Aggregate / summarize multiple variables per group (e.g. sum, mean)

Using the data.table package, which is fast (useful for larger datasets)

https://github.com/Rdatatable/data.table/wiki

library(data.table)
df2 <- setDT(df1)[, lapply(.SD, sum), by=.(year, month), .SDcols=c("x1","x2")]
setDF(df2) # convert back to dataframe

Using the plyr package

require(plyr)
df2 <- ddply(df1, c("year", "month"), function(x) colSums(x[c("x1", "x2")]))

Using summarize() from the Hmisc package (column headings are messy in my example though)

# need to detach plyr because plyr and Hmisc both have a summarize()
detach(package:plyr)
require(Hmisc)
df2 <- with(df1, summarize( cbind(x1, x2), by=llist(year, month), FUN=colSums))

Yes, in your formula, you can cbind the numeric variables to be aggregated:

aggregate(cbind(x1, x2) ~ year + month, data = df1, sum, na.rm = TRUE)
   year month         x1          x2
1  2000     1   7.862002   -7.469298
2  2001     1 276.758209  474.384252
3  2000     2  13.122369 -128.122613
...
23 2000    12  63.436507  449.794454
24 2001    12 999.472226  922.726589

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See ?aggregate, the formula argument and the examples.

Where is this year() function from?

You could also use the reshape2 package for this task:

require(reshape2)
df_melt <- melt(df1, id = c("date", "year", "month"))
dcast(df_melt, year + month ~ variable, sum)
#  year month         x1           x2
1  2000     1  -80.83405 -224.9540159
2  2000     2 -223.76331 -288.2418017
3  2000     3 -188.83930 -481.5601913
4  2000     4 -197.47797 -473.7137420
5  2000     5 -259.07928 -372.4563522

With the dplyr package, you can use summarise_all, summarise_at or summarise_if functions to aggregate multiple variables simultaneously. For the example dataset you can do this as follows:

library(dplyr)
# summarising all non-grouping variables
df2 <- df1 %>% group_by(year, month) %>% summarise_all(sum)

# summarising a specific set of non-grouping variables
df2 <- df1 %>% group_by(year, month) %>% summarise_at(vars(x1, x2), sum)
df2 <- df1 %>% group_by(year, month) %>% summarise_at(vars(-date), sum)

# summarising a specific set of non-grouping variables using select_helpers
# see ?select_helpers for more options
df2 <- df1 %>% group_by(year, month) %>% summarise_at(vars(starts_with('x')), sum)
df2 <- df1 %>% group_by(year, month) %>% summarise_at(vars(matches('.*[0-9]')), sum)

# summarising a specific set of non-grouping variables based on condition (class)
df2 <- df1 %>% group_by(year, month) %>% summarise_if(is.numeric, sum)

The result of the latter two options:

    year month        x1         x2
   <dbl> <dbl>     <dbl>      <dbl>
1   2000     1 -73.58134  -92.78595
2   2000     2 -57.81334 -152.36983
3   2000     3 122.68758  153.55243
4   2000     4 450.24980  285.56374
5   2000     5 678.37867  384.42888
6   2000     6 792.68696  530.28694
7   2000     7 908.58795  452.31222
8   2000     8 710.69928  719.35225
9   2000     9 725.06079  914.93687
10  2000    10 770.60304  863.39337
# ... with 14 more rows

Note: summarise_each is deprecated in favor of summarise_all, summarise_at and summarise_if.

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As mentioned in my comment above, you can also use the recast function from the reshape2-package:

library(reshape2)
recast(df1, year + month ~ variable, sum, id.var = c("date", "year", "month"))

which will give you the same result.