Multilevel analysis with independent variables with different levels

[Claire Han]

Hi everyone,

I have an issue regarding the multilevel analysis.
I was supposed to do three-way panel analysis, however, some of my independent variables are only have two dimensions.
I thought multi-level analysis (command: mixed) can partially help me to analyse it.

My data is two-level with region(j) and industry(i) and it's longitudinal.
Dependent variable is new firm formation rate (i,j), and some independent variables are j-level, and the others are i, j.
Getting insight from the stata blog, I used random slope for the year.

So I used the command
mixed Y X1 X2 ... cyear i.ind || reg: || ind: cyear

What I am not sure is how to deal with the independent variables which are at the j-level?
Can I just interprete it with other independent variables which are at the i-level?

Another question is, when I used panel fixed effect, even though some of the variables are only 2-dimensional, it showed the result (with very low within r-square)..
Can I use it for interpretation?

Thank you so much in advance!!!!

[Clyde Schechter]

I don't think I completely understand how you want to model this data, but I can point out a couple of problems with what you've done:

1. You have industry as both a fixed effect (i.ind) and a random effect (|| ind: ). That doesn't make sense, and I am actually surprised you managed to even get it to converge. If you want industry as a fixed effect and also want the effect of cyear to vary by industry, then use an interaction in the fixed effects: i.ind##cyear, and drop the || ind: cyear from the random effects. This approach will have the advantage of also resolving the second problem I list below. Or keep the random slopes part of the model but drop the i.ind fixed effect and grapple with #2 below.

2. Another problem is that your syntax || reg: || ind: implies that industries are nested within regions. Maybe that is true in your data, but it seems odd, and if it's not true then your model is mis-specified here. See the ME manual for how to implement crossed random effects if industries are not nested in regions.

So, I don't think you should interpret the output from the commands you've shown, and you should at least make changes along the lines I've outlined above. Then you still need to carefully consider whether the model you've estimated is the model you actually intend.

[Claire Han]

Thank you so much for your help. Indeed, i.ind was mistakenly taken from the command that I used for panel fixed analysis. I am sorry for such misunderstanding.

My dependent variables are composed of industry, region and time, meaning each region has 16 different industrial level observations.
Even though the dataset itself shows that the industries are nested in the region, as you said so, it seems odd.

As you suggested, cross classified random effect models are best fit to my model, since I need a generalised result which encompasses industries and region.
It helped me really a lot. Thank you so much, sir.