Limited Information Maximum Likelihood (LIML) for Multi-Site Non-Compliance
RCTClinical Trial
Standard Two-Stage Least Squares (2SLS) instrumental variables estimators become biased toward Ordinary Least Squares when combining many weak instruments across multiple experimental sites with varying treatment compliance.
Picture this
Evaluating a multi-branch clinical trial where each hospital location has different patient drop-out rates; using maximum likelihood estimation across all locations prevents poorly complying branches from distorting the overall drug efficacy calculation.
What the evidence says
LIML estimation yielded a pooled causal effectiveness coefficient of 0.955 (p < 0.01, SE = 0.123) while maintaining a minimum first-stage F-statistic of 38 across instrument specifications, eliminating weak-instrument bias concerns.
- Who was studied
- N = 27,255 randomized students in grades 4–8 across 619 randomization blocks in 6 urban school districts.
- How
- Limited Information Maximum Likelihood (LIML) instrumental variables estimation interacting assigned teacher effectiveness with school and randomization block indicators to account for site-level compliance variation.
What to do
Specify LIML instrumental variables estimation when analyzing multi-site randomized field experiments featuring weak instruments or site-specific compliance variation.
From the source
"Moreover, the statistical properties of LIML estimates are superior to other IV estimators such as two-stage least squares in a setting such as ours, with many weak instruments."
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