How to put a covariate into the linear-mixed effects model? In my linear-fixed effect model, I have two fixed factors "Fix-1" and "Fix-2", and a random factor "Ran". I think the continuous factor "Cov" may influence the dependent, and this influence is mainly works on "Fix-1". Now my R code of this model is:
Dependent ~ Fix-1 * Fix-2 + (1 + Fix-1 + Fix-2|Ran)

How can I put the covariate "Cov"?
 A: If I have understood your question correctly, there are really only 2 variables of interest here, Cov and Fix-1.  According to your theory, Cov is a cause of Fix-1. So, the key question is whether Cov is a cause, or a proxy for a cause, of the dependent variable too. If it is, then Cov is a confounder, and you can add it to the model as:
Dependent ~ Fix-1 * Fix-2 + Cov + (1 + Fix-1 + Fix-2|Ran)
or possibly (if supported by theory and the data):
Dependent ~ Fix-1 * Fix-2 + Cov + (1 + Cov + Fix-1 + Fix-2|Ran)
However, if Cov is NOT a cause, or a proxy for a cause, of the dependent variable, then Fix-1 is a mediator, and should not be included in a model with Fix-1 otherwise the reversal paradox may be invoked (Tu et al 2008), and so your model would be:
Dependent ~ Fix-2 + Cov + (1 + Fix-2|Ran)
Of course in this case you may instead wish to retain Fix-1 and çontinue without Cov.
Tu, Yu-Kang, David Gunnell, and Mark S. Gilthorpe. "Simpson's Paradox, Lord's Paradox, and Suppression Effects are the same phenomenon–the reversal paradox." Emerging Themes in Epidemiology 5.1 (2008)
