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

[Jack Solomon]

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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