复合图形可以给出更多的信息，并且更能够观察数据之间的联系。一般所说的复合饼图包括以下两种：

    散点复合饼图（compound scatter and pie chart）可以展示三个数据变量的信息：(x, y, P)，其中x和y决定气泡在直角坐标系中的位置，P表示饼图的数据信息，决定饼图中各个类别的占比情况，如图1(a)所示。

    气泡复合饼图（compound bubble and pie chart）可以展示四个数据变量的信息：(x, y, z, P)，其中x和y决定气泡在直角坐标系中的位置，z决定气泡的大小，P表示饼图的数据信息，决定饼图中各个类别的占比情况，如图1(b)所示。
    P1.png
    P2.png

    具体操作如下：

    1. library(ggforce)
    2. library(dplyr)
    3. data_graph <- read.table(text = "x     y group    nb
    4. 1     0     0     1  1060
    5. 2     0     0     2   361
    6. 3     0     0     3   267
    7. 4     0     1     1   788
    8. 5     0     1     2   215
    9. 6     0     1     3    80
    10. 7     1     0     1   485
    11. 8     1     0     2   168
    12. 9     1     0     3   101
    13. 10     1     1     1  6306
    14. 11     1     1     2  1501
    15. 12     1     1     3   379", header = TRUE)
    17. # make group a factor
    18. data_graph$group <- factor(data_graph$group)
    20. # add case variable that separates the four pies
    21. data_graph <- cbind(data_graph, case = rep(c("Aaaa", "Bbbb", "Cccc", "Dddd"), each = 3))
    23. # calculate the start and end angles for each pie
    24. data_graph <- left_join(data_graph,
    25.                         data_graph %>% 
    26.                           group_by(case) %>%
    27.                           summarize(nb_total = sum(nb))) %>%
    28.   group_by(case) %>%
    29.   mutate(nb_frac = 2*pi*cumsum(nb)/nb_total,
    30.          start = lag(nb_frac, default = 0))
    32. # position of the labels
    33. data_labels <- data_graph %>% 
    34.   group_by(case) %>%
    35.   summarize(x = x[1], y = y[1], nb_total = nb_total[1])
    37. # overall scaling for pie size
    38. scale = .5/sqrt(max(data_graph$nb_total))
    40. # draw the pies
    41. ggplot(data_graph) + 
    42.   geom_arc_bar(aes(x0 = x, y0 = y, r0 = 0, r = sqrt(nb_total)*scale,
    43.                    start = start, end = nb_frac, fill = group)) +
    44.   geom_text(data = data_labels,
    45.             aes(label = case, x = x, y = y + scale*sqrt(nb_total) + .05),
    46.             size =11/.pt, vjust = 0) +
    47.   coord_fixed() +
    48.   scale_x_continuous(breaks = c(0, 1), labels = c("X0", "X1"), name = "x axis") +
    49.   scale_y_continuous(breaks = c(0, 1), labels = c("Y0", "Y1"), name = "y axis") +
    50.   theme_minimal() +
    51.   theme(panel.grid.minor = element_blank())

    最终得到的图形如下所示：

    P3.png