4 level cross-classified model estimation

[slavutich]

Dear MLwiN users,

I would like to estimate a 4-level cross-classified random intercept model in Stata by using the runmlwin command.
The model is similar to the one presented in the paper of Castellaneta and Gottschalg (2016). (The paper is only here for referencing and it does not really matter what each level means, the structure is important).

The authors have the following structure of the data:
1) year observations (level 1) are nested within
2) buyout investments (buyouts) (level 2), which are simultaneously nested (i.e., cross-classified) within both
3) industries (level 3) and private equity (PE) funds (level 3);
4) PE funds are then nested within PE firms (level 4).

The authors used MLwiN software and the Markov Chain Monte Carlo (MCMC) estimation procedure with a Bayesian estimation. The authors ran the MLwiN software in Stata using the runmlwin command.

I extracted a table from the paper to show what I mean (attached picture below).

In one of the forum's topics (https://www.cmm.bristol.ac.uk/forum/viewtopic.php?t=55) I found the information that "there is no way to specify that the cross classification should apply to just certain pairs of levels". It is additionally mentioned that MLwiN looks at the actual data, and "if there is no cross classification present in the data between certain pairs of levels, then treating those levels as cross classified is actually the same thing as treating them as hierarchical" (provided that categories are set up properly).

So, my question is whether the Stata command, which is stated below, is correct with regard to the above-mentioned structure of the data (also depicted in the attachment). Please ignore the fixed effect part. I am only interested in the random effect part.

Code: Select all

runmlwin buyout_performance cons, level5(PE firm: cons) level4(industry: cons) level3(PE fund: cons) level2(buyout: cons) level1(year: cons) mcmc(cc) initsb(b) nopause

I will be very grateful for any help!

References:
Castellaneta, F., & Gottschalg, O. (2016). Does ownership matter in private equity? The sources of variance in buyouts' performance. Strategic Management Journal, 37(2), 330-348.

[billb]

Hi Viacheslav,
Thanks for your email. So to clarify nesting is indeed a special case of the more general relationship that we called crossed-classification or perhaps better called multiple classifications where a response depends on a series of classifying variables. The general case is you have several classifications and the special case is when there is a nesting relationship between them (and in this case we often use the term levels).
So in setting up a model you can put your levels (above 1) in any order you like however you are better off putting them in the partly nested way you have as MLwiN will run IGLS first for starting values and this assumes nesting.
The only thing to be careful of is to give your variable unique ids
So for example if you have industries -> buyouts -> years which are nested then don't use the same ids for buyouts within different industries i.e. if you have the first buyout for industry 1 and the first buyout for industry 2 these are different buyouts and thus need different ids so don't use 1 and 1.
I don't use Stata or runMLwiN so I am cc'ing my colleagues Chris Charlton to confirm your syntax.
Best wishes,
Bill Browne.

[ChrisCharlton]

Your syntax looks correct for setting up a cross-classified model with -runmlwin-. My only comment is that Stata doesn't allow spaces in variable names, so you will need to rename your "PE fund" and "PE firm" variables prior to running the model. -runmlwin- displays a summary of the model structure along with the results, so it is a good idea to check that this matches your expectations. You can get a more detailed view of this by removing the nopause option and examining it via the hierarchy window within MLwiN.

[slavutich]

Dear Chris and Bill,

thank you for your detailed answers!