A flexible partially linear regression with random effects for bimodal data with application in postharvest

Abstract

In the postharvest area of agricultural products, it is common to have data sets in which the dependent variable in general may not be symmetrical and unimodal, therefore, the use of usual regression models is not always appropriate. In addition, the data can also have repeated measurements over time. With this in mind, the aim of this article is to propose a partially linear regression model with random effects for postharvest bimodal data, this extended regression is based on the Birnbaum–Saunders distribution. Additionally we present different mathematical properties of this new model. To verify the impartiality and accuracy of the estimators, a simulation study was carried out. The parameters of partially linear regression with random effects are estimated using the penalized maximum likelihood. The results of the developed model are presented empirically and indicate that the storage temperature can cause a significant change in the lychee’s respiratory metabolism. Thus, according to the model selection and residue analysis measures, it can be concluded that the proposed model is a statistical tool for postharvest data, providing an adequate analysis.