PowerUpR (version 1.0.4)

cra3r3: Three-level Cluster-randomized Trials to Detect Main, Moderation, and Mediation Effects

Description

Use mdes.<design>() to calculate the minimum detectable effect size for the main effect, mdesd.<design>() to calculate the minimum detectable effect size difference for the moderation effect, power.<design>() to calculate the statistical power, and mrss.<design>() to calculate the minimum required sample size. Use <output>.cra3r3() for the main effect, <output>.mod331() for the moderator at level 1, <output>.mod332() for the moderator at level 2, <output>.mod333() for the moderator at level 3. Usepower.med321() for 3-2-1 mediation.

Usage

mdes.cra3r3(power=.80, alpha=.05, two.tailed=TRUE,
            rho2, rho3, p=.50, g3=0, r21=0, r22=0, r23=0,
            n, J, K)
mdesd.mod331(power=.80, alpha=.05, two.tailed=TRUE,
            rho2, rho3, omegam2=0, omegam3=0,
            g1=0, r21=0, r2m2=0, r2m3=0,
            p=.50, q=NULL, n, J, K)
mdesd.mod332(power=.80, alpha=.05, two.tailed=TRUE,
            rho2, rho3, omegam3, g2=0, r21=0, r22=0, r2m3=0,
            p=.50, q=NULL, n, J, K)
mdesd.mod333(power=.80, alpha=.05, two.tailed=TRUE,
            rho2, rho3,  g3=0, r21=0, r22=0, r23=0,
            p=.50, q=NULL, n, J, K)
power.cra3r3(es=.25, alpha=.05, two.tailed=TRUE,
             rho2, rho3, g3=0, r21=0, r22=0, r23=0,
             p=.50, n, J, K)
power.mod331(es=.25, alpha=.05, two.tailed=TRUE,
             rho2, rho3, omegam2, omegam3,
             g1=0, r21=0, r2m2=0, r2m3=0,
             p=.50, q=NULL, n, J, K)
power.mod332(es=.25, alpha=.05, two.tailed=TRUE,
             rho2, rho3, omegam3, g2=0, r21=0, r22=0, r2m3=0,
             p=.50, q=NULL, n, J, K)
power.mod333(es=.25, alpha=.05, two.tailed=TRUE,
             rho2, rho3, g3=0, r21=0, r22=0, r23=0,
             p=.50, q=NULL, n, J, K)
power.med321(esa, esB, two.tailed=TRUE, alpha=.05,
             mc=FALSE, nsims=1000, ndraws=1000,
             rhom3, rho2, rho3, r2m2, r2m3, r21, r22, r23,
             p=.50, n, J, K)
mrss.cra3r3(es=.25, power=.80, alpha=.05, two.tailed=TRUE,
            n, J, K0=10, tol=.10,
            rho2, rho3, p=.50, g3=0, r21=0, r22=0, r23=0)
mrss.mod331(es=.25, power=.80, alpha=.05, two.tailed=TRUE,
            rho2, rho3, omegam2, omegam3,
            g1=0, r21=0, r2m2=0, r2m3=0,
            p=.50, q=NULL, n, J, K0=10, tol=.10)
mrss.mod332(es=.25, power=.80, alpha=.05, two.tailed=TRUE,
            rho2, rho3, omegam3, g2=0, r21=0, r22=0, r2m3=0,
            p=.50, q=NULL, n, J, K0=10, tol=.10)
mrss.mod333(es=.25, power=.80, alpha=.05, two.tailed=TRUE,
            rho2, rho3, g3=0, r21=0, r22=0, r23=0,
            p=.50, q=NULL, n, J, K0=10, tol=.10)

Arguments

power

statistical power \((1-\beta)\).

es, esa, esB

effect size for main/moderator effects, or for path coefficients a (treatment - mediator), or B (overall mediator - outcome) in the mediation model.

alpha

probability of type I error.

two.tailed

logical; TRUE for two-tailed hypothesis testing, FALSE for one-tailed hypothesis testing.

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).

rhom3

proportion of variance in the mediator between level 3 units.

omegam2

ratio of the unconditional variance in the moderator effect that is between level 2 units to the residual variance between level 2 units in the null model.

omegam3

ratio of the unconditional variance in the moderator effect that is between level 3 units to the residual variance between level 3 units in the null model.

p

proportion of level 3 units randomly assigned to treatment.

q

proportion of level 1, level 2, or level 3 units in the moderator subgroup.

g1

number of covariates at level 1.

g2

number of covariates at level 2.

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.

r2m2

proportion of variance in the moderator (or mediator) effect that is explained by level 2 predictors. For the mediation model, proportion of mediator variance at level 2 explained by level 2 predictors.

r2m3

proportion of variance in the moderator (or mediator) effect that is explained by level 3 predictors. For the mediation model, proportion of aggregated mediator variance at level 3 explained by level 3 predictors.

n

harmonic mean of level 1 units across level 2 units (or simple average).

J

harmonic mean of level 2 units across level 3 units (or simple average).

K

level 3 sample size.

K0

starting value for K.

tol

tolerance to end iterative process for finding K.

mc

logical; TRUE for monte carlo simulation based power.

nsims

number of replications, if mc = TRUE.

ndraws

number of draws from the distribution of the path coefficients for each replication, if mc = TRUE.

Value

fun

function name.

parms

list of parameters used in power calculation.

df

degrees of freedom.

ncp

noncentrality parameter.

power

statistical power \((1-\beta)\).

mdes

minimum detectable effect size.

K

number of level 3 units.

See Also

For a more flexible sample size determination see cosa.crd3r3.

Examples

# NOT RUN {
# cross-checks for the main effect
mdes.cra3r3(rho3=.06, rho2=.17, n=15, J=3, K=60)
power.cra3r3(es=.269, rho3=.06, rho2=.17, n=15, J=3, K=60)
mrss.cra3r3(es=.269, rho3=.06, rho2=.17, n=15, J=3)

# cross-checks for the randomly varying cont. L1 moderator effect
mdes.mod331(power=.80, alpha=.05, two.tailed=TRUE,
            rho2=.17, rho3=.06, omegam2=.10, omegam3=.10,
            q=NULL, n=15, J=3, K=60)
power.mod331(es=0.1248, alpha=.05, two.tailed=TRUE,
            rho2=.17, rho3=.06, omegam2=.10, omegam3=.10,
            q=NULL, n=15, J=3, K=60)
mrss.mod331(es=0.1248, alpha=.05, two.tailed=TRUE,
            rho2=.17, rho3=.06, omegam2=.10, omegam3=.10,
            q=NULL, n=15, J=3)

# cross-checks for the non-randomly varying cont. L1 moderator effect
mdesd.mod331(power=.80, alpha=.05, two.tailed=TRUE,
            rho2=.17, rho3=.06, omegam2=0, omegam3=0,
            q=NULL, n=15, J=3, K=60)
power.mod331(es=.0946, alpha=.05, two.tailed=TRUE,
            rho2=.17, rho3=.06, omegam2=0, omegam3=0,
            q=NULL, n=15, J=3, K=60)
mrss.mod331(es=.0946, alpha=.05, two.tailed=TRUE,
            rho2=.17, rho3=.06, omegam2=0, omegam3=0,
            q=NULL, n=15, J=3)

# cross-checks for the randomly varying bin. L1 moderator effect
mdesd.mod331(power=.80, alpha=.05, two.tailed=TRUE,
            rho2=.17, rho3=.06, omegam2=.10, omegam3=.10,
            q=.50, n=15, J=3, K=60)
power.mod331(es=.2082, alpha=.05, two.tailed=TRUE,
            rho2=.17, rho3=.06, omegam2=.10, omegam3=.10,
            q=.50, n=15, J=3, K=60)
mrss.mod331(es=.2082, alpha=.05, two.tailed=TRUE,
            rho2=.17, rho3=.06, omegam2=.10, omegam3=.10,
            q=.50, n=15, J=3)

# cross-checks for the non-randomly varying bin. L1 moderator effect
mdesd.mod331(power=.80, alpha=.05, two.tailed=TRUE,
            rho2=.17, rho3=.06, omegam2=0, omegam3=0,
            q=.50, n=15, J=3, K=60)
power.mod331(es=.1893, alpha=.05, two.tailed=TRUE,
            rho2=.17, rho3=.06, omegam2=0, omegam3=0,
            q=.50, n=15, J=3, K=60)
mrss.mod331(es=.1893, alpha=.05, two.tailed=TRUE,
            rho2=.17, rho3=.06, omegam2=0, omegam3=0,
            q=.50, n=15, J=3)

# 3-2-1 mediation
power.med321(esa= .51, esB = .30, rhom3 = 0.27, rho2 = .15, rho3 = .19,
             r2m2 = .07, r2m3 = .16, r21 = .02, r22 = .41, r23 = .38,
             p = .50, n = 20, J = 4, K = 60)
# }