od.2m.only.mod: Using the first-order derivative method to identify the...

In odr: Optimal Design and Statistical Power for Experimental Studies Investigating Main, Mediation, and Moderation Effects

Using the first-order derivative method to identify the optimal sample allocations for moderation effects in two-level multisite randomized trials (MRTs)

Description

The optimal design of two-level MRTs probing moderation effects identify the optimal sample allocations. The optimal design parameters include the level-1 sample size per level-2 unit (n) and the proportion of level-1 individuals/units assigned to the experimental group (p). This function solves the optimal n and/or p with and without a constraint using the first-order derivative method to minimize the variance of the moderation effect estimator. It includes binary or continuous moderators at level 2 or level 1.

Usage

od.2m.only.mod(
  icc = NULL,
  r12 = NULL,
  r22m = NULL,
  c1 = NULL,
  c1t = NULL,
  c2 = NULL,
  omega = 0.01,
  Q = 0.5,
  n = NULL,
  p = NULL,
  m = NULL,
  iter = 300,
  binary = TRUE,
  mod.level = 2,
  nlim = c(2, 300),
  plim = c(0.01, 0.99),
  varlim = c(0, 0.005),
  by = c("n", "p"),
  varlab = "Variance",
  nlab = "Level-One Sample Size (n)",
  plab = "Proportion (p)",
  vartitle = ""
)

Arguments

icc	The unconditional intraclass correlation coefficient (ICC) in population or in each treatment condition.
r12	The proportion of level-1 variance explained by covariates.
r22m	The proportion of variance of site-specific treatment effect explained by covariates.
c1	The cost of sampling one level-1 unit in control condition.
c1t	The cost of sampling one level-1 unit in treatment condition.
c2	The cost of sampling one level-2 unit (site).
omega	The standardized variance of site-specific treatment effect.
Q	The proportion of units in one group for the binary moderator. Default is 0.5.
n	The level-1 sample size per level-2 unit.
p	The proportion of level-1 units within each level 2 unit to be assigned to treatment.
m	The total cost to plot the variance curve. The default value is the total cost of sampling 60 sites at the optimal allocation.
iter	Number of iterations; default value is 100.
binary	Logical; The moderator is binary if TRUE, and continuous if FALSE. The default is TRUE.
mod.level	The level of the moderator is at. The moderator is at level 1 if mod.level is 1, and at level 2 if mod.level is 2. The default is mod.level = 1.
nlim	The plot range for n, default value is c(2, 50).
plim	The plot range for p, default value is c(0, 1).
varlim	The plot range for variance, default value is c(0, 0.05).
by	Dimensions to plot power curves by the optimal design parameters. The default value is by all optimal design parameters for a type of design. For example, default values are by = "p" for single-level designs, by = c("n", "p") for two-level designs, and by = c("n", "p", "J") for three-level designs.
varlab	The plot label for variance, default value is "Variance".
nlab	The plot label for n, default value is "Level-1 Sample Size: n".
plab	The plot label for p, default value is "Proportion Level-1 Units in Treatment: p".
vartitle	The title of variance plot, default value is NULL.

Examples

myod <- od.2m.only.mod(icc = .2, r12 = .5, r22m = .5,
                       c1 = 10, c1t = 100, c2 = 50, omega = .01)
myod$out

odr documentation built on Nov. 5, 2025, 5:12 p.m.