# [R-sig-ME] Minimum detectable effect size in linear mixed model

Patrick (Malone Quantitative) m@|one @end|ng |rom m@|onequ@nt|t@t|ve@com
Sat Jul 4 00:33:54 CEST 2020

```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 using 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)
> }
>
> # 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]]
>
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--
Patrick S. Malone, Ph.D., Malone Quantitative
NEW Service Models: http://malonequantitative.com

He/Him/His

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