bcrd4r2: Blocked (Random) Cluster-level Regression Discontinuity...

In metinbulus/cosa: Bound Constrained Optimal Sample Size Allocation

Description

Use mdes.bcrd4r2() to calculate minimum detectable effect size, power.bcrd4r2() to calculate statistical power, and use cosa.bcrd4r2() for bound constrained optimal sample size allocation (BCOSSA).

Usage

mdes.bcrd4r2(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, omega3, omega4,
             r21 = 0, r22 = 0, r2t3 = 0, r2t4 = 0, g4 = 0,
             rate.tp = 1, rate.cc = 0, n1, n2, n3, n4)

power.bcrd4r2(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, omega3, omega4,
              r21 = 0, r22 = 0, r2t3 = 0, r2t4 = 0, g4 = 0,
              rate.tp = 1, rate.cc = 0, n1, n2, n3, n4)

cosa.bcrd4r2(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, omega3, omega4,
             g4 = 0, r21 = 0, r22 = 0, r2t3 = 0, r2t4 = 0)

Arguments

score	vector or list; an empirical score variable or an object with class 'score' returned from the inspect.score() function.
dists	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.
k1	left truncation point for (uncentered) empirical, truncated normal, or uniform distribution. Ignored when rhots = 0 or order = 0.
k2	right truncation point for (uncentered) empirical, truncated normal, or uniform distribution. Ignored when rhots = 0 or order = 0.
order	integer >= 0; order of polynomial functional form specification for the score variable.
interaction	logical; if TRUE polynomial specification interacts with the treatment variable.
rhots	obsolote; use order = 0 to obtain results equivalent to random assignment designs.
treat.lower	logical; if TRUE units below the cutoff are treated.
cutoff	decision threshold.
p	proportion of level 2 units in the treatment condition.
power	statistical power (1 - β).
es	effect size (Cohen's d).
alpha	probability of type I error (α).
two.tailed	logical; TRUE for two-tailed hypothesis testing.
df	degrees of freedom.
rho2	proportion of variance in the outcome between level 2 units (unconditional ICC2).
rho3	proportion of variance in the outcome between level 3 units (unconditional ICC3).
rho4	proportion of variance in the outcome between level 4 units (unconditional ICC4).
omega3	ratio of the treatment effect variance between level 3 units to the variance in the outcome between level 3 units.
omega4	ratio of the treatment effect variance between level 4 units to the variance in the outcome between level 4 units.
g4	number of covariates at level 4.
r21	proportion of level 1 variance in the outcome explained by level 1 covariates.
r22	proportion of level 2 variance in the outcome explained by level 2 covariates.
r2t3	proportion of treatment effect variance between level 3 units explained by level 3 covariates.
r2t4	proportion of treatment effect variance between level 4 units explained by level 4 covariates.
rate.tp	treatment group participation rate.
rate.cc	control group crossover rate.
n1	average number of level 1 units per level 2 unit.
n2	average number of level 2 units per level 3 unit.
n3	average number of level 3 units (blocks) per level 4 unit.
n4	number of level 4 units (blocks).
cn1	marginal costs per level 1 unit in treatment and control conditions (positional), e.g. c(10, 5).
cn2	marginal costs per level 2 unit in treatment and control conditions (positional), e.g. c(50, 20).
cn3	marginal cost per level 3 unit.
cn4	marginal cost per level 4 unit.
cost	total cost or budget. Ignored when constrain = "power" or constrain = "es".
p0	starting value for p when rhots = 0 and p = NULL. Starting value is replaced with the average when p is constrained by bounds.
n0	vector of starting values for n1, n2, n3, n4 (positional). Starting values are replaced with the averages when sample sizes are constrained by bounds.
constrain	character; constrains one of the "cost", "power", or "es" at the specified value.
round	logical; TRUE for rounded BCOSSA solution.
max.power	logical; TRUE for maximizing the power rate instead of minimizing the variance. Applies when constrain = "cost".
local.solver	subset of c("LBFGS", "SLSQP").

Value

parms	list of parameters used in the function.
df	degrees of freedom.
sse	standardized standard error.
cosa	BCOSSA solution.
mdes	minimum detectable effect size and (1 - α)% confidence limits.
power	statistical power (1 - β)

Examples

score.obj <- inspect.score(rnorm(1000),
                           order = 1, interaction = FALSE,
                           cutoff = 0, k1 = -1, k2 = 1)

power.bcrd4r2(score.obj,
              es = 0.25, rho2 = .20, rho3 = .10, rho4 = .05,
              omega3 = .30, omega4 = .30,
              g4 = 0, r2t4 = 0,
              n1 = 20, n2 = 3, n3 = 20, n4 = 10)

# minimum required number of level 2 units for each one of the level 3 block
cosa.bcrd4r2(score.obj,
             es = 0.25, rho2 = .20, rho3 = .10, rho4 = .05,
             omega3 = .30, omega4 = .30,
             g4 = 0, r2t4 = 0,
             n1 = 20, n2 = NULL, n3 = 20, n4 = 10)

metinbulus/cosa documentation built on Sept. 9, 2021, 12:04 p.m.