Minimum detectable effect size in linear mixed model

Hi Pat,

Thanks for your quick reply. Yes, I already have the data and the actual
effects, and the analysis was suggested by a reviewer. Can you elaborate on
when do you think such an analysis might be justified?

Thanks!
Han

On Fri, Jul 3, 2020 at 6:34 PM Patrick (Malone Quantitative) <
malone at malonequantitative.com> wrote:

Han,

(1) Usually, yes, but . . .

(2) If you have an actual effect, does that mean you're doing post hoc
power analysis? If so, that's a whole can of worms, for which the best
advice I have is "don't do it." Use the size of the confidence
interval of your estimate as an assessment of sample adequacy.

Pat

On Fri, Jul 3, 2020 at 6:27 PM Han Zhang <hanzh at umich.edu> wrote:

Hello,

I'm trying to find the minimum detectable effect size (MDES) given my
sample, alpha (.05), and desired power (90%) in a linear mixed model
setting. I'm using the simr package for a simulation-based approach.

What I

did is changing the original effect size to a series of hypothetical

effect

sizes and find the minimum effect size that has a 90% chance of

producing a

significant result. Below is a toy code:

library(lmerTest)
library(simr)

# fit the model
model <- lmer(Reaction ~ Days + (Days | Subject), sleepstudy)
summary(model)

Fixed effects:
? ? ? ? ? ? Estimate Std. Error? ? ? df t value Pr(>|t|)
(Intercept)? 251.405? ? ? 6.825? 17.000? 36.838? < 2e-16 ***
Days? ? ? ? ? 10.467? ? ? 1.546? 17.000? 6.771 3.26e-06 ***


Here is the code for minimum detectable effect size:

pwr <- NA

# define a set of reasonable effect sizes
es <- seq(0, 10, 2)

# loop through the effect sizes
for (i in 1:length(es)) {
? # replace the original effect size with new one
? fixef(model)['Days'] =? es[i]
? # run simulation to obtain power estimate
? pwr.summary <- summary(powerSim(
? ? model,
? ? test = fixed('Days', "t"),
? ? nsim = 100,
? ? progress = T
? ))
? # store output
? pwr[i] <- as.numeric(pwr.summary)[3]
}

# display results
cbind("Coefficient" = es,
? ? ? Power = pwr)

Output:

? ? ? ? ? ? ? ? ? ? ? ? ? ? Coefficient? Power
[1,]? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 0? 0.09
[2,]? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 2? 0.24
[3,]? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 4? 0.60
[4,]? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 6? 0.99
[5,]? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 8? 1.00
[6,]? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 10? 1.00

My questions:

(1) Is this the right way to find the MDES?

(2) I have some trouble making sense of the output. Can I say the
following: because the estimated power when the effect = 6 is 99%, and
because the actual model has an estimate of 10.47, then the study is
sufficiently powered? Conversely, imagine that if the actual estimate

was

3.0, then can I say the study is insufficiently powered?

Thank you,
Han
--
Han Zhang, Ph.D.
Department of Psychology
University of Michigan, Ann Arbor
https://sites.lsa.umich.edu/hanzh/

? ? ? ? [[alternative HTML version deleted]]

--
Patrick S. Malone, Ph.D., Malone Quantitative
NEW Service Models: http://malonequantitative.com

He/Him/His

--
Han Zhang, Ph.D.
Department of Psychology
University of Michigan, Ann Arbor
https://sites.lsa.umich.edu/hanzh/