od.1.111m: Jointly optimal sample allocation identification for...

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

Jointly optimal sample allocation identification for single-level randomized controlled trials (RCTs) investigating main and moderation effects (1-1-1m)

Description

The optimal design of single-level RCTs probing main and moderation effects is to identify the jointly optimal sample allocation that use the minimum budget to achieve targeted statistical power for both effects. The optimal design parameter is the proportion of individuals/units assigned to the experimental condition. This function uses the ant colony optimization algorithm to identify the optimal p.

Usage

od.1.111m(
  d = NULL,
  gamma = NULL,
  n = NULL,
  Q = 0.5,
  p = NULL,
  binary = TRUE,
  c1 = NULL,
  c1t = NULL,
  r12 = NULL,
  r.yx = 0,
  r.mx = 0,
  r.ym = 0,
  m = NULL,
  q.main = 1,
  q.mod = 1,
  power.mod = 0.8,
  power.main = 0.8,
  d.p = c(0.1, 0.5),
  sig.level = 0.05,
  two.tailed = TRUE,
  verbose = TRUE,
  nlim = c(20, 1e+07),
  max.value = Inf,
  max.iter = 300,
  e = 1e-10,
  n.of.ants = 10,
  n.of.archive = 50,
  q = 1e-04,
  xi = 0.5
)

Arguments

d	The standardized main effect size.
gamma	Moderated treatment effect.
n	Total number of individuals.
Q	The proportion of individuals in one group the binary moderator. Default value is 0.5, which requires the minimum number of individuals to achieve a targeted power. Change it as necessary.
p	The proportion of individuals assigned to the experimental group.
binary	Logical. The moderator is binary if TRUE and continuous if FALSE. Default is TRUE.
c1	The cost of sampling one unit in control condition.
c1t	The cost of sampling one unit in treatment condition.
r12	The proportion of within-treatment outcome variance explained by covariates in the model that estimated the main effect.
r.yx	Within-treatment correlation between the outcome (y) and the covariate (x) for continuous moderators. Within-treatment within-moderator correlation between the outcome (y) and the covariate (x) for binary moderators.
r.mx	Within-treatment correlation between the moderator (m) and the covariate (x), if specified, for continuous moderators.
r.ym	Within-treatment correlation between the outcome (y) and the moderator (m), if specified, for continuous moderators.
m	Total budget.
q.main	The number of covariates in the model estimating the main effect (besides the treatment, moderator). The default value is 1.
q.mod	The number of covariates in the moderation model (besides the treatment, moderator, and their interaction term). The default value is 1.
power.mod	Statistical power specified for the moderation effect. The default value is .80.
power.main	Statistical power specified for the main effect. The default value is .80.
d.p	The initial sampling domains for p. Default is c(0.10, 0.50).
sig.level	Significance level, default value is .05.
two.tailed	Logical; two-tailed tests if TRUE, otherwise one-tailed tests; default value is TRUE.
verbose	Print out evaluation process if TRUE. The default value is TRUE.
nlim	The range for identifying the root of sample size (n) numerically. Default is c(20, 1e7).
max.value	Maximal value of optimization when used as the stopping criterion. Default is infinite.
max.iter	Maximal number of function evaluations when used as the stopping criterion. The default value is 300.
e	Maximum error value used when solution quality used as the stopping criterion. The default value is 1e-10.
n.of.ants	Number of ants used in each iteration after the initialization stage. The default value is 10.
n.of.archive	Size of the solution archive, default is 20.
q	Locality of the search (0,1). The default value is 0.0001.
xi	Convergence pressure (0, Inf), suggested: (0, 1). The default value is 0.5.

Value

Unconstrained or constrained optimal sample allocation p). The function also returns statistical power for main and moderation effects, function name, design type, and parameters used in the calculation.

Examples

myod <- od.1.111m(d =.1, gamma = .2, r12 = .50,
                 c1 = 10, c1t = 100)
myod

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