Developer Tutorial - Handling Covariates Effectively when Designing Experiments

• What is a Covariate?
  • Input variable(s) we want to account for, but don't have complete control.
  • Uncontrolled, but observable ahead of time.
  • "Candidate Set" approach.
• Why does it matter to Custom Design?
  • Coordinate-Exchange (Custom Design)
    • Start with a "random" design.
    • Go through design element-by-element, make a switch if it improves criterion.
    • Repeat.
    • No requirement for a candidate set.
  • Row-Exchange
    • PROC OPTEX (SAS)
    • Start with a candidate set of possible runs.
    • Initial design is a subset of the candidate set.
    • Consider swapping rows not in the design, making the switch if it improves criterion.
• Prior to JMP 16 (starting with JMP 10)
  • Row-exchange on the covariates (D-optimality).
  • Coordinate-exchange on the controllable factors.
  • Covariates were fixed from the beginning and we couldn't go back to see if there's something better.
• JMP 16
  • Hybrid approach with row-exchange or coordinate-exchange as we go through the design.
  • Allows for different optimality criteria to be considered for the covariates.
  • More flexibility for your design creation (best of both worlds).
  • Much more visible to the user.
  • How to use
    • Does not require JMP Pro.
    • Need a data table with candidate set (covariates with our possible runs).
    • Add covariates in Custom Design using Add Factor->Covariate (JMP 10+) or the "Covariates/Candidate Set" outline (JMP 16+).
• Two typical use cases
  • Using all rows
    • We have observable, uncontrollable factors for our experimental units that we want to account for.
    • We want to force a particular structure for a subset of inputs (that may even be controllable).
  • Choosing a subset of rows
    • Pick an optimal subset (NOT a random subset).
    • Maximizing our information for our budget.

• Example 1 - Using all Rows

  • We want 12 runs, 5 2-level factors, but factor A needs 2/3 of the levels at "L1" and 1/3 at "L2".

• Example 2 - Using all Rows
  • Use Big Class data set, want to assign one of 2 treatments to each student.
  • We want to account for gender, height, and weight.
• Example 3 - Using all Rows
  • Blocks of size 4, an 8-level categorical, and 4 continuous factors.
  • 56 runs total.
  • Use a balanced incomplete block design (BIBD) to start.

• Example 4 - Using subset of Rows

  • Only want to pick 20 students from Big Class.

  • What about if there are certain students we want to ensure are chosen?

  • Add the batch label, but remove it from the model

Resources

• Meyer, R. K., & Nachtsheim, C. J. The coordinate-exchange algorithm for constructing exact optimal experimental designs. Technometrics, 37(1), 60-69, 1995. PDF version.
• Fedorov, V.V.  Theory of Optimal Experiments. Academic Press, New York, 1992.
• Goos, P & Jones, B. Optimal Design of Experiments - A Case Study Approach, Wiley, 2011.
• How to create an experiment design that is robust to a linear time trend in the response blog by Bradley Jones.
• JMP Documentation on covariate DOE
• JMP Wish List: Product suggestions for our Development Team about what your organization needs to get the most out of JMP.