Optimal Covariate Allocation in Asymmetrical Factorial Designs: A Comparative Analysis of Design Choices

Abstract

Factorial designs play a crucial role in experimental research, enabling the examination of multiple factors and their influence on an outcome variable. This study delves into asymmetrical factorial designs, which are particularly useful when factors have differing numbers of levels. Expanding upon the work of Sinha et al. (2014, 2019), we examine a specific asymmetrical factorial design featuring two factors: one with two levels and the other with three, resulting in six distinct treatment combinations. We consider three design choices for assigning covariate values to these treatment pairs, aiming to optimize the estimation of treatment contrasts and two regression parameters. Each design offers a distinct covariate configuration, and we assess their efficiency through the information matrix and the average variance of treatment contrasts. The paper includes a comprehensive explanation of the statistical model, an evaluation of the information matrix and variance efficiency for each design, and a comparison of the average variance of treatment contrasts. Our results provide valuable insights into optimizing experimental designs in asymmetrical factorial contexts, emphasizing the trade-offs between various design strategies.

IJSS, Vol. 24(2) Special, December, 2024, pp 49-66