Regarding linear mixed models, I am looking for a reference that advocates first determining the appropriate structure of random effects (by first modelling only random effects), and then incorporating fixed effects into models. The OP here refers to references that aren't specified

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    $\begingroup$ You can't model random effects in isolation, random effects are modeled by subtracting off the fixed part and estimating covariance structures using the residuals, then using those weights to restimate the fixed effects, and proceding iteratively until convergence of estimates to some target value. $\endgroup$ – AdamO Dec 18 '18 at 18:59
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    $\begingroup$ When Ben discusses "finding" the right structure, he refers to exploratory analyses or aprior specification of models. Asking about what exploratory analyses can help identify correlation structures is a somewhat different question. $\endgroup$ – AdamO Dec 18 '18 at 19:01

Because the choice of the random-effects structure can be affected by the chosing fixed effects, often the advice is to start with a “full” specification of your fixed-effects structure (i.e., define the most general model structure including the factors you want to control for, and possible interactions and nonlinear terms), then select the appropriate random-effects structure starting from random intercepts and including additional random effects and testing in each step if they are required, and finally return to the fixed effects and see which terms seem to play a role in your outcome.

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