Fitting the relational model

Interpretation of α and β

Alpha and beta are the two parameters that come out of the Brass relational two parameter system. They suggest that your observed mortality data is fitted best by taking the agreed standard and changing it in two ways.

The first way is given by alpha and this increases or decreases the overall level of mortality, compared to the standard. In graphical terms the plotted line simply moves up or down the y scale in a parallel fashion – and the intercept is the value of alpha.

The second way is that the balance of young age mortality and older age mortality (left and right side of graph respectively) shifts. In graphical terms the plotted line pivots at a particular age, but the line stays linear. The slope of the line is given by beta.

To fit the life table (the new l_x column) we therefore take the standard l_x column and adjust it according to the formula

$$new\left(fitted\right)logitlxvalues=\alpha +\beta .logitlsxvaluesofstandard$$

And then take ant-logit values to get our fitted table.

These two parameters satisfy the early findings showing that mortality schedules vary primarily by overall level of mortality and secondarily by the balance of younger and older mortality (see p6_1 of this session).

A typical spreadsheet layout for the fitting procedure is shown on the next page.