Geometric Mean: is there a built-in?

Question

No, but there are a few people who have written one, such as here.

Another possibility is to use this:

exp(mean(log(x)))

Here is a vectorized, zero- and NA-tolerant function for calculating geometric mean in R. The verbose mean calculation involving length(x) is necessary for the cases where x contains non-positive values.

gm_mean = function(x, na.rm=TRUE){
  exp(sum(log(x[x > 0]), na.rm=na.rm) / length(x))
}

Thanks to @ben-bolker for noting the na.rm pass-through and @Gregor for making sure it works correctly.

I think some of the comments are related to a false-equivalency of NA values in the data and zeros. In the application I had in mind they are the same, but of course this is not generally true. Thus, if you want to include optional propagation of zeros, and treat the length(x) differently in the case of NA removal, the following is a slightly longer alternative to the function above.

gm_mean = function(x, na.rm=TRUE, zero.propagate = FALSE){
  if(any(x < 0, na.rm = TRUE)){
    return(NaN)
  }
  if(zero.propagate){
    if(any(x == 0, na.rm = TRUE)){
      return(0)
    }
    exp(mean(log(x), na.rm = na.rm))
  } else {
    exp(sum(log(x[x > 0]), na.rm=na.rm) / length(x))
  }
}

Note that it also checks for any negative values, and returns a more informative and appropriate NaN respecting that geometric mean is not defined for negative values (but is for zeros). Thanks to commenters who stayed on my case about this.

We can use psych package and call geometric.mean function.

The

exp(mean(log(x)))

will work unless there is a 0 in x. If so, the log will produce -Inf (-Infinite) which always results in a geometric mean of 0.

One solution is to remove the -Inf value before calculating the mean:

geo_mean <- function(data) {
    log_data <- log(data)
    gm <- exp(mean(log_data[is.finite(log_data)]))
    return(gm)
}

You can use a one-liner to do this but it means calculating the log twice which is inefficient.

exp(mean(log(i[is.finite(log(i))])))

I use exactly what Mark says. This way, even with tapply, you can use the built-in mean function, no need to define yours! For example, to compute per-group geometric means of data$value:

exp(tapply(log(data$value), data$group, mean))