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ForLion: An R Package for Finding Optimal Experimental Designs with Mixed Factors

Siting Lin, Yifei Huang, Jie Yang

Abstract

Optimal design is crucial for experimenters to maximize the information collected from experiments and estimate the model parameters most accurately. ForLion algorithms have been proposed to find D-optimal designs for experiments with mixed types of factors. In this paper, we introduce the ForLion package which implements the ForLion algorithm to construct locally D-optimal designs and the Expected Weighted (EW) ForLion algorithm to generate robust EW D-optimal designs, which maximize the determinant of the expected Fisher information matrix under parameter uncertainty. The package supports experiments under linear models (LM), generalized linear models (GLM), and multinomial logistic models (MLM) with continuous, discrete, or mixed-type factors. It provides both optimal approximate designs and an efficient function converting approximate designs into exact designs with integer-valued allocations of experimental units. Tutorials are included to show the package's usage across different scenarios.

ForLion: An R Package for Finding Optimal Experimental Designs with Mixed Factors

Abstract

Optimal design is crucial for experimenters to maximize the information collected from experiments and estimate the model parameters most accurately. ForLion algorithms have been proposed to find D-optimal designs for experiments with mixed types of factors. In this paper, we introduce the ForLion package which implements the ForLion algorithm to construct locally D-optimal designs and the Expected Weighted (EW) ForLion algorithm to generate robust EW D-optimal designs, which maximize the determinant of the expected Fisher information matrix under parameter uncertainty. The package supports experiments under linear models (LM), generalized linear models (GLM), and multinomial logistic models (MLM) with continuous, discrete, or mixed-type factors. It provides both optimal approximate designs and an efficient function converting approximate designs into exact designs with integer-valued allocations of experimental units. Tutorials are included to show the package's usage across different scenarios.

Paper Structure

This paper contains 14 sections, 18 equations, 5 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Method
  3. ForLion algorithm
  4. Lift-one algorithm
  5. EW ForLion algorithm
  6. Rounding algorithm
  7. ForLion Package Structure
  8. Examples
  9. An MLM example: Emergence of house flies experiment
  10. A GLM example: Electrostatic discharge (ESD) experiment
  11. Summary and Discussion
  12. Function arguments
  13. Assessing the sensitivity of the locally D-optimal design against random seeds
  14. Another example: A model with a three-level discrete factor and an interaction involving the continuous factor

Figures (5)

  • Figure 1: An outline of the ForLion algorithm under a general statistical model.
  • Figure 2: An outline of the GLM-adapted ForLion algorithm.
  • Figure 3: An outline of the rounding algorithm.
  • Figure 4: The key functions in the ForLion package and the corresponding structure.
  • Figure S1: Number of design points, minimum distance among design points (rounded to two decimals), and relative efficiency w.r.t. the design with $\delta=0.15$ and random seed 123