Assumptions underpinning the use of maximum likelihood estimation (MLE) with xtreg.

[Craig Knott]

I've been analysing data pooled from 38 studies, exploring a non-linear dose-response relationship between a continuous exposure (positively skewed) and a binary outcome.

The two primary steps I've been using are:

• xtreg to create polynomial transformations of the exposure, exploring the degree of heterogeneity, the case for an RE model, and the role of a priori covariates upon the primary relationship of interest.
• glst to pool study-specific estimates, accounting for covariance (non-independence) between any groups of observations drawn from the same study.

The syntax would be:

fp <dose>, scale center(0) replace: xtreg logrr <dose>, i(study_id) mle
mvmeta_make glst logrr dose_1 dose_2, cov(total_n cases) se(se) ci pfirst(study_id study_t) saving(ssest_fp) replace by(study_id) names(b V)
use ssest_fp, clear
mvmeta b V, ml

Since running these models, I've been wondering whether any important assumptions underpin the model when using MLE, as per OLS. Thus far I've been unable to find a clear answer, but have seen reference to two potential considerations:

1. That the distribution of residuals be homoscedastic;
2. That the residuals be normally distributed.

The second of the two points is mentioned on a Stata FAQ as follows:

The ML random-effects method xtreg, mle also requires that u_i follow the normal distribution. This distributional assumption should not be taken lightly because sometimes this assumption may not be valid.

Anyone more familiar with MLE know whether these assumptions are valid in this instance? Additionally, whether there are any useful resources outlining these and their rationale.