Longitudinal Concordance Correlation Function Based on Variance Components: An Application in Fruit Color Analysis
- 128 Downloads
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.
KeywordsColorimeter 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.
- Darrigues, A., Hall, J., Knaap, E. V. D., Francis, D. M., Dujmovic, N., and Gray, S. Tomato analyzer-color test: A new tool for efficient digital phenotyping. Journal of the American Society for Horticultural Science, 133(4):579–586, 2008.Google Scholar
- Evans, E. A. and Ballen, F. H. An overview of global papaya production, trade, and technical report, University of Florida, Florida, 2015.Google Scholar
- Ihaka, R., Murrell, P., Hornik, K., Fisher, J. C., and Zeileis, A. Color Space Manipulation, 2015.Google Scholar
- Kimball, S., Mattis, P., and The GIMP Development Team. GNU Image Manipulation Program, 2014. URL http://www.gimp.org/.
- Konica Minolta. Precise colour communication, colour control from perception to instrumentation. Konica Minolta Sensing, 2003.Google Scholar
- Krippendorff, K. Bivariate agreement coefficients for reliability of data. Sociological Methodology, 2:139–150, 1970. ISSN 07591063.Google Scholar
- Minolta. Chroma meter instruction manual. Minolta Company, Japan, 1991.Google Scholar
- Munsell Color Company. Munsell color charts for plant tissues. Munsell Color Company, Baltimore, 1952.Google Scholar
- Oliveira, T. P., Zocchi, S. S., and Jacomino, A. P. Measuring color hue in ’Sunrise Solo’ papaya using a flatbed scanner. Revista Brasileira de Fruticultura, 2017.Google Scholar
- R core Team. The R environment, 2015. URL https://www.r-project.org/.
- Silva-Ayala, T., Schnell, R. J., Meerow, A. W., Winterstein, M., Cervantes, C., and Brown, J. S. Determination of color and fruit traits of half-sib families of mango (Mangifera indica L .). Proceedings of the Florida State Horticultural Society, 118:253–257, 2005.Google Scholar
- Sivakumar, D. and Wall, M. M. Papaya fruit quality management during the postharvest supply chain. Food Reviews International, 29:24–48, 2013. ISSN 87559129.Google Scholar