MR Dictionary

Limited Information Maximum Likelihood (LIML) method

A method that calculates the maximum likelihood of the causal estimate and of each parameter in the specified model. The LIML method will generate the same causal estimate as two-stage least squares (TSLS) and the Wald ratio method when used with a single instrumental variable (IV).

Whilst the LIML method is not as commonly used within one-sample MR analyses with individual-level data than the TSLS or Wald ratio methods, it is particularly encouraged where there are many weak IVs. In such instances, the median of the LIML estimator distribution is relatively unbiased.