Use mdes.bird4()
to calculate minimum detectable effect size, power.bird4()
to calculate statistical power, and cosa.bird4()
for bound constrained optimal sample size allocation (BCOSSA).
mdes.bird4(score = NULL, dists = "normal", k1 = -6, k2 = 6,
order = 1, interaction = FALSE,
treat.lower = TRUE, cutoff = 0, p = NULL,
power = .80, alpha = .05, two.tailed = TRUE, df = n4 - g4 - 1,
rho2, rho3, rho4, omega2, omega3, omega4,
r21 = 0, r2t2 = 0, r2t3 = 0, r2t4 = 0, g4 = 0,
rate.tp = 1, rate.cc = 0, n1, n2, n3, n4)power.bird4(score = NULL, dists = "normal", k1 = -6, k2 = 6,
order = 1, interaction = FALSE,
treat.lower = TRUE, cutoff = 0, p = NULL,
es = .25, alpha = .05, two.tailed = TRUE, df = n4 - g4 - 1,
rho2, rho3, rho4, omega2, omega3, omega4,
r21 = 0, r2t2 = 0, r2t3 = 0, r2t4 = 0, g4 = 0,
rate.tp = 1, rate.cc = 0, n1, n2, n3, n4)
cosa.bird4(score = NULL, dists = "normal", k1 = -6, k2 = 6, rhots = NULL,
order = 1, interaction = FALSE,
treat.lower = TRUE, cutoff = 0, p = NULL,
cn1 = 0, cn2 = 0, cn3 = 0, cn4 = 0, cost = NULL,
n1 = NULL, n2 = NULL, n3 = NULL, n4 = NULL,
n0 = c(10, 3, 100, 5 + g4), p0 = .499,
constrain = "power", round = TRUE, max.power = FALSE,
local.solver = c("LBFGS", "SLSQP"),
power = .80, es = .25, alpha = .05, two.tailed = TRUE,
rho2, rho3, rho4, omega2, omega3, omega4,
g4 = 0, r21 = 0, r2t2 = 0, r2t3 = 0, r2t4 = 0)
vector or list; an empirical score variable or an object with class 'score' returned from the inspect.score()
function.
character; distribution of the score variable, "normal"
or "uniform"
. By default, dists = "normal"
specification implies a truncated normal distribution with k1 = -6
and k2 = 6
.
left truncation point for (uncentered) empirical, truncated normal, or uniform distribution. Ignored when rhots = 0
or order = 0
.
right truncation point for (uncentered) empirical, truncated normal, or uniform distribution. Ignored when rhots = 0
or order = 0
.
integer >= 0; order of polynomial functional form specification for the score variable.
logical; if TRUE
polynomial specification interacts with the treatment variable.
obsolote; use order = 0
to obtain results equivalent to random assignment designs.
logical; if TRUE
units below the cutoff are treated.
decision threshold.
proportion of level 1 units in the treatment condition.
statistical power (1 - \(\beta\)).
effect size (Cohen's d).
probability of type I error (\(\alpha\)).
logical; TRUE
for two-tailed hypothesis testing.
degrees of freedom.
proportion of variance in the outcome between level 2 units (unconditional ICC2).
proportion of variance in the outcome between level 3 units (unconditional ICC3).
proportion of variance in the outcome between level 4 units (unconditional ICC4).
ratio of the treatment effect variance between level 2 units to the variance in the outcome between level 2 units.
ratio of the treatment effect variance between level 3 units to the variance in the outcome between level 3 units.
ratio of the treatment effect variance between level 4 units to the variance in the outcome between level 4 units.
number of covariates at level 4.
proportion of level 1 variance in the outcome explained by level 1 covariates.
proportion of treatment effect variance between level 2 units explained by level 2 covariates.
proportion of treatment effect variance between level 3 units explained by level 3 covariates.
proportion of treatment effect variance between level 4 units explained by level 4 covariates.
treatment group participation rate.
control group crossover rate.
average number of level 1 units per level 2 unit.
average number of level 2 units (blocks) per level 3 unit.
average number of level 3 units (blcoks) per level 4 unit.
number of level 4 units (blocks).
marginal costs per level 1 unit in treatment and control conditions (positional), e.g. c(10, 5)
.
marginal cost per level 2 unit.
marginal cost per level 3 unit.
marginal cost per level 4 unit.
total cost or budget. Ignored when constrain = "power"
or constrain = "es"
.
starting value for p
when rhots = 0
and p = NULL
. Starting value is replaced with the average when p
is constrained by bounds.
vector of starting values for n1, n2, n3, n4
(positional). Starting values are replaced with the averages when sample sizes are constrained by bounds.
character; constrains one of the "cost"
, "power"
, or "es"
at the specified value.
logical; TRUE
for rounded BCOSSA solution.
logical; TRUE
for maximizing the power rate instead of minimizing the variance. Applies when constrain = "cost"
.
subset of c("LBFGS", "SLSQP")
.
list of parameters used in the function.
degrees of freedom.
standardized standard error.
BCOSSA solution.
minimum detectable effect size and (1 - \(\alpha\))% confidence limits.
statistical power (1 - \(\beta\))
# NOT RUN {
score.obj <- inspect.score(rnorm(1000),
order = 1, interaction = FALSE,
cutoff = 0, k1 = -1, k2 = 1)
power.bird4(score.obj,
es = .25, rho2 = .20, rho3 = .10, rho4 = .05,
omega2 = .30, omega3 = .30, omega4 = .30,
g4 = 0, r2t4 = 0, n1 = 20, n2 = 3, n3 = 20, n4 = 5)
# minimum required number of level 1 units for each one of the level 2 block
cosa.bird4(score.obj, order = 2,
es = .25, rho2 = .20, rho3 = .10, rho4 = .05,
omega2 = .30, omega3 = .30, omega4 = .30,
g4 = 0, r2t4 = 0, n1 = NULL, n2 = 3, n3 = 20, n4 = 5)
# }
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