Latin Hypercube Design Under Second and Third-Order Models: A Prediction Variance Approach

JASDS: Journal of Applied Statistics and Data Science
Vol. 3 No. 1 (2026): Journal of Applied Statistics and Data Science

Prediction variance describes the error involved with making a prediction using a response surface model. This study examines the prediction variance performance of Latin Hypercube Designs (LHDs) within second- and third-order response surface models. G-optimality, I-optimality criteria, and Fraction of Design Space (FDS) plots were employed to assess the predictive capabilities and accuracy of LHDs. The findings reveal that LHDs perform better under third-order models when evaluated using the G-optimality criterion, while under the I-optimality criterion, LHDs perform better in second-order models. The FDS plots further indicate that as the number of factors increases, the prediction errors across models become approximately similar.