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

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Abstract

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.

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Acknowledgements

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.

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Authors and Affiliations

  1. Departamento de Ciências Exatas, Escola Superior de Agricultura Luiz de Queiroz, Universidade de São Paulo (USP), Av. Pádua Dias, 11, Piracicaba, SP, 13418-900, Brazil

    Thiago de Paula Oliveira & Silvio Sandoval Zocchi

  2. School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, University Rd, Galway, Ireland

    John Hinde

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  1. Thiago de Paula Oliveira
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  2. John Hinde
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  3. Silvio Sandoval Zocchi
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Correspondence to Thiago de Paula Oliveira.

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Oliveira, T.d.P., Hinde, J. & Zocchi, S.S. Longitudinal Concordance Correlation Function Based on Variance Components: An Application in Fruit Color Analysis. JABES 23, 233–254 (2018). https://doi.org/10.1007/s13253-018-0321-1

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