This function can calculate power, required sample size/budget for desired power, or minimum detectable moderation effect size (MDMES) under a fixed budget in two-level CRTs. It also can perform conventional power analyses (e.g., required sample size, power, and MDMES calculation).
power.2.mod(
cost.model = TRUE,
expr = NULL,
constraint = NULL,
sig.level = 0.05,
two.tailed = TRUE,
gamma = NULL,
power.mod = NULL,
m = NULL,
n = NULL,
J = NULL,
p = NULL,
icc = NULL,
r12 = NULL,
r22 = NULL,
r12m = NULL,
r22m = NULL,
q.mod = 1,
c1 = NULL,
c2 = NULL,
c1t = NULL,
c2t = NULL,
gammalim = c(0, 5),
powerlim = c(1e-10, 1 - 1e-10),
Jlim = c(5.5, 1e+10),
binary = TRUE,
mlim = NULL,
rounded = TRUE,
Q = 0.5
)Required budget (and/or required level-2 sample size), statistical power, or MDMES depending on the specification of parameters. The function also returns the function name, design type, and parameters used in the calculation.
Logical; power analyses accommodating costs and budget (e.g., required budget for desired power, power/MDES under fixed budget) if TRUE, otherwise conventional power analyses (e.g., required sample size, power, or MDES calculation); default value is TRUE.
Returned objects from function od.2.mod; default is NULL;
if expr is specified, parameter values of icc,
r12, r22, r12m, r22m,
c1, c2,
c1t, c2t, p, and n
used or solved in function od.2.mod will
be passed to the current function;
only the values of p and n that specified or solved in
function od.2.mod can be overwritten
if constraint is specified.
Specify the constrained values of p and/or n
in list format to overwrite those from expr; default value is NULL.
Significance level or type I error rate, default value is 0.05.
Two tailed test, the default value is TRUE.
The standardized moderated treatment effect (i.e., regression coefficient of the interaction term of moderator and treatment).
Statistical power specified for moderation. The default value is .80.
Total budget.
The level-1 sample size per level-2 unit.
The total level-2 sample size.
The proportion of level-2 clusters/units to be assigned to treatment.
The unconditional intraclass correlation coefficient (ICC) in population or in each treatment condition.
The proportion of level-1 variance explained by covariates.
The proportion of level-2 variance explained by covariates.
The proportion of outcome variance at the individual level explained by covariates in the model with the moderator.
The proportion of outcome variance at the cluster level explained by covariates in the model with the moderator.
The number of cluster-level covariates in the model (except the treatment indicator, moderator, and the interaction term). The default value is 1.
The cost of sampling one level-1 unit in control condition.
The cost of sampling one level-2 unit in control condition.
The cost of sampling one level-1 unit in treatment condition.
The cost of sampling one level-2 unit in treatment condition.
The range for numerically solving the root of standardized moderation effect (gamma). Default is c(0, 5).
The range for solving the root of power (power) numerically,
default value is c(1e-10, 1 - 1e-10).
The range for numerically solving the root of
the sample size requirement(J).
Logical; The moderator is binary if TRUE, and continuous if FALSE. The default is TRUE.
The range for numerically solving the root of budget (m).
The default is NULL, which mlim = Jlim times the costs for each site and
its members.
Logical; round n and p that are from functions od.2
to integer and two decimal places, respectively if TRUE,
otherwise no rounding; default value is TRUE.
The proportion of binary moderator that coded as 1. Default is 0.50.
Statistical power.mod for a moderation effect.
myod <- od.2.mod(icc = .2, r12 = .5, r22 = .5,
c1 = 10, c1t = 100, c2 = 50, c2t = 500,
gamma = 0.2, d = 0.2)
mypower <- power.2.mod(expr = myod, m=myod$out$m, gamma = 0.2); mypower$out
mym <- power.2.mod(expr = myod, power.mod = .80, gamma = 0.2); mym$out
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