[R-sig-ME] A newbie: When to allow residuals to correlate?

[Jack Solomon]

ps. To be clear, I understand that lowest level errors within each level of
a grouping variable with respect to 'time' are correlated due to repeated
measurements. But what I don't understand is why correlating random-effects
alone can't account for such correlation.

On Sun, Mar 21, 2021 at 6:10 PM Jack Solomon <kj.jsolomon using gmail.com> wrote:

> Hello List Members,
>
> I apologize in advance for the simplicity of my question. But I'm
> struggling to understand the following in plain English:
>
> What is the difference between the correlation among the random-effects
> and the correlation among the residuals (i.e., lowest level errors within
> each level of a grouping variable perhaps with respect to 'time')?
>
> What type of correlation (dependency) in data is accounted for by
> correlating the random-effects, and what type of correlation in data is
> accounted for by correlating the residuals?
>
> Here are two conceptual models to contextualize this discussion:
>
> #== Correlation among random-effects (intercepts & time slopes) only:
> nlme::lme(y ~ gender*time, random = ~ time | ID, data = data)
>
> #== Correlation among random-effects + Unstructured correlation among
> residuals:
> nlme::lme(y ~ gender*time, random = ~ time | ID, data = data, correlation
> = corSymm(form = ~ 1 | ID))
>
> Many thanks for your consideration of my basic question,
> Jack Solomon
>

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