SIGNED LIKELIHOOD ROOT WITH A SIMPLE SKEWNESS CORRECTION: REGULAR MODELS, SECOND ORDER

Abstract

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.