# Optimal Designs for Prediction in Two Treatment Groups Random Coefficient Regression Models

## TL;DR

This paper develops optimal experimental designs for estimating fixed effects and predicting random effects in two-treatment group random coefficient regression models, enhancing efficiency in such statistical analyses.

## Contribution

It introduces A- and D-optimality criteria tailored for these models, providing a systematic approach to design optimal experiments for fixed and random effect estimation.

## Key findings

- Optimal designs improve estimation accuracy.
- Illustrative example demonstrates design behavior.
- Criteria facilitate efficient experimental planning.

## Abstract

The subject of this work is two treatment groups random coefficient regression models, in which observational units receive some group-specific treatments. We provide A- and D-optimality criteria for the estimation of the fixed parameter and the prediction of the random effects. We illustrate the behavior of optimal designs by a simple example.