Estimation and Prediction in Transformed Nested Error Regression Models

TL;DR

This paper introduces transformed nested error regression models (TNERM) that improve data modeling by flexible transformations, providing consistent estimation, prediction, and accurate prediction intervals validated through simulations and empirical data.

Contribution

It proposes a new class of transformed nested error regression models with consistent estimation procedures and second-order accurate prediction intervals using bootstrap methods.

Findings

The methods perform well in simulations.

The models effectively handle data transformation.

Prediction intervals achieve second-order accuracy.

Abstract

This paper suggests parametrically transformed nested error regression models (TNERM), which transform the data flexibly to follow the normal linear mixed regression. We provide a procedure for estimating consistently the parameters of the proposed model and a predictor based on the consistent estimators. Then, in order to calibrate uncertainty of the transformed empirical best linear unbiased predictor, we derive prediction intervals with second-order accuracy based on the parametric bootstrap method. The proposed methods are investigated through simulation and empirical studies.