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I'm currently running a model to determine if people vary in their daily levels of variable Y, and if daily levels of variable X predict daily levels of variable Y. I collected measurements of both X and Y from the same people on multiple days, and I'm using multilevel modeling/HLM.

As a first step, ran a null model, with only the "person" variable predicting the mean of Y using the lme function from the nlme package in R. In the output, I can see a value corresponding to what I think is the between-person variance (the intercept variance), and a value corresponding to the "residual" variance (which I think includes both within-person variance and measurement error). I was wondering if there is a way to distinguish between how much of the residual variance is within-person variance and how much of it is measurement error? Apologies if this is a basic question, I am still quite a beginner with this type of analysis.

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  • $\begingroup$ In my opinion, this is a good question. To the best of my understanding, the answer is you can't. The residual variance covers both within-person variance and error. You could enter "day" as random effect but that likely wouldn't help, because any particular day would be different for each participant. In designs in which same participants go through several controlled situations, you can enter both person and situation as random effects and get separate variance estimates for both, as well as a separate residual. But in ESM/diary studies it's typically impossible to have this type of control. $\endgroup$
    – Sointu
    Commented Aug 31, 2022 at 7:42

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