rpe function

Relative precision and efficiency (RPE) calculation

Calculate the relative precision and efficiency (RPE) between two designs, it returns same results as those from function re.

rpe(od, subod, rounded = TRUE, verbose = TRUE)

Arguments

• od: Returned object of first design (e.g., unconstrained optimal design) from function od.1, od.2, od.3, od.4, od.2m, od.3m, or od.4m.

• subod: Returned object of second design (e.g., constrained optimal design) from function od.1, od.2, od.3, od.4, od.2m, od.3m, or od.4m.

• rounded: Logical; round the values of p, n/J/K

  that are from functions to two decimal places and integer, respectively if TRUE, no rounding if FALSE; default is TRUE.

• verbose: Logical; print the value of relative precision and efficiency if TRUE, otherwise not; default is TRUE.

Returns

Relative precision and efficiency value.

Examples

# Unconstrained optimal design of 2-level CRT #----------
  myod1 <- od.2(icc = 0.2, r12 = 0.5, r22 = 0.5, c1 = 1, c2 = 5, c1t = 1, c2t = 50,
              varlim = c(0.01, 0.02))
# Constrained optimal design with n = 20
  myod2 <- od.2(icc = 0.2, r12 = 0.5, r22 = 0.5, c1 = 1, c2 = 5, c1t = 1, c2t = 50,
              n = 20, varlim = c(0.005, 0.025))
# Relative precision and efficiency (RPE)
  myrpe <- rpe(od = myod1, subod= myod2)
  myrpe$rpe # RPE = 0.88
# Constrained optimal design with p = 0.5
  myod2 <- od.2(icc = 0.2, r12 = 0.5, r22 = 0.5, c1 = 1, c2 = 5, c1t = 1, c2t = 50,
             p = 0.5, varlim = c(0.005, 0.025))
# Relative precision and efficiency (RPE)
  myrpe <- rpe(od = myod1, subod= myod2)
  myrpe$rpe # RPE = 0.90

# Unconstrained optimal design of 3-level CRT #----------
  myod1 <- od.3(icc2 = 0.2, icc3 = 0.1, r12 = 0.5, r22 = 0.5, r32 = 0.5,
             c1 = 1, c2 = 5, c3 = 25, c1t = 1, c2t = 50, c3t = 250,
             varlim = c(0.005, 0.025))
# Constrained optimal design with J = 20
  myod2 <- od.3(icc2 = 0.2, icc3 = 0.1, r12 = 0.5, r22 = 0.5, r32 = 0.5, J = 20,
             c1 = 1, c2 = 5, c3 = 25, c1t = 1, c2t = 50, c3t = 250,
             varlim = c(0, 0.025))
# Relative precision and efficiency (RPE)
  myrpe <- rpe(od = myod1, subod= myod2)
  myrpe$rpe # RPE = 0.53

# Unconstrained optimal design of 4-level CRT #---------
  myod1 <- od.4(icc2 = 0.2, icc3 = 0.1, icc4 = 0.05, r12 = 0.5,
              r22 = 0.5, r32 = 0.5, r42 = 0.5,
              c1 = 1, c2 = 5, c3 = 25, c4 = 125,
              c1t = 1, c2t = 50, c3t = 250, c4t = 2500,
              varlim = c(0, 0.01))
# Constrained optimal design with p = 0.5
  myod2 <- od.4(icc2 = 0.2, icc3 = 0.1, icc4 = 0.05, r12 = 0.5, p = 0.5,
              r22 = 0.5, r32 = 0.5, r42 = 0.5,
              c1 = 1, c2 = 5, c3 = 25, c4 = 125,
              c1t = 1, c2t = 50, c3t = 250, c4t = 2500,
              varlim = c(0, 0.01))
# Relative precision and efficiency (RPE)
  myrpe <- rpe(od = myod1, subod= myod2)
  myrpe$rpe # RPE = 0.78

References

(1) Shen, Z., & Kelcey, B. (2020). Optimal sample allocation under unequal costs in cluster-randomized trials. Journal of Educational and Behavioral Statistics, 45(4): 446–474. https://doi.org/10.3102/1076998620912418 (2) Shen, Z., & Kelcey, B. (in press). Optimal sample allocation in multisite randomized trials. The Journal of Experimental Education. https://doi.org/10.1080/00220973.2020.1830361 (3) Shen, Z., & Kelcey, B. (in press). Optimal sampling ratios in three-level multisite experiments. Journal of Research on Educational Effectiveness.