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

Abstract

Papaya (Carica papaya L.) is a tropical and climacteric fruit with antioxidant, anticarcinogenic and anti-mutagenic properties, containing carotenoids and high nutritional value.• Brazil is ranked second in the world for papaya production with 17.5% of global production.• One of the most important criteria for determining the ripeness stage over time is the peel color.

Peer Review #1 of "lcc: an R package to estimate the concordance correlation, Pearson correlation and accuracy over time (v0.1)"

“…Since the variance components are estimated using the REML approach, their estimates are asymptotically normally distributed and the bias is smaller when compared to the maximum likelihood (ML) approach. Moreover, Oliveira et al (2018) showed a satisfactory performance of the LCC even in settings with severe imbalance and only a small number of subjects (N = 20).…”

“…denotes the location shift at time t k relative to the scale (Lin, 1989;Oliveira et al, 2018). Consequently, when Var Y i jkl = Var Y i j ′ kl and E Y i jkl = E Y i j ′ kl then C j j ′ (t k ) = 1 and there is no deviation from the 45 • line.…”

“…Point estimation and statistical inference for the LCC ρ j j ′ (t k ) has been proposed by Oliveira et al (2018). It is estimated by replacing β β β and the variance components by their respective REML estimates:…”

“…A confidence interval (CI) for ρ j j ′ (t k ) can be constructed using a nonparametric bootstrap based on M (e.g. 5000) bootstrap samples with either the percentile method (recommended for N ≤ 30) or, otherwise, a normal approximation confidence interval, as described by Oliveira et al (2018).…”

“…Nevertheless, sometimes the researcher is not interested in reducing the CCC for repeated measurements to a single value, as proposed by Carrasco et al (2009) and Carrasco et al (2013), but in describing the extent of agreement between methods over time, as discussed by Liao (2005) in a non-parametric case. However, in the parametric case, we can consider a linear or non-linear function of the time and/or covariates in the model to describe the response variable, as proposed by Rathnayake and Choudhary (2017) and Oliveira et al (2018). Here, we present the implementation of this methodology as an R (R core Team, 2019) package lcc (Oliveira et al, 2019), which provides functions for estimating the longitudinal concordance correlation (LCC) between methods based on variance components and fixed effects using polynomial mixed-effects models.…”