Transformation

Preamble

Commonly, when collating summaries by group, one wants to:

Split up a big data structure into homogeneous pieces,
Apply a function to each piece
Combine all the results back together.

For example, one might want to:

Calculate summary statistics for each category (read: group)
Perform group-wise transformations (read: apply) like summary or re-scaling/standardization
Fit the same model to different subset of the data

The tidyverse package, through the dplyr, comes to the rescue.

Similar to ggplot2 they feature a Domain Specific Language (DSL) specially designed for data summaries.
Developed by Hadley Wickam, the creator ggplot2 and other useful tools.

Essentially dplyr offer a collection of simple but powerful commands (think of them as verbs) that facilitate this process:

filter: keep observations (rows) matching criteria
select: pick variables (columns) by name
arrange: order the observations (rows) according to a variable (column)
mutate: add new or modify existing variables (column)
summarise: reduce variables to some summary values
group_by: gives the group to apply the analysis functions to

The structure of these commands is always the same:

First argument to the function is a data frame
Subsequent arguments say what to do with data frame, typically what variables to operate on.
Always return a data frame
this is the key difference of the tidyverse vs. base R approach
It recognizes the variables (columns) of the data.frame as variables, that is one only need to write variable_name instead of dat$variable_name

Each of the main dplyr-functions normally does one thing only (but does it “well”) so one normally uses a combination of the above functions. Below we will jump right into using the pipe (|> or %>%).

Reading material

The pipe

We need to load the library {tidyverse} into our current session and we will use the minke-data for demonstation:

library(tidyverse)
w <- 
  "ftp://ftp.hafro.is/pub/data/csv/minke.csv" |> 
  read_csv()

The code structure above is a little bit different than used up to now:

w <- read_csv("ftp://ftp.hafro.is/pub/data/csv/minke.csv")

and is just to gently introduce you to the |>-concept (often read as: “pipe”-concept) that needs a bit of extra explaining:

Noticed that the first argument (“file”) in read_csv in the first code-chunk is missing. Writing just read_csv() on its own would give you an error: ‘argument “file” is missing, with no default’.
The |> operator takes the stuff on the left (here actually in the line above) and places it as the first argument to function on the right hand side.

Recomended that you “read” the |> as “then”. Hence the above can be read as:

create a text string “ftp://ftp.hafro.is/pub/data/csv/minke.csv”.
then (|>) pass it as the first argument into the next function (read_csv).

Some notes on function and arguments can be found here.

store the data in object “w” (here declared in the first line).

Some even go the whole way in code-writing from “left-to-right”, like:

"ftp://ftp.hafro.is/pub/data/csv/minke.csv" |> 
  read_csv() ->
  w

Note that Rstudio has a built in shortcut for the |> operator: [ctrl] + [shift] + M.

Operation on observations (rows)

filter: Extract observations

One can extract observations that meet logical criteria by using the filter command. The first argument is the name of the data frame with subsequent argument(s) being logical expressions. E.g. one subsets the minke data containing only year 2004 (the years in the dataset are from 2003 to 2007) by:

w |> filter(year == 2004)

# A tibble: 25 × 13
      id date                  lon   lat area  length weight   age sex   
   <dbl> <dttm>              <dbl> <dbl> <chr>  <dbl>  <dbl> <dbl> <chr> 
 1     1 2004-06-10 22:00:00 -21.4  65.7 North    780     NA  11.3 Female
 2   690 2004-06-15 17:00:00 -21.4  65.7 North    793     NA  NA   Female
 3   926 2004-06-22 01:00:00 -19.8  66.5 North    858     NA  15.5 Female
 4  1430 2004-06-22 09:00:00 -19.8  66.5 North    840     NA  15.9 Female
 5  1432 2004-06-26 05:00:00 -19.6  65.9 North    761     NA  14   Female
 6  1434 2004-07-04 16:00:00 -21.0  65.5 North    819     NA  16.6 Female
 7  1435 2004-06-04 19:00:00 -22.5  64.6 South    836     NA  46.8 Male  
 8  1437 2004-06-15 13:00:00 -23.0  64.2 South    764     NA   9.9 Male  
 9  1439 2004-06-08 07:00:00 -22.8  64.6 South    774   4620  10.9 Female
10  1440 2004-06-16 11:00:00 -23.4  64.2 South    778     NA  25.3 Male  
# ℹ 15 more rows
# ℹ 4 more variables: maturity <chr>, stomach.volume <dbl>,
#   stomach.weight <dbl>, year <dbl>

Same as:

w |> filter(year %in% 2004)

Only data from 2004 and onwards:

w |> filter(year >= 2004)

Filter observations by some interval:

w |> filter(year >= 2004, year < 2006)  # the "," here should be read as "and"
w |> filter(year >= 2004 & year < 2006) # same as above, here more explicit
w |> filter(between(year, 2004, 2005))  # same as above

All but the year 2004 would be:

w |> filter(year != 2004)     # "!=" should be read as not equal too

But this would give year 2005 to 2007:

w |> filter(year %in% 2005:2007)

Which would be the same as:

filter(w, !year %in% 2003:2004)   # again "!" stands for "not" in R

Filter takes any logical statement:

x == a    # x is equal to a
x != a    # x is not equal to a
x %in% a  # x is "in" a
!x %in% a # x is "not in" a
x > a    # x is greater than a
x >= a   # x is greater or equal to a
x < a    # x is less than a
x <= a   # x is less or equal to a
a & b    # a and b
a | b    # a or b
is.na(x) # is a equal to NA (missing)
...      # ...

The arguments can operate on different variables. E.g. to extract mature males caught in 2007 one would write:

w |> filter(maturity == "mature", sex == "Male", year == 2007)
w |> filter(maturity == "mature" & sex == "Male" & year == 2007) # same thing, more explicit

NOTE: A “comma” is recognized as “AND”. If one were to specify “OR” use the “|”:

filter(w, maturity == "mature" | sex == "Male" | year == 2007)

Exercise

Find all males caught in the northern area in 2006 and 2007
Find all males that are either immature or pregnant
Find all whales caught that did not have a maturity status determined
Find all whales that were caught in year 2007 or were mature males

Solution

w |> filter(sex == "Male", area == "North", year %in% 2006:2007)
w |> filter(sex == "Male", maturity %in% c("immature", "pregnant")) 
w |> filter(is.na(maturity))
w |> filter(year == 2007 | (maturity == "mature" & sex == "Male"))

arrange: Order observations

To sort the data we employ the arrange-function. Sorting by length is as follows (in ascending order):

w |> arrange(length)

# A tibble: 190 × 13
      id date                  lon   lat area  length weight   age sex   
   <dbl> <dttm>              <dbl> <dbl> <chr>  <dbl>  <dbl> <dbl> <chr> 
 1 20927 2006-07-19 15:00:00 -19.2  66.3 North    461     NA   3.4 Female
 2 20254 2005-08-10 16:00:00 -16.8  66.4 North    474     NA   3.4 Male  
 3 20421 2005-07-19 17:00:00 -15.9  64.1 South    482     NA   3.6 Male  
 4  1481 2004-07-03 09:00:00 -15.8  64   South    502     NA   6.7 Female
 5  1344 2003-08-26 16:00:00 -19.3  66.2 North    508     NA  NA   Male  
 6  1504 2003-08-18 17:00:00 -23.9  65.0 South    520     NA  13.3 Male  
 7  1335 2003-09-16 16:00:00 -18.7  66.2 North    526     NA   9.6 Female
 8  1343 2003-08-28 19:00:00 -15.8  66.4 North    542     NA  NA   Female
 9 19211 2005-07-23 16:00:00 -14.2  65.8 North    564     NA   5.2 Female
10 20427 2005-08-03 15:00:00 -23.1  64.6 South    566   1663   6.1 Male  
# ℹ 180 more rows
# ℹ 4 more variables: maturity <chr>, stomach.volume <dbl>,
#   stomach.weight <dbl>, year <dbl>

and in descending order:

w |> arrange(desc(length))

You can also arrange by more that one column:

w |> arrange(sex, desc(length))

Above first orders the data by sex (alphabetical, first Female then Male) and then by increasing length.

distinct

distinct can be used extract unique observations in a data frame. The command below would operate on all the variables in the dataframe (so if there were duplicate observations you would only get unique records):

w |> distinct()

The minke data actally has distinct records so the above example is a bit meaningless. One however normally operates on selected variables like:

w |> distinct(sex)

# A tibble: 2 × 1
  sex   
  <chr> 
1 Female
2 Male

w |> distinct(sex, maturity)   # so no record of a pregnant male!

# A tibble: 8 × 2
  sex    maturity  
  <chr>  <chr>     
1 Female pregnant  
2 Male   immature  
3 Female immature  
4 Male   pubertal  
5 Male   mature    
6 Female anoestrous
7 Female <NA>      
8 Male   <NA>

If we wanted to get the distinct records in a particular order we could do:

w |> 
  distinct(sex, maturity) |> 
  arrange(sex, maturity)

# A tibble: 8 × 2
  sex    maturity  
  <chr>  <chr>     
1 Female anoestrous
2 Female immature  
3 Female pregnant  
4 Female <NA>      
5 Male   immature  
6 Male   mature    
7 Male   pubertal  
8 Male   <NA>

This is an example of combining the dplyr-functions in a single pipe-flow, something we will do a lot of in this course.

Operations on variables (columns)

select: Extract variables

The select functions allows you to extract certain variables of interest.

Select columns by name:

w |> select(id, sex, maturity)

# A tibble: 190 × 3
      id sex    maturity
   <dbl> <chr>  <chr>   
 1     1 Female pregnant
 2   690 Female pregnant
 3   926 Female pregnant
 4  1333 Male   immature
 5  1334 Female immature
 6  1335 Female immature
 7  1336 Female pregnant
 8  1338 Female pregnant
 9  1339 Male   pubertal
10  1341 Male   mature  
# ℹ 180 more rows

Select all columns between length and age:

w |> select(length:age)

You can also omit certain columns using negative indexing: for example you can select all columns except those between sex and stomach.weight

w |> select(!sex:stomach.weight)

# A tibble: 190 × 9
      id date                  lon   lat area  length weight   age  year
   <dbl> <dttm>              <dbl> <dbl> <chr>  <dbl>  <dbl> <dbl> <dbl>
 1     1 2004-06-10 22:00:00 -21.4  65.7 North    780     NA  11.3  2004
 2   690 2004-06-15 17:00:00 -21.4  65.7 North    793     NA  NA    2004
 3   926 2004-06-22 01:00:00 -19.8  66.5 North    858     NA  15.5  2004
 4  1333 2003-09-30 16:00:00 -21.6  65.7 North    567     NA   7.2  2003
 5  1334 2003-09-25 15:00:00 -15.6  66.3 North    774     NA  12.3  2003
 6  1335 2003-09-16 16:00:00 -18.7  66.2 North    526     NA   9.6  2003
 7  1336 2003-09-12 17:00:00 -21.5  65.7 North    809     NA  17.3  2003
 8  1338 2003-09-09 12:00:00 -22.8  66.1 North    820     NA  13.8  2003
 9  1339 2003-08-31 13:00:00 -17.5  66.6 North    697     NA  12.2  2003
10  1341 2003-08-30 17:00:00 -14.7  66.2 North    777     NA  15.4  2003
# ℹ 180 more rows

A combination of non-adjacent variables to drop could be written as:

w |> select(-c(weight, maturity))

You can select all categorical values by:

w |> select(where(is.character))

# A tibble: 190 × 3
   area  sex    maturity
   <chr> <chr>  <chr>   
 1 North Female pregnant
 2 North Female pregnant
 3 North Female pregnant
 4 North Male   immature
 5 North Female immature
 6 North Female immature
 7 North Female pregnant
 8 North Female pregnant
 9 North Male   pubertal
10 North Male   mature  
# ℹ 180 more rows

The select function has some useful helper function:

starts_with('stomach')  # Finds all columns that start with "stomach"
ends_with('weight')     # Finds all columns that end with "weight"
contains('mach')        # Finds all columns that contain "mach"

And you can of course combine these at will:

w |> select(id, length, starts_with('stomach'))

# A tibble: 190 × 4
      id length stomach.volume stomach.weight
   <dbl>  <dbl>          <dbl>          <dbl>
 1     1    780             58         31.9  
 2   690    793             90         36.3  
 3   926    858             24          9.42 
 4  1333    567             25          3.64 
 5  1334    774             85          5.51 
 6  1335    526             18          1.17 
 7  1336    809            200         99    
 8  1338    820            111         64.3  
 9  1339    697              8          0.801
10  1341    777             25          1.42 
# ℹ 180 more rows

select also allows you to rename columns as you select them:

w |> select(id, yr = year)

# A tibble: 190 × 2
      id    yr
   <dbl> <dbl>
 1     1  2004
 2   690  2004
 3   926  2004
 4  1333  2003
 5  1334  2003
 6  1335  2003
 7  1336  2003
 8  1338  2003
 9  1339  2003
10  1341  2003
# ℹ 180 more rows

but this only selects the requested columns, others are dropped.

rename: Rename columns

If you just want to rename a couple of columns in the data frame leaving the other columns intact you can use the function rename:

w |> rename(time = date, stomach_volume = stomach.volume)

# A tibble: 190 × 13
      id time                  lon   lat area  length weight   age sex   
   <dbl> <dttm>              <dbl> <dbl> <chr>  <dbl>  <dbl> <dbl> <chr> 
 1     1 2004-06-10 22:00:00 -21.4  65.7 North    780     NA  11.3 Female
 2   690 2004-06-15 17:00:00 -21.4  65.7 North    793     NA  NA   Female
 3   926 2004-06-22 01:00:00 -19.8  66.5 North    858     NA  15.5 Female
 4  1333 2003-09-30 16:00:00 -21.6  65.7 North    567     NA   7.2 Male  
 5  1334 2003-09-25 15:00:00 -15.6  66.3 North    774     NA  12.3 Female
 6  1335 2003-09-16 16:00:00 -18.7  66.2 North    526     NA   9.6 Female
 7  1336 2003-09-12 17:00:00 -21.5  65.7 North    809     NA  17.3 Female
 8  1338 2003-09-09 12:00:00 -22.8  66.1 North    820     NA  13.8 Female
 9  1339 2003-08-31 13:00:00 -17.5  66.6 North    697     NA  12.2 Male  
10  1341 2003-08-30 17:00:00 -14.7  66.2 North    777     NA  15.4 Male  
# ℹ 180 more rows
# ℹ 4 more variables: maturity <chr>, stomach_volume <dbl>,
#   stomach.weight <dbl>, year <dbl>

Exercise

Select age, length and id from the minke dataset, and rename id to “whale_id”
Select the id column and all columns that contain the text “weight”.

Solution

w |> select(age, length, whale_id = id)
w |> select(id, contains("weight"))

mutate: Compute new variable

mutate allows you to add new columns to your data. Let’s calculate the approximate weight:

w |> 
  select(id, length, weight) |> 
  mutate(computed_weight = 0.00001 * length^3)

# A tibble: 190 × 4
      id length weight computed_weight
   <dbl>  <dbl>  <dbl>           <dbl>
 1     1    780     NA           4746.
 2   690    793     NA           4987.
 3   926    858     NA           6316.
 4  1333    567     NA           1823.
 5  1334    774     NA           4637.
 6  1335    526     NA           1455.
 7  1336    809     NA           5295.
 8  1338    820     NA           5514.
 9  1339    697     NA           3386.
10  1341    777     NA           4691.
# ℹ 180 more rows

You can also do more than one “mutation”:

w |> 
  select(id, length, weight) |> 
  mutate(computed_weight = 0.00001 * length^3,
         weight2 = ifelse(is.na(weight), 0.00001 * length^3, weight))

# A tibble: 190 × 5
      id length weight computed_weight weight2
   <dbl>  <dbl>  <dbl>           <dbl>   <dbl>
 1     1    780     NA           4746.   4746.
 2   690    793     NA           4987.   4987.
 3   926    858     NA           6316.   6316.
 4  1333    567     NA           1823.   1823.
 5  1334    774     NA           4637.   4637.
 6  1335    526     NA           1455.   1455.
 7  1336    809     NA           5295.   5295.
 8  1338    820     NA           5514.   5514.
 9  1339    697     NA           3386.   3386.
10  1341    777     NA           4691.   4691.
# ℹ 180 more rows

To make our lives a bit easier mutate “remembers” earlier transformations within the sequence:

w |> 
  select(id, length, weight) |> 
  mutate(computed_weight = 0.00001 * length^3,
         approx_weight = ifelse(is.na(weight), computed_weight, weight))

One can also overwrite existing variables:

w |> 
  select(id, length, weight) |> 
  mutate(computed_weight = 0.00001 * length^3,
         weight = ifelse(is.na(weight), computed_weight, weight))

And even not create a temporary variable (here computed_weight):

w |> 
  select(id, length, weight) |> 
  mutate(weight = ifelse(is.na(weight),  0.00001 * length^3, weight))

Exercise

Calculate the Fullton’s condition factor for whales where observations of weights exists. The formula is:

$K = 100 (W / L^{3})$

Note: the weights need to be in grams, the length in cm

Hint: Use the function is.na (in the sense of !is.na) to filter out records with observed weight.

Solution

w |> 
  filter(!is.na(weight)) |> 
  select(id, length, weight) |> 
  mutate(K = 100 * (1000 * weight / length^3))

# another way:
w |> 
  select(id, length, weight) |> 
  drop_na() |> 
  mutate(K = 100 * (1000 * weight / length^3))

Summarise cases

summarise:

To summarise data one uses the summarise-function. Below we calculate the number of observations (using the cl("n")-function and the mean minke length.

w |> 
  summarise(n.obs = n(),
            ml = mean(length, na.rm = TRUE))

# A tibble: 1 × 2
  n.obs    ml
  <int> <dbl>
1   190  753.

group_by:

The power of the command summarise is revealed when used in conjunction with group_by-function. The latter functions splits the data into groups based on one or multiple variables. E.g. one can split the minke table by maturity:

w |> 
  group_by(maturity)

# A tibble: 190 × 13
# Groups:   maturity [6]
      id date                  lon   lat area  length weight   age sex   
   <dbl> <dttm>              <dbl> <dbl> <chr>  <dbl>  <dbl> <dbl> <chr> 
 1     1 2004-06-10 22:00:00 -21.4  65.7 North    780     NA  11.3 Female
 2   690 2004-06-15 17:00:00 -21.4  65.7 North    793     NA  NA   Female
 3   926 2004-06-22 01:00:00 -19.8  66.5 North    858     NA  15.5 Female
 4  1333 2003-09-30 16:00:00 -21.6  65.7 North    567     NA   7.2 Male  
 5  1334 2003-09-25 15:00:00 -15.6  66.3 North    774     NA  12.3 Female
 6  1335 2003-09-16 16:00:00 -18.7  66.2 North    526     NA   9.6 Female
 7  1336 2003-09-12 17:00:00 -21.5  65.7 North    809     NA  17.3 Female
 8  1338 2003-09-09 12:00:00 -22.8  66.1 North    820     NA  13.8 Female
 9  1339 2003-08-31 13:00:00 -17.5  66.6 North    697     NA  12.2 Male  
10  1341 2003-08-30 17:00:00 -14.7  66.2 North    777     NA  15.4 Male  
# ℹ 180 more rows
# ℹ 4 more variables: maturity <chr>, stomach.volume <dbl>,
#   stomach.weight <dbl>, year <dbl>

The table appears “intact” because it still has 190 observations but it has 6 groups, representing the different values of the maturity scaling in the data (anoestrous, immature, mature, pregnant, pubertal and “NA”).

The summarise-command respects the grouping, as shown if one uses the same command as used above, but now on a dataframe that has been grouped:

w |> 
  group_by(maturity) |> 
  summarise(n.obs = n(),
            mean = mean(length))

# A tibble: 6 × 3
  maturity   n.obs  mean
  <chr>      <int> <dbl>
1 anoestrous     6  784.
2 immature      25  619.
3 mature        74  758.
4 pregnant      66  800.
5 pubertal       6  692.
6 <NA>          13  752.

Excercise

Calculate the number of observations and minimum, median, mean, standard deviation and standard error of whale lengths in each year
The function names in R are:
- n
- min
- max
- median
- mean
- sd

The function for standard error is not availble in R. A remedy is that you use college statistical knowledge to derive them from the appropriate variables you derived above.

Solution

w |> 
  group_by(year) |> 
  summarise(n = n(),
            min = min(length),
            max = max(length),
            median = median(length),
            mean = mean(length),
            sd = sd(length),
            se = sd / sqrt(n))