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/