Heckman correction in Multilevel Mixed Effects models

#1
Dear Talkstats,

I am estimating a Multilevel Mixed Effects model in stata, likelihood ratio tests imply that this model is preferred over a normal OLS model.

Additionally, I suspected my data set to be subject of sample selection bias on an observable variable and therefore performed a Heckman test. The results indicate significant sample selection bias and hence that I should include the Mills ratio estimated by the Heckman test.

My question is if I can now just include the Mills ratio in my Multilevel Mixed Effects model. I can find very little information on correcting for Sample selection bias in Multilevel Mixed Effect models and wonder if a Heckman correction can be used in a Multilevel Mixed Effects model at all as it is normally used in OLS models.

Thanks for your help in advance,

Fabrizio
 

hlsmith

Omega Contributor
#2
I am not familiar with the "Heckman test". I usually select between MLM and OLS, by running an empty MLM, which only controls for clustering. If controlling for clusters explains a reasonable amount of variability I use the MLM model.
 

hlsmith

Omega Contributor
#3
I just skimmed the Wikipedia page on the Heckman Correction. Interesting material which kind of seems familiar. I may loosely likened it to perhaps propensity scores. I know things will get trickier now when using MLM. In particular the Wiki page may have mentioned the SEs are inconsistent when using the Heckman correction and can be estimated using a bootstrapping approach. This is straightforward in an OLS scenario but a little more difficult in MLM.

I guess a follow-up question is why do you think you have a possible MLM? In addition, if you have a MLM and you neglect to control for the underlying dependency issues related to clustered data you risk type 1 errors. Some people who believe the dependency may not to be an overt issue use robust SEs with their estimates to indirectly address type I risk, but this seems like an area of issue for the SEs that may be inconsistent when using the Heckman Correction.

@Jake - any MLM advice related to getting bootstrapped SEs. Do you just need a loop to randomly pull from sample and within clusters. I think once a long time ago I saw some code to do this with State clustered data.