[R-sig-ME] Implications of modeling residuals in multilevel models

[Simon Harmel]

Hello All,

Just a follow-up, can we say the model I sketched above is a location-scale
model?

Thanks,
Simon

On Sat, Dec 16, 2023 at 9:30 PM Simon Harmel <sim.harmel using gmail.com> wrote:

> Hello All,
>
> I have a highly skewed dataset. But, my MODEL of choice below shows
> drastically improved, normally distributed residuals (and predicted values)
> compared to other models whose residuals are not modeled.
>
> Three quick questions:
>
> 1- Is MODEL below assuming that my data come from a population that looks
> normal once "X1_categorical" and "X2_numeric" are taken into account
> as modeled in MODEL?
>
> 2- Do these normally distributed predictions work better for a subject
> randomly drawn from a similarly skewed population with a
> known "X1_categorical" and "X2_numeric"?
>
> 3- I think the distribution of residuals mirrors that of the data. If so,
> is it correct to say MODEL below is actually **trimming** my highly skewed
> data as if it was distributed as:
> ```
> hist(resid(MODEL, type = "normalized"))
> ```
>
>  MODEL <- nlme::lme(y ~ X1_categorical + X2_numeric ...,
>          random = ~1| subject,
>          data = data,
>          correlation = corSymm(~1|subject),
>          weights = varComb(varIdent(form = ~ 1 |  X1_categorical ),
>                                           varPower(form = ~  X2_numeric )))
>
> Thanks,
> Simon
>

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