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Rmd 9ae1c27 Dave Tang 2022-04-26 Aggregation with dplyr

Investopedia has a good definition of an aggregate function:

An aggregate function is a mathematical computation involving a range of values that results in just a single value expressing the significance of the accumulated data it is derived from. Aggregate functions are often used to derive descriptive statistics.

In base R, aggregation is achieved using the aggregate function, which according to its help page, computes summary statistics of data subsets. I wrote a post on using the aggregate function because the function was not intuitive to me (at the time I wrote the post). In this post, I will use the ChickWeight dataset to illustrate aggregation. The ChickWeight data frame contains 578 rows and 4 columns from an experiment on the effect of diet on early growth of chicks. Use ?ChickWeight to find out more about the dataset.

data("ChickWeight")
str(ChickWeight)
Classes 'nfnGroupedData', 'nfGroupedData', 'groupedData' and 'data.frame':  578 obs. of  4 variables:
 $ weight: num  42 51 59 64 76 93 106 125 149 171 ...
 $ Time  : num  0 2 4 6 8 10 12 14 16 18 ...
 $ Chick : Ord.factor w/ 50 levels "18"<"16"<"15"<..: 15 15 15 15 15 15 15 15 15 15 ...
 $ Diet  : Factor w/ 4 levels "1","2","3","4": 1 1 1 1 1 1 1 1 1 1 ...
 - attr(*, "formula")=Class 'formula'  language weight ~ Time | Chick
  .. ..- attr(*, ".Environment")=<environment: R_EmptyEnv> 
 - attr(*, "outer")=Class 'formula'  language ~Diet
  .. ..- attr(*, ".Environment")=<environment: R_EmptyEnv> 
 - attr(*, "labels")=List of 2
  ..$ x: chr "Time"
  ..$ y: chr "Body weight"
 - attr(*, "units")=List of 2
  ..$ x: chr "(days)"
  ..$ y: chr "(gm)"

Groups of chicks were fed the same diet and most chicks had 12 measurements.

table(ChickWeight$Diet, ChickWeight$Chick)
   
    18 16 15 13  9 20 10  8 17 19  4  6 11  3  1 12  2  5 14  7 24 30 22 23 27
  1  2  7  8 12 12 12 12 11 12 12 12 12 12 12 12 12 12 12 12 12  0  0  0  0  0
  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 12 12 12 12 12
  3  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
  4  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
   
    28 26 25 29 21 33 37 36 31 39 38 32 40 34 35 44 45 43 41 47 49 46 50 42 48
  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
  2 12 12 12 12 12  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
  3  0  0  0  0  0 12 12 12 12 12 12 12 12 12 12  0  0  0  0  0  0  0  0  0  0
  4  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 10 12 12 12 12 12 12 12 12 12

These 12 measurements correspond to different timepoints (days since birth) where their weight was measured.

ChickWeight[ChickWeight$Chick == 13, ]
    weight Time Chick Diet
144     41    0    13    1
145     48    2    13    1
146     53    4    13    1
147     60    6    13    1
148     65    8    13    1
149     67   10    13    1
150     71   12    13    1
151     70   14    13    1
152     71   16    13    1
153     81   18    13    1
154     91   20    13    1
155     96   21    13    1

Aggregating weight (using mean) as a function of diet can show us whether different diets resulted in different weights.

aggregate(weight ~ Diet, data = ChickWeight, mean)
  Diet   weight
1    1 102.6455
2    2 122.6167
3    3 142.9500
4    4 135.2627

The weight ~ Diet expression is a R formula, which is commonly used to generate design matrices but can be used as a general expression.

class(weight ~ Diet)
[1] "formula"

The same expression can be used for boxplots.

boxplot(weight ~ Diet, ChickWeight)

However, using R formula may not be intuitive and the following dplyr approach may make more sense, especially to those familiar with the group by statement.

group_by(ChickWeight, Diet) %>%
  summarise(weight = mean(weight))
# A tibble: 4 × 2
  Diet  weight
  <fct>  <dbl>
1 1       103.
2 2       123.
3 3       143.
4 4       135.

To aggregate with two factors.

head(aggregate(weight ~ Diet + Time, data = ChickWeight, mean))
  Diet Time weight
1    1    0  41.40
2    2    0  40.70
3    3    0  40.80
4    4    0  41.00
5    1    2  47.25
6    2    2  49.40

Using a dplyr approach.

group_by(ChickWeight, Diet, Time) %>%
  summarise(weight = mean(weight)) %>%
  head()
`summarise()` has grouped output by 'Diet'. You can override using the `.groups`
argument.
# A tibble: 6 × 3
# Groups:   Diet [1]
  Diet   Time weight
  <fct> <dbl>  <dbl>
1 1         0   41.4
2 1         2   47.2
3 1         4   56.5
4 1         6   66.8
5 1         8   79.7
6 1        10   93.1

Aggregating and calculating two summaries.

aggregate(
  weight ~ Diet,
  data = ChickWeight,
  FUN = function(x) c(mean = mean(x), n = length(x))
)
  Diet weight.mean weight.n
1    1    102.6455 220.0000
2    2    122.6167 120.0000
3    3    142.9500 120.0000
4    4    135.2627 118.0000

Using a dplyr approach.

group_by(ChickWeight, Diet) %>%
  summarise(
    weight.mean = mean(weight),
    weight.n = length(weight)
  )
# A tibble: 4 × 3
  Diet  weight.mean weight.n
  <fct>       <dbl>    <int>
1 1            103.      220
2 2            123.      120
3 3            143.      120
4 4            135.      118

Aggregating on a data subset, for example only keeping chicks with 12 measurements.

chick_table <- table(ChickWeight$Chick)
my_keep <- as.integer(names(chick_table[chick_table == 12]))

aggregate(
  weight ~ Diet,
  data = subset(ChickWeight, Chick %in% my_keep),
  FUN = function(x) c(mean = mean(x), n = length(x))
)
  Diet weight.mean weight.n
1    1    107.6406 192.0000
2    2    122.6167 120.0000
3    3    142.9500 120.0000
4    4    138.3333 108.0000

Using a dplyr approach.

ChickWeight %>%
  filter(Chick %in% my_keep) %>%
  group_by(Diet) %>%
  summarise(
    weight.mean = mean(weight),
    weight.n = length(weight)
  )
# A tibble: 4 × 3
  Diet  weight.mean weight.n
  <fct>       <dbl>    <int>
1 1            108.      192
2 2            123.      120
3 3            143.      120
4 4            138.      108

In summary, the group_by function from dplyr helps with carrying out aggregation functions within factors.


sessionInfo()
R version 4.1.2 (2021-11-01)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Ubuntu 20.04.3 LTS

Matrix products: default
BLAS/LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.8.so

locale:
 [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
 [3] LC_TIME=en_US.UTF-8        LC_COLLATE=en_US.UTF-8    
 [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8   
 [7] LC_PAPER=en_US.UTF-8       LC_NAME=C                 
 [9] LC_ADDRESS=C               LC_TELEPHONE=C            
[11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C       

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
 [1] forcats_0.5.1   stringr_1.4.0   dplyr_1.0.7     purrr_0.3.4    
 [5] readr_2.1.1     tidyr_1.1.4     tibble_3.1.6    ggplot2_3.3.5  
 [9] tidyverse_1.3.1 workflowr_1.7.0

loaded via a namespace (and not attached):
 [1] Rcpp_1.0.8       lubridate_1.8.0  getPass_0.2-2    ps_1.6.0        
 [5] assertthat_0.2.1 rprojroot_2.0.2  digest_0.6.29    utf8_1.2.2      
 [9] R6_2.5.1         cellranger_1.1.0 backports_1.4.1  reprex_2.0.1    
[13] evaluate_0.14    highr_0.9        httr_1.4.2       pillar_1.6.5    
[17] rlang_1.0.0      readxl_1.3.1     rstudioapi_0.13  whisker_0.4     
[21] callr_3.7.0      jquerylib_0.1.4  rmarkdown_2.11   munsell_0.5.0   
[25] broom_0.7.11     compiler_4.1.2   httpuv_1.6.5     modelr_0.1.8    
[29] xfun_0.29        pkgconfig_2.0.3  htmltools_0.5.2  tidyselect_1.1.1
[33] fansi_1.0.2      crayon_1.4.2     tzdb_0.2.0       dbplyr_2.1.1    
[37] withr_2.4.3      later_1.3.0      grid_4.1.2       jsonlite_1.7.3  
[41] gtable_0.3.0     lifecycle_1.0.1  DBI_1.1.2        git2r_0.29.0    
[45] magrittr_2.0.2   scales_1.1.1     cli_3.1.1        stringi_1.7.6   
[49] fs_1.5.2         promises_1.2.0.1 xml2_1.3.3       ellipsis_0.3.2  
[53] generics_0.1.1   vctrs_0.3.8      tools_4.1.2      glue_1.6.1      
[57] hms_1.1.1        processx_3.5.2   fastmap_1.1.0    yaml_2.2.2      
[61] colorspace_2.0-2 rvest_1.0.2      knitr_1.37       haven_2.4.3