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How to calculate the elder generation’ maximum education year in one family

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Suppose I have dataframe like this:

   family relationship meanings              edu
 1      1 A            respondent             12
 2      1 B            respondent's spouse    18
 3      1 C            A's father             10
 4      1 D            A's mother              9
 5      1 E1           A's first son          15
 6      1 F1           E1's spouse            14
 7      1 G11          E1's first son          3
 8      1 G12          E1's second son         1
 9      1 E2           A's second son         13
10      2 A            respondent             21
11      2 B            respondent's spouse    16
12      2 C            A's father             12
13      2 D            A's mother             16
14      2 E1           A's first son          18
15      2 F1           E1's spouse            15
16      2 E2           A's second son         17
17      2 E3           A's third son          16

family indicates family number. relationship indicates relationships in one family. meanings indicates the meanings of the second column, relationship.

relationship in the first family

I want to calculate the father generation’s maximum education year in one family. We do not need spouse's information.

The expected results are as follows:

   family id      edu fedu 
 1      1 A        12 10   
 2      1 C        10 NA   
 3      1 E1       15 18   
 4      1 E2       13 18   
 5      1 G11       3 15   
 6      1 G12       1 15   
 7      2 A        21 16   
 8      2 C        12 NA   
 9      2 E1       18 21   
10      2 E2       17 21   
11      2 E3       16 21

Here is the data:

 d = structure(list(family = c(1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2), relationship = c("A", "B", "C", "D", "E1", "F1", "G11", "G12", "E2", "A", "B", "C", "D", "E1", "F1", "E2", "E3"), meanings = c("respondent", "respondent's spouse", "A's father","A's mother", "A's first son", "E1's spouse", "E1's first son","E1's second son", "A's second son", "respondent", "respondent's spouse","A's father", "A's mother", "A's first son", "E1's spouse", "A's second son","A's third son"), edu = c(12, 18, 10, 9, 15, 14, 3, 1, 13, 21,16, 12, 16, 18, 15, 17, 16)), row.names = c(NA, -17L), class = c("tbl_df", "tbl", "data.frame"))

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