Refer to Example 8.13 and Table 8.28
(a) Repeat the 0-mode analysis of Table 8.28 using the weights Wt and f1 and compare to Williams (1978). What do you conclude?
(b) Reanalyze the data using R-mode analysis, that is, using the age distribution as the rows of the data matrix (Table 8.28). Can you determine the historical (time) behavior of the different age groups across race and sex?
Example 8.13
Williams (1978) provides a set of age-distribution histograms of the US population classified by sex, race, and the decade in which the census was taken (Table 8.28). The data are given in percentages and represent the (n x m) matrix pT, scaled by 100. Note that the array PT can also be taken as an r-way contingency table, which indicates the similarity of the method to procedures described in the preceding sections of the chapter. Since the discrete set x1, x2 , , x„ is here represented by time-ordered (age) categories, the elements of the latent vectors Ak (Eq. 8.75f) of the 𝒬-mode analysis of P can be plotted on a time axis and the global age-time behavior of the racial groups, by sex, can he observed. Note also that Williams chooses the total 1930 age distribution as the weights wj and equal frequencies fi rather than the row and column totals of the Table 8.28 (Exercise 8.14).
