Brass Relational Logit Model

Coale-Demeny model life tables are a fixed catalogue of empirically derived schedules indexed by region and level, from which you select the closest match. The Brass system is instead a continuous two-parameter transform of a single standard, so it can produce any logit-linear variant of that standard rather than choosing from a discrete set. Brass is more flexible for graduation and interpolation, while model life-table families encode region-specific empirical age patterns directly.

β governs the relative balance of mortality across ages. With β equal to one the fitted schedule has the same age shape as the standard, differing only in level via α. A β above one tilts mortality toward older ages relative to the standard, while a β below one shifts relative mortality toward childhood. It effectively rotates the logit-transformed survival curve around the standard.

Pick a standard whose age pattern is plausibly similar to the target population — for example a regional or historical schedule, or a general standard such as Brass's own. Because the model can only reproduce logit-linear transforms of the standard, a poorly chosen standard with a structurally different age pattern will fit badly. When two parameters are insufficient, multi-parameter relational systems that add curvature terms can be used.