Mixed-effect Linear Regression

[Alhanouf Almubarak]

Hello,

I am using the below model as I have two levels of data: (Company level (high level) and Employee reviews level (low level)).

mixed DV IV Control 1 Control 2 Control 3 Control 4 Control 5 i.Year || ID:

I used i.Year to indicate a year-fixed effect.

However, my question is:

Q1: I have a different output that I don't understand:

1-var(_cons)
2- var(Residual)

Are those the same as the following?
1- lns1_1_1: _cons
2- lnsig_e:_cons

Whether the answer is yes or no, what do those four things explain?

Q2: What are the essential outputs I should report for the mixed-effects model, as this is my first time using this model? Please help.


Thank you in advance for your time.

[Clyde Schechter]

Those things are not the same, but they are closely related.

var(_cons) = (exp(lns1_1_1: _cons))2
var(Residual) = (exp(lnsig_e:_cons))2

The reason these closely related things are both there is that var(_cons) and var(Residual) are the estimates of the random effects variance component and the residual variance component of the model as one normally writes a mixed model: y_ij = b0 + b1x1_ij + ... + bnxn_ij + u_i + e_ij. (Some of the x's might be subscripted only by i or only by j.) So var(_cons) is the estimate of the variance of the u's and var(Residual) is the estimate of the variance of the e's. Now, what is the point of those other lns... terms. It turns out that computationally, it is much easier and more efficient to calculate maximum likelihood estimates of these lns... statistics and then transform to the variance components using the equations shown above than it is to calculate maximum likelihood estimates of the variance components directly.

As for what you should report: the var() statistics are the ones directly representing the mixed model and should be reported in preference to the ln... statistics. However, depending on your audience, you might not report any of these. It really depends who you are communicating to, their expectations, and their understanding of thees models. When I report an epidemiologic study to a lay audience, I generally don't report the variance components, as most people would not understand what they are, and usually they are not important to understanding the findings that provide the direct answer to the research question. But to a professional audience, I would show them, though usually not comment on them unless some special circumstance makes them unusually interesting.

[Alhanouf Almubarak]

Thank you so much Clyde for your clear explanation.