Signed Likelihood Root with a Simple Skewness Correction: Regular Models, Second Order

A standardized maximum likelihood departure, a standardized score departure, the signed likelihood root: these are familiar inference outputs from statistical packages, with the signed likelihood root often viewed as the most reliable. A third-order adjusted signed likelihood root called r∗ is available from likelihood theory, but the formulas and development methods are not always easily implemented. We use a log-model Taylor expansion to develop a simple second order adjustment to the signed likelihood root, an adjustment that is easy to calculate and easy to explain, and easy to motivate. The theory is developed, simulations are recorded to indicate repetition accuracy, real data are analyzed, and connections to alternatives are discussed.