simr：如何在 lm() 或 aov() 模型中指定预期效果大小？

Question

I am trying to use simR to assess the power of simple GLMs to detect a particular effect size, given a set of pilot data. For example:

library(simr)
m1 = lm(y ~ x, data=simdata)
powerSim(m1)

I have no problem doing this when testing power to detect the "observed" effect size (ie whatever effect size is present in the pilot data), however I would like to specify an "expected" effect size. This is easy to do when dealing with LMER models, using the fixef function, for example:

m2 = lmer(y ~ x + (1|g), data=simdata)
fixef(m2)['x'] = <expected effect size>

Unfortunately this function does not work with aov() or lm() models. For example, using...

fixef(m1)['x'] = <expected effect size>

Results in the following error:

Error in UseMethod("fixef") : 
  no applicable method for 'fixef' applied to an object of class "c('aov', 'lm')"

Is there another method/package/workaround I can use to change effect sizes for aov() or lm() ? I imagine this might entail "hacking" the summary output in a way that alters the F value (for aov() ) or coefficient value (for lm() ), however I haven't had any luck getting this to work.

Any advice would be greatly appreciated!

Edits

To clarify, by 'effect size' I mean the fixed effect coefficient generated by the model. So in the following output:

# Call:
# lm(formula = y ~ x, data = simdata)

# Coefficients:
# (Intercept)            x  
#     10.6734      -0.2398

The 'effect size' of x is -0.2398. In the context of power analysis, changing the effect size should directly affect statistical power (because large effects require less power to detect, and vice-versa). For example, when using LMER, changing the effect size with fixef() directly affects statistical power:

m2 = lmer(y ~ x + (1|g), data=simdata)
summary(powerSim(m2, progress=F, nsim=100)

#   successes trials mean     lower     upper
# 1        96    100 0.96 0.9007428 0.9889955

Specify smaller effect size and re-assess power:

fixef(m2)['x'] = 0.05
summary(powerSim(m2, progress=F, nsim=100)
#   successes trials mean     lower     upper
# 1        12    100 0.12 0.0635689 0.2002357

I have tried to modify the coefficient values for lm() with the following approach:

m1 = lm(y ~ x, data=simdata)
m1$coefficients['x'] = <expected effect size>

However this has no effect on power, eg when changing the coefficient from 0.9 to 0.09

m1$coefficients['x'] = 0.9
summary(powerSim(m1, progress=F, nsim=100))
#   successes trials mean     lower     upper
# 1        22    100 0.22 0.1433036 0.3139197

m1$coefficients['x'] = 0.09
summary(powerSim(m1, progress=F, nsim=100))
#  successes trials mean     lower     upper
# 1        24    100 0.24 0.1602246 0.3357355

So I suppose a more accurate wording of my question would be: how do I change effect sizes for aov() / lm() models in a way that reflects changes in statistical power?

Answer 1

You need to use:

coef(m1)['x'] = <expected effect size>

Instead of

fixef(m1)['x'] = <expected effect size>

Answer 2

The simplest solution to this is to avoid powerSim altogether and instead use pwr.f2.test from the package pwr. This provides a precise measure of power (as opposed to simulated power), given particular model parameters and the expected effect size.

m1 = lm(y ~ x, data=simdata)
anova(m1) 

# Analysis of Variance Table
# 
# Response: y
# Df  Sum Sq Mean Sq F value Pr(>F)
# x          1  14.231 14.2308  1.5943 0.2171
# Residuals 28 249.925  8.9259 

Use the df values from anova(m1) for the u and v arguments to pwr.f.test

pwr.f2.test(u=1, v=28, f2=<expected effect size>)

Thanks to @StupidWolf for figuring this out!