The following example obtains sample size estimates for a simple mediation model to obtain a power of \(1 - \beta = .80\). Specifically, four sample sizes (\(N\)) are solved by varying the coefficients associated with the equations
For simplicity the independent variable \(X\) is constrained to be a dichotomous variable, though this is not a requirement and users are free to change this distribution to suit their applications. Residuals (\(e\)) are assumed to be independent and distributed \(e \sim N(0,1)\). The simple mediation model itself is fitted using the lavaan package’s maximum-likelihood estimation criteria.
library(SimDesign)
Design <- createDesign(N = NA,
a = sqrt(.35),
b = sqrt(c(.02, .07, .15, .35)),
cprime=.39)
Design # solve for NA's# A tibble: 4 × 4
N a b cprime
<dbl> <dbl> <dbl> <dbl>
1 NA 0.59161 0.14142 0.39
2 NA 0.59161 0.26458 0.39
3 NA 0.59161 0.38730 0.39
4 NA 0.59161 0.59161 0.39#~~~~~~~~~~~~~~~~~~~~~~~~
#### Step 2 --- Define generate, analyse, and summarise functions
Generate <- function(condition, fixed_objects = NULL) {
Attach(condition)
X <- rep(0:1, each=N)
M <- a*X + rnorm(N)
Y <- b*M + cprime*X + rnorm(N)
dat <- data.frame(X, Y, M)
dat
}
Analyse <- function(condition, dat, fixed_objects = NULL) {
model <- ' # direct effect
Y ~ c*X
# mediator
M ~ a*X
Y ~ b*M
# indirect effect (a*b)
ab := a*b
# total effect
total := c + (a*b)
'
fit <- lavaan::sem(model, data=dat)
if(!lavInspect(fit, 'converged')) stop('Model did not converge')
PE <- parameterEstimates(fit)
ret <- PE$pvalue[PE$lhs == 'ab'] # joint test
ret
}
Summarise <- function(condition, results, fixed_objects = NULL) {
ret <- EDR(results, alpha = .05)
ret
}Solve each \(N\) given the rows in Design
# Initial search between N = [10,500] for each row using the default
# integer solver (integer = TRUE)
# In this example, b = target power of 80%
interval <- c(20, 1000) # needless wide for most, but shows the point
# Search is terminated when either 100 iterations reached or the
# prediction CI is within [.795, .805]
solved <- SimSolve(design=Design, b=.8, interval=interval,
generate=Generate, analyse=Analyse, summarise=Summarise,
packages='lavaan', parallel=TRUE,
ncores = ceiling(parallel::detectCores()/2),
verbose=FALSE, check.interval=FALSE,
maxiter=100, predCI.tol=.01)This is lavaan 0.6-19
lavaan is FREE software! Please report any bugs.# A tibble: 4 × 4
N a b cprime
<dbl> <dbl> <dbl> <dbl>
1 262.73 0.59161 0.14142 0.39
2 87.086 0.59161 0.26458 0.39
3 49.470 0.59161 0.38730 0.39
4 33.637 0.59161 0.59161 0.39$condition_1
$root
[1] 262.7264
$predCI.root
CI_2.5 CI_97.5
258.5502 266.9366
$b
[1] 0.8
$predCI.b
[1] 0.7951403 0.8047727
$terminated_early
[1] TRUE
$time
[1] 02m 3.49s
$iterations
[1] 94
$total.replications
[1] 29900
$tab
y x reps
11 0.7516129 236 310
13 0.7863636 250 660
15 0.7823529 253 340
17 0.7701493 255 670
18 0.8152174 256 460
19 0.7974576 257 1180
20 0.7942308 258 520
21 0.7852459 259 1220
22 0.7913333 260 3000
23 0.7996721 261 3050
24 0.7983294 262 4190
25 0.8077143 263 3500
26 0.8130769 264 1300
27 0.8014388 265 1390
28 0.8216216 266 370
29 0.7924138 267 1450
30 0.7964029 268 1390
32 0.8413043 274 460
33 0.8187500 275 480
34 0.8318182 277 440
35 0.7900000 278 400
36 0.8023810 280 420
41 0.8219512 291 410
$condition_2
$root
[1] 87.08581
$predCI.root
CI_2.5 CI_97.5
86.12608 87.94639
$b
[1] 0.8
$predCI.b
[1] 0.7950895 0.8048218
$terminated_early
[1] FALSE
$time
[1] 02m 1.36s
$iterations
[1] 100
$total.replications
[1] 32900
$tab
y x reps
5 0.7833333 82 660
6 0.7722628 83 1370
7 0.7878549 84 6340
8 0.7920635 85 3780
9 0.7988506 86 4350
10 0.8023256 87 4730
11 0.7948571 88 3500
12 0.8113333 89 6000
14 0.8017857 91 560
15 0.8620000 93 500
$condition_3
$root
[1] 49.46952
$predCI.root
CI_2.5 CI_97.5
49.10490 49.82108
$b
[1] 0.8
$predCI.b
[1] 0.7947319 0.8051660
$terminated_early
[1] FALSE
$time
[1] 02m 1.50s
$iterations
[1] 100
$total.replications
[1] 32900
$tab
y x reps
2 0.7763158 46 380
3 0.7632653 47 490
4 0.7768638 48 11670
5 0.7922311 49 5020
6 0.8111801 50 12880
7 0.8136000 51 1250
$condition_4
$root
[1] 33.63727
$predCI.root
CI_2.5 CI_97.5
33.50299 33.77255
$b
[1] 0.8
$predCI.b
[1] 0.7951342 0.8047786
$terminated_early
[1] TRUE
$time
[1] 02m 0.83s
$iterations
[1] 98
$total.replications
[1] 31900
$tab
y x reps
1 0.7355072 32 6900
2 0.7712743 33 9260
3 0.8133072 34 10220
4 0.8430876 35 4340# also can plot median history and estimate precision
plot(solved, 1, type = 'history')plot(solved, 1, type = 'density')Warning in density.default(x, weights = reps/sum(reps)): Selecting bandwidth
*not* using 'weights'RetroSearch is an open source project built by @garambo | Open a GitHub Issue
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