On choosing an indexing variable in demographic analysis

Abstract

Demographic analysis has generally made use of age as its primary indexing variable, in recognition of the fact that most demographic behavior varies greatly over the life span. Yet despite the important implications involved in the choice of an indexing variable, no clear guidelines exist as to how the choice should be made. To provide such a criterion, it is proposed that the better of two sets of singly indexed rates is the set which is more highly correlated with the elements of the array of doubly indexed rates that has the two sets of singly indexed rates as marginals. The correlation criterion is then applied to several specific cases in fertility, divorce, and mortality analysis. England-Wales,1965, data suggest that, for once-married women, age is a better predictor of legitimate fertility than duration of marriage, when 5-year groupings are used for both variables. Divorce data for California males,1969, and Hungary females,1960, imply that the duration of first marriage is better than age as a predictor of divorce. For the United States,1950, the use of age and sex is preferable to the use of age and race in mortality analysis. To determine which marginal index is more closely correlated with the array variables in any specific situation, a simple test is derived which can be applied even if the array of doubly indexed variables is not known. Finally, the square of the correlation coefficient between a marginal variable and the array represents a measure of the error made by ignoring the other variable. The results for California males,1969, indicate that it is advisable to use both age and duration of marriage as index variables in divorce analysis, as either index alone accounts for less than half of the joint variability.