od.2m.mod: Optimal sample allocation identification for two-level...

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

Optimal sample allocation identification for two-level multisite randomized trials (MRTs) investigating main and moderation effects

Description

The optimal design of two-level MRTs probing main and 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.

Usage

od.2m.mod(
  n = NULL,
  p = NULL,
  icc = NULL,
  r12 = NULL,
  r22m = NULL,
  c1 = NULL,
  c2 = NULL,
  c1t = NULL,
  omega = NULL,
  m = NULL,
  plots = TRUE,
  plot.by = list(n = "n", p = "p"),
  verbose = TRUE,
  iter = 100,
  tol = 1e-10,
  q = 1,
  q.mod = 1,
  d = 0.1,
  gamma = 0.1,
  power = 0.8,
  power.mod = 0.8,
  mod.level = 1,
  d.p = c(0.1, 0.5),
  d.n = c(2, 1000),
  sig.level = 0.05,
  two.tailed = TRUE,
  Jlim = c(2.5, 1e+10),
  binary = TRUE,
  nrange = c(2, 10000),
  Q = 0.5,
  max.value = Inf,
  max.iter = 300,
  e = 1e-10,
  n.of.ants = 10,
  n.of.archive = 50,
  q.aco = 1e-04,
  xi = 0.5
)

Arguments

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.
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.
c2	The cost of sampling one level-2 unit (site).
c1t	The cost of sampling one level-1 unit in treatment condition.
omega	The treatment-by-site variance of the outcome.
m	Total budget, default is the total costs of sampling 60 sites.
plots	Logical, provide variance plots if TRUE, otherwise not; default value is TRUE.
plot.by	Plot the variance by n and/or p; default value is plot.by = list(n = "n", p = "p").
verbose	Logical; print the values of n and p if TRUE, otherwise not; default value is TRUE.
iter	Number of iterations; default value is 100.
tol	Tolerance for convergence; default value is 1e-10.
q	The number of covariates in the model detecting the main/average treatment effect. The default is 1.
q.mod	The number of predictors at the moderator level in the moderation model.
d	Standardized effect size, default is 0.1.
gamma	The standardized moderated treatment effect.
power	Statistical power specified for the main effect. The default is .80.
power.mod	Statistical power for the moderation effect. The default is .80.
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.
d.p	The initial sampling domains for p. Default is c(0.1, 0.5).
d.n	The initial sampling domain for n. Default is c(2, 1000).
sig.level	Significance level or type I error rate, default value is 0.05.
two.tailed	Logical; two-tailed tests if TRUE, otherwise one-tailed tests; default value is TRUE.
Jlim	The range for solving the root of level-2 sample size (J) numerically. Change the default values to a larger range (e.g., starting with a smaller value) if f() values at end points are not of opposite sign. For example, use Jlim = c(1.5, 1e10).
binary	Logical; The moderator is binary if TRUE, and continuous if FALSE. The default is TRUE.
nrange	The range of the level-1 sample size per level-2 unit that used to exclude unreasonable values. Default value is c(2, 10000).
Q	The proportion of units in one group for the binary moderator. Default is 0.5.
max.value	Maximal value of optimization when used as the stopping criterion. Default is -Inf.
max.iter	Maximal number of function evaluations when used as the stopping criterion.
e	Maximum error value used when solution quality used as the stopping criterion, default is 1e-10.
n.of.ants	Number of ants used in each iteration after the initialization of power analysis for calculating required budget, default value is 10.
n.of.archive	Size of the solution archive, default is 100.
q.aco	The locality of the search (0, 1)
xi	Convergence pressure (0, Inf), suggested: (0, 1), default is 0.5.

Value

Unconstrained or constrained optimal sample allocation (n and p). The function also returns statistical power formulas, function name, design type, and parameters used in the calculation.

Examples

myod <- od.2m.mod(icc = .2, r12 = .5, r22m = .5,
                  c1 = 10, c1t = 100, c2 = 50, omega = .01,
                  gamma = 0.1)
myod$out

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