crd3 {cosa}

Cluster-level Regression Discontinuity (Three-level Design, Discontinuity at Level 3, w/ or w/o Strata or Fixed Blocks)

Description

Use mdes.crd3() to calculate minimum detectable effect size, power.crd3() to calculate statistical power, and cosa.crd3() for bound constrained optimal sample size allocation (BCOSSA). If higher level strata or fixed blocks exist, use mdes.bcrd4f3() to calculate minimum detectable effect size, power.bcrd4f3() to calculate statistical power, and cosa.bcrd4f3() for BCOSSA.

Usage

mdes.crd3(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 = n3 - g3 - order * (1 + interaction) - 2,
          rho2, rho3, r21 = 0, r22 = 0, r23 = 0,
          g3 = 0, rate.tp = 1, rate.cc = 0, n1, n2, n3)

power.crd3(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 = n3 - g3 - order * (1 + interaction) - 2,
           rho2, rho3, r21 = 0, r22 = 0, r23 = 0,
           g3 = 0, rate.tp = 1, rate.cc = 0, n1, n2, n3)

cosa.crd3(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, cost = NULL,
          n1 = NULL, n2 = NULL, n3 = NULL,
          n0 = c(10, 3, 100), 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, g3 = 0, r21 = 0, r22 = 0, r23 = 0)

mdes.bcrd4f3(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 * (n3 - 2) - g3 - order * (1 + interaction),
             rho2, rho3, r21 = 0, r22 = 0, r23 = 0, g3 = 0,
             rate.tp = 1, rate.cc = 0, n1, n2, n3, n4)

power.bcrd4f3(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 * (n3 - 2) - g3 - order * (1 + interaction),
              rho2, rho3, r21 = 0, r22 = 0, r23 = 0, g3 = 0,
              rate.tp = 1, rate.cc = 0, n1, n2, n3, n4)

cosa.bcrd4f3(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 + g3 + order * (1 + interaction), 5), 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, g3 = 0, r21 = 0, r22 = 0, r23 = 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 3 units in the treatment condition.

power

statistical power (1 - \beta).

es

effect size (Cohen's d).

alpha

probability of type I error (\alpha).

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).

g3

number of covariates at level 3.

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.

r23

proportion of level 3 variance in the outcome explained by level 3 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

number of level 3 units(per stratum or block, if exists).

n4

number of stratum or fixed 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, 30).

cn3

marginal costs per level 3 unit in treatment and control conditions (positional), e.g. c(80, 50).

cn4

marginal cost per stratum or fixed block.

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 or 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 - \alpha)% confidence limits.

power

statistical power (1 - \beta)

Examples

score.obj <- inspect.score(rnorm(1000),
                           order = 1, interaction = FALSE,
                           cutoff = 0, k1 = -1, k2 = 1)
# single site (no blocks)
power.crd3(score.obj,
           es = .25, rho2 = .20, rho3 = .10,
           g3 = 0, r23 = 0, n1 = 20, n2 = 3, n3 = 40)

# with 5 blocks (note that r23 is modified but g3 remains the same)
power.bcrd4f3(score.obj,
              es = .25, rho2 = .20, rho3 = .10,
              g3 = 0, r23 = .30,
              n1 = 20, n2 = 3, n3 = 40, n4 = 5)

# minimum required number of level 3 units for each block
cosa.bcrd4f3(score.obj,
             es = .25, rho2 = .20, rho3 = .10,
             g3 = 0, r23 = .30,
             n1 = 20, n2 = 2, n3 = NULL, n4 = 5)