Solution to Separation Issues

Without correction for separation, the trials where separation occurs would need to be removed from analysis to avoid the bias in estimating R1 previously mentioned. This would lead to large loss of information where many trials are small and therefore prone to separation.

An alternative, more promising solution to the issue of separation is the use of penalized maximum likelihood (Firth, 1993). Although originally introduced to reduce small sample bias in maximum likelihood estimates, it has been found to be useful in dealing with separation (Heinze and Schemper, 2002). Firth (1993) found that bias occurred in estimates when trying to derive the score function (first derivative of the log-likelihood), which has no maximum in the case of separation, and suggested adding a bias term to the score function to resolve this.

Heinze and Schemper (2002) applied the technique of Firth (1993) to deal with separation. The bias term they applied to the score function was based on the information matrix of the parameter affected by separation, and produces finite parameter estimates that are superior to uncorrected estimates.

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