Many mortality studies have demonstrated that the level is the major component of "explained" variation in mortality curves (Ledermann and Breas, 1959; Bourgeois-Pichat, 1962; Messinger, 1980). Its impact is so considerable that it prevents closer inspection of weaker, but not less informative and important, differences in the shape of mortality curves. In particular, the shape of the mortality curve, or the age pattern of mortality, may reflect specific conditions of life among a population better than does the level. For example, elevated child mortality relative to other ages is a feature of the Coale-Demeny South model life table that reflects increased risk of intestinal infections produced by climatic, sanitary, dietetic, cultural, and behavioral features of the lifestyle of Southern Europeans at the end of the nineteenth and first half of the twentieth centuries (Coale and Demeny, 1966; Coale et al., 1983). Social class groupings are distinguished not only by level, but also by the shape of the mortality curve, which is thus useful for the study of social inequality in mortality (Anson, 1994). The shape of the mortality curve can also reflect peculiarities of the process of the epidemiological transition (Vassin, 1994).
The shape of the mortality curve is supposed to be more stable than the level, for even when the level varies considerably, a relative shape is maintained (Valaouras, 1974). This adherence to an underlying shape enables the construction of regional model life tables, and also emphasizes that the shape is more strongly connected to the specific character of a social situation than the level.
To analyze mortality profiles by the shape of the curve, it is necessary to eliminate differences in level and to identify the underlying typical patterns. There are different approaches to classifying life tables according to mortality profiles. A major classification effort was carried out by Coale and Demeny (1966; Coale et al., 1983), resulting in the widely used four regional families of model life tables. To find typical mortality patterns, Coale and Demeny visually analyzed several hundred mortality patterns. In this chapter, we employ a more formal approach based on a generalized concept of profile structure developed a number of years ago by Cronbach and Gleser (1953).3 This concept allows the use of cluster analysis to find mortality curves with identical shapes. According to this concept, any profile consists of three components: elevation, scatter, and shape. The level is equivalent to an average of the profile (expressed, e.g., as a simple or geometric average). Scatter is a measure of variation (like variance), whereas shape is something that remains in the profile after the first two components have been removed, similar to the product-moment of correlation between profiles. In demographic practice, the shape of a profile is understood to be all that remains after elimination of differences in level only. We have not departed