Understanding random effects output

[Leah Ricketson]

Hi all,
I am new to this forum and new to longitudinal analysis with a mixed effects model. I've run this model and I am unsure of how to report/interpret the random effects parameters. Can anyone give me some advice on this? My understanding is that the mixed model has an additional error term for the random effects. But I am unsure how to report this additional error in a table for a manuscript or whether it needs to be reported. manuscripts in my field with similar analyses seem to vary on whether it is reported. Thanks!

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Random-effects parameters | Estimate Std. err. [95% conf. interval]
-----------------------------+------------------------------------------------
id: Unstructured |
var(antigenweeks) | .000403 .0001076 .0002388 .0006801
var(_cons) | .607097 .0882465 .4565928 .8072112
cov(antigenweeks,_cons) | -.0027719 .0023288 -.0073364 .0017925
-----------------------------+------------------------------------------------
var(Residual) | .7317589 .0473705 .6445631 .8307506
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LR test vs. linear model: chi2(3) = 260.11 Prob > chi2 = 0.0000

[Clyde Schechter]

So, it appears your model contains not only random intercepts (effects) but a random slope as well. Whether and how to report these will depend on your target audience as well as the conventions and policies of whatever journal you want to place them in. The interpretation of these effects will completely elude an audience that has limited or no statistical background, and for such an audience it is probably best to omit them from your presentation. At the other extreme, for an audience that is statistically sophisticated, reporting them more or less as they look in your Stata output, as additional rows to your regression results table, would be de rigeur. I think I would change the order, putting the var(_cons) row first, and I would call it "Intercept at id level." I would probably call var(antigenweeks) "Variance of antigenweeks slope", and cov(antigenweeks, _cons) "Covariance of angitenweeks slope and id level intercept." var(Residual) could be called "Residual variance."

For a mixed audience (no pun intended), I would both show the results and also include a brief explanation of what they are in the text of your manuscript. In particular, I would explain that the random slope in your model allow each individual id to have its own slope (coefficient) for the antigenweeks variable, with the distribution of those slopes being normal with mean zero. I would also explain that the random intercept allows each individual id to have its own intercept (base level) of the outcome variable, again the distribution of those being normal with mean equal to the _cons term in the fixed effects part of the model.