[R-sig-ME] Fwd: Re: Power calculations for lmer mixed designs

[Diana Michl]

Dear Phillip,

thank you very much for your good answer - it helped me a lot.

Now that I've been through it a few times, I'm still unclear about a few 
things:

>> - The qlogis function, I don't get what it does exactly and what to
>> enter instead of 0.7 as in the example
>>
>> |beta <- c(qlogis(0.7), -0.2)|
> See the paragraph above that code: "baseline range (fraction of grid
> cells sampled) is 70% (logit(0.7)=0.8473)". qlogis() is the quantile
> function for the logistic distribution, so qlogis returns the point in
> that distribution where the density is equal to the value mentioned.
> This is used here to compute logit(0.7):
>> qlogis(0.7)
> [1] 0.8472979
>
> Which is the value in the paragraph given for logit(0.7). This is just
> converting effect size to the link (logit) scale (as mentioned in the
> introduction: ' "beta" is the fixed-effects parameters, in this case
> (intercept,treat) – also all on the logit scale.').
>
> Note that this is the intercept term ("baseline range").

My intercept and effect size is already on the logit scale - the 
intercept is 7.2. But whenever I enter it directly into the qlogis 
function, I'm warned that NaNs are produced. This happens whenever I 
enter anything over 1.0. Does this mean I actually need to enter a 
percentage rather than the absolute value...? Or is the problem an 
entirely different one?

>> - What exactly the resulting graphs mean, both here and in my own
>> example. What does the read bar at -0.2 tell me?
> Skimming the text, -0.2 is the coefficient/coefficient for the treatment
> (already on the link scale -- note that it is not transformed, so it
> represents log odds). In the explanatory text, "decrease log-odds of
> range by 0.4", i.e. -0.4 is used -- maybe Ben Bolker can explain why the
> number changed / what obvious transformation step I'm missing.
>
> So the redline represents the "ground truth", i.e. the real parameter
> value (because you chose it) and the other plots tell your simulated
> estimates -- how close they were (see esp. the CI plot).
So if I'm seeing this correctly, this way of calculating power is not a 
direct one, but you're rather meant to draw your own conclusions from 
looking at the graphs of the simulations and get a general feel of how 
far off or on your effect size is?


>> Is there a way to give power as a number between 0 and 1?
>> - How to do this for more than 1 treatment (my attempts to do it for 4
>> all failed, I seem to miss places in the exampe I need to change. For
>> example, I tried adding values to the beta-qlogis line above and others,
>> but it gave errors)
> You calculate your power based on the ability of models you fit to the
> simulated datasets to detect the effect. The general work flow is:
>
> 1. define "ground truth" model based on some theoretical assumptions
> 2. simulate lots of datasets of a certain size
> 3. fit models to those datasets.
> 4. number of models able to detect effect / number of models = power
> 5. if power to low, repeat with bigger simulated datasets
So you can't properly attempt this very way with 4 effects? The author 
implies that you can, but I'm getting the impression it'd be quite 
complicated... I'm not sure running each effect separately would be 
correct.

> There are also "analytic" tools that try to compute power without
> simulation, see for exmaple Jake Westfall's Shiny apps (and read his
> papers on power issues in mixed effects models!):
>
> https://jakewestfall.shinyapps.io/pangea/
> https://jakewestfall.shinyapps.io/crossedpower/
I'll try those, thanks very much!

Best
Diana

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