[R-sig-ME] Predictor standardized transformation in GLMM

[Di Zeng]

Hi Dr. Benjamin Bolker,

I got it.

Thanks so much for your ideas and suggestions.

Cheers,

Di


> ------------------------------
>
> Message: 2
> Date: Thu, 21 Oct 2021 21:44:20 -0400
> From: Ben Bolker
> To: r-sig-mixed-models using r-project.org
> Subject: Re: [R-sig-ME] Predictor standardized transformation in GLMM
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> The first way is more standard and makes more sense to me.
>
> Note that standardizing variables doesn't make any difference to the
> *statistical* results; it may improve the computational stability of the
> model, and it definitely changes the interpretation of the parameters.
>
> I understand the meaning of the parameters in the first case: "what
> is the expected change in log-odds of the outcome for a 1-SD change in
> predictor x1, holding everything else fixed"? I'm not so sure how I
> would interpret "1 SD of the unique values of x1", but if you can (and
> can explain it!), and that version makes more sense, then you should go
> ahead and use it.
>
> The structure of your example seems a bit odd -- is this a nested
> design, i.e. the predictors only vary across levels of the
> random-effects grouping factor, not within them? In that case (if your
> real data follow the same structure), you would probably be better
> collapsing the values rather than dealing with the complexities of a
> random-effect linear regression - in other words,
>
> y <- c(mean(1:3), mean(4:5), 6, 7)
> x1 <- c(6,5,4,3)
> x2 <- c(11, 5, 6, 8)
>
> lm(y~x1 + x2, weights=c(3,2,1,1))
>
> (see Murtaugh, "Simplicity and complexity in ecological data analysis”)
>
>
> --
> Dr. Benjamin Bolker
> Professor, Mathematics & Statistics and Biology, McMaster University
> Director, School of Computational Science and Engineering
> Graduate chair, Mathematics & Statistics
>
>
>
>
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