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
A newbie: When to allow residuals to correlate?
2 messages · 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 at 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