How calculate growth rate in long format data frame?

Question

With data structured as follows...

df <- data.frame(Category=c(rep("A",6),rep("B",6)),
      Year=rep(2010:2015,2),Value=1:12)

I'm having a tough time creating a growth rate column (by year) within category. Can anyone help with code to create something like this...

Category Year Value Growth  
    A   2010    1   
    A   2011    2   1.000  
    A   2012    3   0.500  
    A   2013    4   0.333  
    A   2014    5   0.250  
    A   2015    6   0.200  
    B   2010    7     
    B   2011    8   0.143  
    B   2012    9   0.125  
    B   2013    10  0.111  
    B   2014    11  0.100  
    B   2015    12  0.091  

Answer 1

For these sorts of questions ("how do I compute XXX by category YYY")? there are always solutions based on by(), the data.table() package, and plyr. I generally prefer plyr, which is often slower, but (to me) more transparent/elegant.

df <- data.frame(Category=c(rep("A",6),rep("B",6)),
  Year=rep(2010:2015,2),Value=1:12)


library(plyr)
ddply(df,"Category",transform,
         Growth=c(NA,exp(diff(log(Value)))-1))

The main difference between this answer and @krlmr's is that I am using a geometric-mean trick (taking differences of logs and then exponentiating) while @krlmr computes an explicit ratio.

Mathematically, diff(log(Value)) is taking the differences of the logs, i.e. log(x[t+1])-log(x[t]) for all t. When we exponentiate that we get the ratio x[t+1]/x[t] (because exp(log(x[t+1])-log(x[t])) = exp(log(x[t+1]))/exp(log(x[t])) = x[t+1]/x[t]). The OP wanted the fractional change rather than the multiplicative growth rate (i.e. x[t+1]==x[t] corresponds to a fractional change of zero rather than a multiplicative growth rate of 1.0), so we subtract 1.

I am also using transform() for a little bit of extra "syntactic sugar", to avoid creating a new anonymous function.

Answer 2

Using R base function (ave)

> dfdf$Growth <- with(df, ave(Value, Category, 
                      FUN=function(x) c(NA, diff(x)/x[-length(x)]) ))
> df
   Category Year Value     Growth
1         A 2010     1         NA
2         A 2011     2 1.00000000
3         A 2012     3 0.50000000
4         A 2013     4 0.33333333
5         A 2014     5 0.25000000
6         A 2015     6 0.20000000
7         B 2010     7         NA
8         B 2011     8 0.14285714
9         B 2012     9 0.12500000
10        B 2013    10 0.11111111
11        B 2014    11 0.10000000
12        B 2015    12 0.09090909

@Ben Bolker's answer is easily adapted to ave:

transform(df, Growth=ave(Value, Category, 
                         FUN=function(x) c(NA,exp(diff(log(x)))-1)))