R - recursively create dataframe columns via index inside function - r

Question

I have a dataframe with a large amount of annual data. For example consider the following toy example like so:
dat <- data.frame(id = 1:2, quantity = 3:4, agg_2002 = 5:6, agg_2003 = 7:8, agg_2020 = 9:10)
What I would like to do is the following:
Look for columns named "agg_",in the set of column names, names(df)
Substitute the "agg_" in names(df) for "change_"
Calculate the relative change from year to year, so for example,
df$change_2002 <- df$agg_2002/df$agg_2002 (since 2002 is first year)
df$change_2003 <- df$agg_2003/df$agg_2002
df$change_2004 <- df$agg_2004/df$agg_2003...all the way up to 2020 or the latest value with "agg_" in the column name.
What I have so far is the following function:
func <- function(dat, overwrite = FALSE) {
nms <- grep("agg_[0-9]+$", names(dat), value = TRUE)
revnms <- gsub("agg_", "chg_", nms)
for i = 1:ncol(df) %in% revnms{
dat[, rvnms][i] <- lapply(dat[, rvnms][i], `/`, dat[, rvnms][i-1])
}
dat
}
What I am struggling with is the indexing. How do I get R to make the above calculations recursively without having to do it manually? The desired result is the "chg_" columns appended to the original dataframe:
id quantity agg_2002 agg_2003 agg_2020 chg_2002 chg_2003 chg_2020
1 1 3 5 7 9 1 1.40 1.28
2 2 4 6 8 10 1 1.33 1.25
I would like to modify the specified function above to produce the desired result via lapply if possible. All ideas are welcome. Thank you.
UPDATE: I would much prefer something using lapply or something that can accomodate differing data types

Answer 1

You can make table to long form, change name (can use gsub), then spread back
library(tidyverse)
library(stringr)
df <- dat %>% pivot_longer(-c(id,quantity), names_to = "agg", values_to = "year") %>%
mutate(agg = str_replace(agg, "agg", "change")) %>%
group_by(id) %>%
mutate(year = ifelse(is.na(lag(year)), year/year, year/lag(year))) %>% # Divide itself if there is no lag(year)
pivot_wider(names_from = "agg", values_from = "year")
inner_join(dat, df, by = c("id","quantity"))
id quantity agg_2002 agg_2003 agg_2020 change_2002 change_2003 change_2020
1 1 3 5 7 9 1 1.400000 1.285714
2 2 4 6 8 10 1 1.333333 1.250000

Answer 2

Here is a solution with dplyr and tidyr:
library(tidyr)
library(dplyr)
dat %>%
pivot_longer(cols = starts_with("agg"),
names_to = "year",
names_prefix = "agg_",
values_to = "agg") %>%
group_by(id) %>%
arrange(year) %>%
mutate(change = agg / lag(agg, 1)) %>%
pivot_wider(names_from = year, values_from = c("agg", "change"))