R: How to calculate lag for multiple columns by group for data table

Question

I would like to calculate the diff of variables in a data table, grouped by id. Here is some sample data. The data is recorded at a sample rate of 1 Hz. I would like to estim

Answer 1

You can try

 setnames(dt[, lapply(.SD, function(x) c(NA,diff(x))), by=id], 
                2:3, c('dx', 'dy'))[]
 #    id dx dy
  #1:  1 NA NA
  #2:  1  1  2
  #3:  1  1  1
  #4:  2 NA NA
  #5:  2  4 -6
  #6:  2  1  1

Another option would be to use dplyr

 library(dplyr)
 df %>% 
     group_by(id) %>%
     mutate_each(funs(c(NA,diff(.))))%>%
     rename(dx=x, dy=y)

Update

You can repeat the step twice

dt[, c('dx', 'dy'):=lapply(.SD, function(x) c(NA, diff(x))), by=id]
dt[,c('dx2', 'dy2'):= lapply(.SD, function(x) c(NA, diff(x))),
                                            by=id, .SDcols=4:5]
 dt
 #   x y id dx dy dx2 dy2
 #1: 1 2  1 NA NA  NA  NA
 #2: 2 4  1  1  2  NA  NA
 #3: 3 5  1  1  1   0  -1
 #4: 1 8  2 NA NA  NA  NA
 #5: 5 2  2  4 -6  NA  NA
 #6: 6 3  2  1  1  -3   7

Or we can use the shift function from data.table

dt[, paste0("d", c("x", "y")) := .SD - shift(.SD), by = id
  ][, paste0("d", c("x2", "y2")) := .SD - shift(.SD) , by =  id, .SDcols = 4:5 ]