R data.table selecting the previous row within group blocks

R data.table selecting the previous row within group blocks

I have the following example data frame.
id value
a 3
a 4
a 8
b 9
b 8
I want to convert it so that I can calculate differences in the column
"value" between successive rows. So the expected result is
id value prevValue
a 3 0
a 4 3
a 8 4
b 9 0
b 8 9
Notice within each group I want the sequence of values to start with a 0
and successive values are from the one prior. I tried the following
x = x[,list(
prevValue = c(0,value[1:(.N-1)])
),by=id]
but no luck. Thanks in advance.