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General Social Survey.8 The data consisted of six observed variables, x1: father's occupation level, x2: son's income, x3: father's education, x4: son's occupation level, x5: son's education, x6**: number of siblings. The sample size was**
1,380. Fig. 6 shows domain knowledge about their causal relations: K**(1)=**{1, 3, 6}, K(2)={5}, K(3)={4} and K(4)={2}**. In this section, we represent such relations**
by {1, 3, 6}<{5}<{4}<{2} to save space. Note that if {i, j}<{k}, xi and xj **could** directly and/or indirectly cause xk**, but not vice versa.**
In this experiment, Alg. 1 was applied since the number of variables is small.

We tested several numbers of nearest neighbors kneig = 40, 50, 60, **70 to compute** mutual information using the k**-nearest neighbor approach [6] for GroupLiNGAM.** The estimated networks were not sensitive to the choice of the number of nearest neighbors kneig**, and essentially the same results were obtained for the values of**
kneig. We show the results under kneig**=50 in Tab. 1, where a smaller threshold** value for independence δ **gives a network between larger groups of variables.**
We first analyzed all the six variables. The estimated orders by ICA-LiNGAM
[11], Direct-LiNGAM [12] and GroupLiNGAM are shown at the second top of Tab. 1. Those estimated orders are difficult to interpret since son's **income (**x2)
and/or son's education (x5) could cause father's variables (x1,x3**), but not vice versa. The orders are not reasonable to their temporal**
orderings.

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