Reconsidering the estimation of costs of phenotypic plasticity using the robust ridge estimator

Abstract

No coherent message has emerged from previous studies that have attempted to detect cost of plasticity. We infer that a major cause of this lack of coherence arises from the use of an inappropriate statistical method—ordinary least squares (OLS) estimation—which gives poor estimates in the presence of multicollinearity and outliers in data. The robust ridge estimator can handle the problems of multicollinearity and outliers simultaneously. In some simulation scenarios, this estimator has been observed to be resistant to outliers and less affected by multicollinearity compared with the OLS estimator. This paper aims to confirm the reliability of the robust ridge estimator in an extreme scenario (small sample size, few explanatory variables, high levels of multicollinearity, and high rates of outliers) wherein we faced underestimating costs of plasticity. We conducted simulations to compare the performance of the robust ridge estimator with the OLS estimator. The robust ridge estimator performed better than the OLS estimator did. We applied the robust ridge estimator for two ecological datasets, where the conventional OLS estimator incorrectly underestimated costs of plasticity. We concluded that cost of plasticity is a detectable entity in ecological data under rigorous experiment with an appropriate statistical analysis.