UID HHID PERID ActNo
1   1000 1     1
2   1000 1     2
3   1000 1     3
4   1000 2     1
5   1000 2     2
6   2000 1     1
7   2000 1     2
8   2000 1     3
9   2000 1     4
10  2000 2     1
11  2000 2     2

UID HHID PERID ActNo MaxAct
1   1000 1     1     3
2   1000 1     2     3
3   1000 1     3     3
4   1000 2     1     2
5   1000 2     2     2
6   2000 1     1     4
7   2000 1     2     4
8   2000 1     3     4
9   2000 1     4     4
10  2000 2     1     2
11  2000 2     2     2

dat$MaxAct <- with(dat, ave(ActNo, HHID, PERID, FUN=max) )

dat$MaxAct <- with(dat, ave(ActNo, HHID, PERID, FUN=function(x) max(x, na.rm=TRUE) )  )

library(data.table)
DT <- data.table(DF)
DT[,MaxAct := max(ActNo), by = list(HHID, PERID)]

DT[,MaxAct := .N, by = list(HHID, PERID)]

require(plyr)
ddply(dat, .(HHID, PERID), transform, MaxAct = max(ActNo))

   UID HHID PERID ActNo MaxAct
1    1 1000     1     1      3
2    2 1000     1     2      3
3    3 1000     1     3      3
4    4 1000     2     1      2
5    5 1000     2     2      2
6    6 2000     1     1      4
7    7 2000     1     2      4
8    8 2000     1     3      4
9    9 2000     1     4      4
10  10 2000     2     1      2
11  11 2000     2     2      2

df <- read.table(textConnection("UID HHID PERID ActNo
1   1000 1     1
2   1000 1     2
3   1000 1     3
4   1000 2     1
5   1000 2     2
6   2000 1     1
7   2000 1     2
8   2000 1     3
9   2000 1     4
10  2000 2     1
11  2000 2     2"), header=T)


> ddply(df, .(HHID, PERID), transform, MaxAct = length(unique(ActNo)) )
   UID HHID PERID ActNo MaxAct
1    1 1000     1     1      3
2    2 1000     1     2      3
3    3 1000     1     3      3
4    4 1000     2     1      2
5    5 1000     2     2      2
6    6 2000     1     1      4
7    7 2000     1     2      4
8    8 2000     1     3      4
9    9 2000     1     4      4
10  10 2000     2     1      2
11  11 2000     2     2      2