which period the two methods are likely to be in agreement and where the simpler colorimeter method could be used. The performance of the LCC is evaluated using a small simulation study. Supplementary materials accompanying this paper appear online.


Colorimeter Digital image analysis Longitudinal data Mixed-effects model Postharvest 



The authors are grateful to FAPESP (Grants #2010/16955-1, São Paulo Research Foundation-FAPESP), CNPq (National Counsel of Technological and Scientific Development), University of São Paulo, and National University of Ireland that supported this research project. In addition, we would like to thank the professors Clarice Garcia Borges Demétrio and Renata Alcarde Sermarini for their important contributions on this research.

Supplementary material

13253_2018_321_MOESM1_ESM.csv (31 kb)
Supplementary material 1 (csv 30 KB)
13253_2018_321_MOESM2_ESM.r (30 kb)
Supplementary material 2 (R 30 KB)


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© International Biometric Society 2018

Authors and Affiliations

  1. 1.Departamento de Ciências Exatas, Escola Superior de Agricultura Luiz de QueirozUniversidade de São Paulo (USP)PiracicabaBrazil
  2. 2.School of Mathematics, Statistics and Applied MathematicsNational University of Ireland, GalwayGalwayIreland

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