How to normalize to the previous value in a sequence

Question

A conceptually simple question that I'm struggling with. I have observations ('Values') grouped by ID over time and want to normalize each observation to its previous observation. In the example below I can normalize each 'Value' to the first 'Time' observation within ID group (ie 10 to 10, 20 to 10, 30 to 10, etc) but I want to normalize each 'Value' to the previous observation (ie 20 to 10, 30 to 20, etc) and am having trouble getting it to work.

ID <- c(rep("A", 4), rep("B", 3), rep("C", 3))
Time <- c(10, 20, 30, 40, 10, 20, 30, 10, 20, 30)
Value <- sample(1:100, 10)
dat <- cbind(ID, Time, Value)

newDat <- dat %>%
  arrange(Time) %>%
  group_by(ID) %>%
  mutate(ratio = Value/first(Value))

Answer 1

Use lag to get previous value.

library(dplyr)

dat %>%
  arrange(ID, Time) %>%
  group_by(ID) %>%
  mutate(ratio = Value/lag(Value))


#   ID     Time Value  ratio
#   <fct> <dbl> <int>  <dbl>
# 1 A        10    53  NA    
# 2 A        20    16  0.302
# 3 A        30    57  3.56 
# 4 A        40    74  1.30 
# 5 B        10    38  NA    
# 6 B        20    54  1.42 
# 7 B        30    61  1.13 
# 8 C        10    78  NA    
# 9 C        20    41  0.526
#10 C        30    83  2.02 

We can also use head and tail

dat %>%
  arrange(ID, Time) %>%
  group_by(ID) %>%
  mutate(ratio = c(NA, tail(Value, -1)/head(Value, -1)))

data

ID <- c(rep("A", 4), rep("B", 3), rep("C", 3))
Time <- c(10, 20, 30, 40, 10, 20, 30, 10, 20, 30)
Value <- sample(1:100, 10)
dat <- data.frame(ID, Time, Value)

Answer 2

We can use data.table methods

library(data.table)
setDT(df1)[order(Time), ratio := Value/shift(Value), ID]