measures differences in scatter, and the third measures differences in shape (Cronbach and Gleser, 1953; Skinner, 1978).

  • 4.  

    Nine regional model life table families were produced (four Coale-Demeny and five U.N. families) with MORTPAK software (United Nations, 1988). The data included 31 life tables for each sex and family from the level of e(0) = 20 to 80 years in 2-year increments, resulting in 31 x 9 = 279 life tables for each sex. Variation in the life tables with respect to level was enormously high. To make the weights of age groups more equal, we applied logit-transformation to the age-specific probabilities of death, qx: logit(qx) = 0.51n(qx/(1 - qx)). Cluster analysis was then used to group separately the male and female life tables, using the hierarchical method Two Stage Density linkage Cluster Analysis (SAS Cluster Procedure). This method identifies any natural clusters that exist based on density. Evaluation of the number of natural clusters that exist in each of two sets of model life tables showed that there are nine clusters in each set, which coincides exactly with families predetermined by Coale and Demeny for their models and by Larry Heligman for the U.N. models.

  • 5.  

    In other words, we averaged the outputs of cluster analysis according to Cronbach-Gleser's approach, the outputs being scores of double standardized logit q(x) for each profile.

  • 6.  

    Classification of life tables by shape was performed on logits of q(x) (see note 3). Curves plotted in Figures 3-1a and 3-1b are the output of cluster analysis done by Ward's hierarchical method, that is, they represent scores of logits of q(x) after their transformation by Cronbach and Gleser's formula.

  • 7.  

    Logit scores are rather abstract and inconvenient indicators. On the same graph, the results of the cluster analysis are given in terms of age components of life expectancy (bold lines, left y-axis). This type of analysis is used also by Shkolnikov et al. (in this volume). Like logit scores, the components of e(0) for each cluster sum to zero and reference the difference in e(0) level between each cluster life table and the average life table for all of Russia. The age components of e(0) mirror the deviations based on the logit scores. The former reflect survival and are in units of years of life expectancy, while the latter reflect mortality and are in abstract scores. The age and cause-of-death component analysis is used later in the identification of the underlying cause-of-death structure of each cluster profile, which is discussed in the next section and shown in Figures 3-2a through 3-2f.

  • 8.  

    We shifted levels of expectation of life of the clusters to the levels of the Russian average life tables by using the Brass model of mortality with b = 1:

    Y'(x) = a + b Y(x),

    where logits of the initial life table Y(x) = 0.5 x 1n[1(x)/{ 1 1(x)} ], and Y'(x) are the logits of the reference life table with a fixed level of e(0) (see Brass, 1971; Carrier and Hobcraft, 1971.)

  • 9.  

    Two of the profiles do not follow this general pattern of rural-urban attributes. We can recognize female cluster 6, "Caucasus Autonomous." as rural because of the slope of its profile (high infant and child mortality to low old-age mortality), but it consists of three rural and four urban life tables. The male cluster "Special Russian City" consists mainly of urban life tables, but its profile has no distinguishing features of urban mortality; rather, it represents mixed urban-rural features. The size of its deviation in Figure 3-1a shows that it is very close to the Russian average profile, which represents mortality for both male subpopulations.

  • 10.  

    Female rural cluster 3 is labeled "Kuban and Center" and refers to Rostov province, Stavropolskiy, and Krasnodarskiy krai. This label is used to differentiate between these provinces and four autonomous republics of North Caucasus since large social and cultural differences exist between these two parts of the North Caucasus region.

  • 11.  

    Other sources include the following: for Finland, Suomen tillastollinen vuosikirja (Tilastokeskus, Helsenki); for France, Annuaire statistique de la France (Paris); for Hungary, Demografiai evconyv (Budapest); for the United States, life tables for 1959-1961; decennial life tables for 1969-1971, and life tables for 1964, 1970, 1975, and 1977 (Washington).

  • 12.  

    Although not discussed in the text, the similarity of profiles in this section was measured by the sum of the absolute deviations of (nonstandardized) logits of the compared tables' mortality from those of the base tables. It is a crude measure because it does not take into account the shape of the age profile of these deviations, but it reflects rather well the general similarity among profiles.

The National Academies | 500 Fifth St. N.W. | Washington, D.C. 20001
Copyright © National Academy of Sciences. All rights reserved.
Terms of Use and Privacy Statement