Dear Statalist members,

I am currently running some multi-level models. However, I wonder how to decide between different COV() options in the Stata mixed command?

Specifically, I study a number of business units (such as the Healthcare business unit of General Electric). In my model, I estimate how a certain strategy of a business unit affects its financial performance. Given that the business units are nested in firms, I run a multilevel model (mixed).

In my model, I have two random intercepts (BU_ID and Firm_ID), as well as two random slopes at both levels (first, for the size of the business unit, and second, for the R&D expenditure of the firm to which the business unit belongs).

Code:
mixed BU_performance BU_strategy BU_size Firm_Leverage Firm_R&D
|| Firm_ID: BU_size Firm_R&D
|| SBU_ID: BU_size Firm_R&D
,cluster(Firm_ID)
  • From what I understand, cov(unstructured) seems to be the “safest” choice?
  • Cov(independent) is the default option – and also seems fairly safe to me
Yet I wonder about the other two options, and in particular, about cov(exchangeable). Specifically, I wonder which assumptions I am making when choosing cov(exchangeable) instead of cov(unstructured)?
I fear that going for cov(exchangeable) may not necessarily be a safe and correct choice.

Does going for cov(exchangeable) require one to make strong assumptions?

In the help file for the mixed command, the cov(exchangeable) option is described as follows: It “specifies one common variance for all random effects and one common pairwise covariance”. Yet reading this description, my brain has a very hard time really understanding what these two parts of the description really mean.

“One common variance for all random effects” would mean that I assume the variance of my two random slopes (the size of the business unit and the R&D expenditures) to have the same variance? But what would this really mean?

Also, I am unfortunately struggling to understand the meaning of “one common pairwise covariance” and what this statement exactly refers to.

Overall, would my choice for one of the different COV() options come from theory?

And/or is there any explicit test one could run, to check whether using the cov(exchangeable) option would be alright (or not)?

Thanks so much and all the best,

Franz