Assessing aquatic toxicity assessment via a clustered variance model

Abstract

Motivated by the need to assess consistency in the outcomes of aquatic toxicity tests conducted by different labs at different time points, we propose a clustering of variance method in linear mixed models. The proposed method, referred as CVM, is able to identify the cluster structure of the variances and estimate model parameters simultaneously. In our proposed method, a penalized approach based on pairwise penalties is proposed to identify the cluster structure. We construct an optimization problem and develop an algorithm based on the alternating direction method of multipliers. Simulation studies show that the proposed approach can identify the cluster structure well and outperforms traditional methods based on k-means. In the end, the proposed approach is applied to the aquatic toxicity assessment data, which gives a more reasonable cluster structure than the traditional methods.