collapse and dplyr
Fast (Weighted) Aggregations and Transformations in a Piped Workflow
Sebastian Krantz
2021-01-04
Source:vignettes/collapse_and_dplyr.Rmd
collapse_and_dplyr.RmdThis vignette focuses on the integration of collapse and the popular dplyr package by Hadley Wickham. In particular it will demonstrate how using collapse’s fast functions and some fast alternatives for dplyr verbs can substantially facilitate and speed up basic data manipulation, grouped and weighted aggregations and transformations, and panel data computations (i.e. between- and within-transformations, panel-lags, differences and growth rates) in a dplyr (piped) workflow.
Notes:
This vignette is targeted at dplyr / tidyverse users. collapse is a standalone package and can be programmed efficiently without pipes or dplyr verbs.
The ‘Introduction to collapse’ vignette provides a thorough introduction to the package and a built-in structured documentation is available under
help("collapse-documentation")after installing the package. In additionhelp("collapse-package")provides a compact set of examples for quick-start.Documentation and vignettes can also be viewed online.
1. Fast Aggregations
A key feature of collapse is it’s broad set of Fast
Statistical Functions
(fsum, fprod, fmean, fmedian, fmode, fvar, fsd, fmin, fmax, fnth, ffirst, flast, fnobs, fndistinct)
which are able to substantially speed-up column-wise, grouped and
weighted computations on vectors, matrices or data frames. The functions
are S3 generic, with a default (vector), matrix and data frame method,
as well as a grouped_df method for grouped tibbles used by
dplyr. The grouped tibble method has the following
arguments:
FUN.grouped_df(x, [w = NULL,] TRA = NULL, [na.rm = TRUE,]
use.g.names = FALSE, keep.group_vars = TRUE, [keep.w = TRUE,] ...)where w is a weight variable, and TRA and
can be used to transform x using the computed statistics
and one of 10 available transformations
("replace_fill", "replace", "-", "-+", "/", "%", "+", "*", "%%", "-%%",
discussed in section 2). na.rm efficiently removes missing
values and is TRUE by default. use.g.names
generates new row-names from the unique combinations of groups (default:
disabled), whereas keep.group_vars (default: enabled) will
keep the grouping columns as is custom in the native
data %>% group_by(...) %>% summarize(...) workflow in
dplyr. Finally, keep.w regulates whether a
weighting variable used is also aggregated and saved in a column. For
fsum, fmean, fmedian, fnth, fvar, fsd and
fmode this will compute the sum of the weights in each
group, whereas fprod returns the product of the
weights.
With that in mind, let’s consider some straightforward applications.
1.1 Simple Aggregations
Consider the Groningen Growth and Development Center 10-Sector Database included in collapse and introduced in the main vignette:
library(collapse)
head(GGDC10S)
# Country Regioncode Region Variable Year AGR MIN MAN PU
# 1 BWA SSA Sub-saharan Africa VA 1960 NA NA NA NA
# 2 BWA SSA Sub-saharan Africa VA 1961 NA NA NA NA
# 3 BWA SSA Sub-saharan Africa VA 1962 NA NA NA NA
# 4 BWA SSA Sub-saharan Africa VA 1963 NA NA NA NA
# 5 BWA SSA Sub-saharan Africa VA 1964 16.30154 3.494075 0.7365696 0.1043936
# 6 BWA SSA Sub-saharan Africa VA 1965 15.72700 2.495768 1.0181992 0.1350976
# CON WRT TRA FIRE GOV OTH SUM
# 1 NA NA NA NA NA NA NA
# 2 NA NA NA NA NA NA NA
# 3 NA NA NA NA NA NA NA
# 4 NA NA NA NA NA NA NA
# 5 0.6600454 6.243732 1.658928 1.119194 4.822485 2.341328 37.48229
# 6 1.3462312 7.064825 1.939007 1.246789 5.695848 2.678338 39.34710
# Summarize the Data:
# descr(GGDC10S, cols = is_categorical)
# aperm(qsu(GGDC10S, ~Variable, cols = is.numeric))
# Efficiently converting to tibble (no deep copy)
GGDC10S <- qTBL(GGDC10S)Simple column-wise computations using the fast functions and pipe operators are performed as follows:
library(dplyr)
GGDC10S %>% fnobs # Number of Observations
# Country Regioncode Region Variable Year AGR MIN MAN PU
# 5027 5027 5027 5027 5027 4364 4355 4355 4354
# CON WRT TRA FIRE GOV OTH SUM
# 4355 4355 4355 4355 3482 4248 4364
GGDC10S %>% fndistinct # Number of distinct values
# Country Regioncode Region Variable Year AGR MIN MAN PU
# 43 6 6 2 67 4353 4224 4353 4237
# CON WRT TRA FIRE GOV OTH SUM
# 4339 4344 4334 4349 3470 4238 4364
GGDC10S %>% select_at(6:16) %>% fmedian # Median
# AGR MIN MAN PU CON WRT TRA FIRE GOV
# 4394.5194 173.2234 3718.0981 167.9500 1473.4470 3773.6430 1174.8000 960.1251 3928.5127
# OTH SUM
# 1433.1722 23186.1936
GGDC10S %>% select_at(6:16) %>% fmean # Mean
# AGR MIN MAN PU CON WRT TRA FIRE GOV
# 2526696.5 1867908.9 5538491.4 335679.5 1801597.6 3392909.5 1473269.7 1657114.8 1712300.3
# OTH SUM
# 1684527.3 21566436.8
GGDC10S %>% fmode # Mode
# Country Regioncode Region Variable Year
# "USA" "ASI" "Asia" "EMP" "2010"
# AGR MIN MAN PU CON
# "171.315882316326" "0" "4645.12507642586" "0" "1.34623115930777"
# WRT TRA FIRE GOV OTH
# "21.8380052682527" "8.97743416914571" "40.0701608636442" "0" "3626.84423577048"
# SUM
# "37.4822945751317"
GGDC10S %>% fmode(drop = FALSE) # Keep data structure intact
# # A tibble: 1 × 16
# Country Regioncode Region Variable Year AGR MIN MAN PU CON WRT TRA FIRE GOV
# * <chr> <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
# 1 USA ASI Asia EMP 2010 171. 0 4645. 0 1.35 21.8 8.98 40.1 0
# # ℹ 2 more variables: OTH <dbl>, SUM <dbl>Moving on to grouped statistics, we can compute the average value added and employment by sector and country using:
GGDC10S %>%
group_by(Variable, Country) %>%
select_at(6:16) %>% fmean
# # A tibble: 85 × 13
# Variable Country AGR MIN MAN PU CON WRT TRA FIRE GOV OTH SUM
# <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
# 1 EMP ARG 1420. 52.1 1932. 1.02e2 7.42e2 1.98e3 6.49e2 628. 2043. 9.92e2 1.05e4
# 2 EMP BOL 964. 56.0 235. 5.35e0 1.23e2 2.82e2 1.15e2 44.6 NA 3.96e2 2.22e3
# 3 EMP BRA 17191. 206. 6991. 3.65e2 3.52e3 8.51e3 2.05e3 4414. 5307. 5.71e3 5.43e4
# 4 EMP BWA 188. 10.5 18.1 3.09e0 2.53e1 3.63e1 8.36e0 15.3 61.1 2.76e1 3.94e2
# 5 EMP CHL 702. 101. 625. 2.94e1 2.96e2 6.95e2 2.58e2 272. NA 1.00e3 3.98e3
# 6 EMP CHN 287744. 7050. 67144. 1.61e3 2.09e4 2.89e4 1.39e4 4929. 22669. 3.10e4 4.86e5
# 7 EMP COL 3091. 145. 1175. 3.39e1 5.24e2 2.07e3 4.70e2 649. NA 1.73e3 9.89e3
# 8 EMP CRI 231. 1.70 136. 1.43e1 5.76e1 1.57e2 4.24e1 54.9 128. 6.51e1 8.87e2
# 9 EMP DEW 2490. 407. 8473. 2.26e2 2.09e3 4.44e3 1.48e3 1689. 3945. 9.99e2 2.62e4
# 10 EMP DNK 236. 8.03 507. 1.38e1 1.71e2 4.55e2 1.61e2 181. 549. 1.11e2 2.39e3
# # ℹ 75 more rowsSimilarly we can aggregate using any other of the above functions.
It is important to not use dplyr’s summarize
together with these functions since that would eliminate their speed
gain. These functions are fast because they are executed only once and
carry out the grouped computations in C++, whereas
summarize will apply the function to each group in the
grouped tibble.
Excursus: What is Happening Behind the Scenes?
To better explain this point it is perhaps good to shed some light on what is happening behind the scenes of dplyr and collapse. Fundamentally both packages follow different computing paradigms:
dplyr is an efficient implementation of the Split-Apply-Combine computing paradigm. Data is split into groups, these data-chunks are then passed to a function carrying out the computation, and finally recombined to produce the aggregated data.frame. This modus operandi is evident in the grouping mechanism of dplyr. When a data.frame is passed through group_by, a ‘groups’ attribute is attached:
GGDC10S %>% group_by(Variable, Country) %>% attr("groups")
# # A tibble: 85 × 3
# Variable Country .rows
# <chr> <chr> <list<int>>
# 1 EMP ARG [62]
# 2 EMP BOL [61]
# 3 EMP BRA [62]
# 4 EMP BWA [52]
# 5 EMP CHL [63]
# 6 EMP CHN [62]
# 7 EMP COL [61]
# 8 EMP CRI [62]
# 9 EMP DEW [61]
# 10 EMP DNK [64]
# # ℹ 75 more rowsThis object is a data.frame giving the unique groups and in the third
(last) column vectors containing the indices of the rows belonging to
that group. A command like summarize uses this information
to split the data.frame into groups which are then passed sequentially
to the function used and later recombined. These steps are also done in
C++ which makes dplyr quite efficient.
Now collapse is based around one-pass grouped computations
at the C++ level using its own grouped statistical functions. In other
words the data is not split and recombined at all but the entire
computation is performed in a single C++ loop running through that data
and completing the computations for each group simultaneously. This
modus operandi is also evident in collapse grouping objects.
The method GRP.grouped_df takes a dplyr grouping
object from a grouped tibble and efficiently converts it to a
collapse grouping object:
GGDC10S %>% group_by(Variable, Country) %>% GRP %>% str
# Class 'GRP' hidden list of 9
# $ N.groups : int 85
# $ group.id : int [1:5027] 46 46 46 46 46 46 46 46 46 46 ...
# $ group.sizes : int [1:85] 62 61 62 52 63 62 61 62 61 64 ...
# $ groups :List of 2
# ..$ Variable: chr [1:85] "EMP" "EMP" "EMP" "EMP" ...
# .. ..- attr(*, "label")= chr "Variable"
# .. ..- attr(*, "format.stata")= chr "%9s"
# ..$ Country : chr [1:85] "ARG" "BOL" "BRA" "BWA" ...
# .. ..- attr(*, "label")= chr "Country"
# .. ..- attr(*, "format.stata")= chr "%9s"
# $ group.vars : chr [1:2] "Variable" "Country"
# $ ordered : Named logi [1:2] TRUE FALSE
# ..- attr(*, "names")= chr [1:2] "ordered" "sorted"
# $ order : NULL
# $ group.starts: NULL
# $ call : language GRP.grouped_df(X = .)This object is a list where the first three elements give the number
of groups, the group-id to which each row belongs and a vector of
group-sizes. A function like fsum uses this information to
(for each column) create a result vector of size ‘N.groups’ and the run
through the column using the ‘group.id’ vector to add the i’th data
point to the ’group.id[i]’th element of the result vector. When the loop
is finished, the grouped computation is also finished.
It is obvious that collapse is faster than dplyr since it’s method of computing involves less steps, and it does not need to call statistical functions multiple times. See the benchmark section.
1.2 More Speed using collapse Verbs
collapse fast functions do not develop their maximal
performance on a grouped tibble created with group_by
because of the additional conversion cost of the grouping object
incurred by GRP.grouped_df. This cost is already minimized
through the use of C++, but we can do even better replacing
group_by with collapse::fgroup_by.
fgroup_by works like group_by but does the
grouping with collapse::GRP (up to 10x faster than
group_by) and simply attaches a collapse grouping
object to the grouped_df. Thus the speed gain is 2-fold: Faster grouping
and no conversion cost when calling collapse functions.
Another improvement comes from replacing the dplyr verb
select with collapse::fselect, and, for
selection using column names, indices or functions use
collapse::get_vars instead of select_at or
select_if. Next to get_vars, collapse
also introduces the predicates num_vars,
cat_vars, char_vars, fact_vars,
logi_vars and date_vars to efficiently select
columns by type.
GGDC10S %>% fgroup_by(Variable, Country) %>% get_vars(6:16) %>% fmedian
# # A tibble: 85 × 13
# Variable Country AGR MIN MAN PU CON WRT TRA FIRE GOV OTH SUM
# <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
# 1 EMP ARG 1325. 47.4 1988. 1.05e2 7.82e2 1.85e3 5.80e2 464. 1739. 866. 9.74e3
# 2 EMP BOL 943. 53.5 167. 4.46e0 6.60e1 1.32e2 9.70e1 15.3 NA 384. 1.84e3
# 3 EMP BRA 17481. 225. 7208. 3.76e2 4.05e3 6.45e3 1.58e3 4355. 4450. 4479. 5.19e4
# 4 EMP BWA 175. 12.2 13.1 3.71e0 1.90e1 2.11e1 6.75e0 10.4 53.8 31.2 3.61e2
# 5 EMP CHL 690. 93.9 607. 2.58e1 2.30e2 4.84e2 2.05e2 106. NA 900. 3.31e3
# 6 EMP CHN 293915 8150. 61761. 1.14e3 1.06e4 1.70e4 9.56e3 4328. 19468. 9954. 4.45e5
# 7 EMP COL 3006. 84.0 1033. 3.71e1 4.19e2 1.55e3 3.91e2 655. NA 1430. 8.63e3
# 8 EMP CRI 216. 1.49 114. 7.92e0 5.50e1 8.98e1 2.55e1 19.6 122. 60.6 7.19e2
# 9 EMP DEW 2178 320. 8459. 2.47e2 2.10e3 4.45e3 1.53e3 1656 3700 900 2.65e4
# 10 EMP DNK 187. 3.75 508. 1.36e1 1.65e2 4.61e2 1.61e2 169. 642. 104. 2.42e3
# # ℹ 75 more rows
microbenchmark(collapse = GGDC10S %>% fgroup_by(Variable, Country) %>% get_vars(6:16) %>% fmedian,
hybrid = GGDC10S %>% group_by(Variable, Country) %>% select_at(6:16) %>% fmedian,
dplyr = GGDC10S %>% group_by(Variable, Country) %>% select_at(6:16) %>% summarise_all(median, na.rm = TRUE))
# Unit: microseconds
# expr min lq mean median uq max neval
# collapse 236.406 263.6095 303.309 295.9175 337.061 419.635 100
# hybrid 2699.317 2894.9690 3573.611 2998.3505 3119.772 56249.212 100
# dplyr 15923.908 16297.8280 18810.943 16742.5140 18578.105 71125.939 100Benchmarks on the different components of this code and with larger
data are provided under ‘Benchmarks’. Note that a grouped tibble created
with fgroup_by can no longer be used for grouped
computations with dplyr verbs like mutate or
summarize. fgroup_by first assigns the class
GDP_df which is for printing grouping information and
subsetting, then the object classes (tbl_df,
data.table or whatever else), followed by classes
grouped_df and data.frame, and adds the grouping
object in a ‘groups’ attribute. Since tbl_df is assigned before
grouped_df, the object is treated by the dplyr
ecosystem like a normal tibble.
class(group_by(GGDC10S, Variable, Country))
# [1] "grouped_df" "tbl_df" "tbl" "data.frame"
class(fgroup_by(GGDC10S, Variable, Country))
# [1] "GRP_df" "tbl_df" "tbl" "grouped_df" "data.frame"The function fungroup removes classes ‘GDP_df’ and
‘grouped_df’ and the ‘groups’ attribute (and can thus also be used for
grouped tibbles created with dplyr::group_by).
Note that any kind of data frame based class can be grouped with
fgroup_by, and still retain full responsiveness to all
methods defined for that class. Functions performing aggregation on the
grouped data frame remove the grouping object and classes afterwards,
yielding an object with the same class and attributes as the input.
The print method shown below reports the grouping variables, and then
in square brackets the information
[number of groups | average group size (standard-deviation of group sizes)]:
fgroup_by(GGDC10S, Variable, Country)
# # A tibble: 5,027 × 16
# Country Regioncode Region Variable Year AGR MIN MAN PU CON WRT TRA FIRE GOV
# <chr> <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
# 1 BWA SSA Sub-s… VA 1960 NA NA NA NA NA NA NA NA NA
# 2 BWA SSA Sub-s… VA 1961 NA NA NA NA NA NA NA NA NA
# 3 BWA SSA Sub-s… VA 1962 NA NA NA NA NA NA NA NA NA
# 4 BWA SSA Sub-s… VA 1963 NA NA NA NA NA NA NA NA NA
# 5 BWA SSA Sub-s… VA 1964 16.3 3.49 0.737 0.104 0.660 6.24 1.66 1.12 4.82
# 6 BWA SSA Sub-s… VA 1965 15.7 2.50 1.02 0.135 1.35 7.06 1.94 1.25 5.70
# 7 BWA SSA Sub-s… VA 1966 17.7 1.97 0.804 0.203 1.35 8.27 2.15 1.36 6.37
# 8 BWA SSA Sub-s… VA 1967 19.1 2.30 0.938 0.203 0.897 4.31 1.72 1.54 7.04
# 9 BWA SSA Sub-s… VA 1968 21.1 1.84 0.750 0.203 1.22 5.17 2.44 1.03 5.03
# 10 BWA SSA Sub-s… VA 1969 21.9 5.24 2.14 0.578 3.47 5.75 2.72 1.23 5.59
# # ℹ 5,017 more rows
# # ℹ 2 more variables: OTH <dbl>, SUM <dbl>
#
# Grouped by: Variable, Country [85 | 59 (7.7) 4-65]Note further that fselect and get_vars are
not full drop-in replacements for select because they do
not have a grouped_df method:
GGDC10S %>% group_by(Variable, Country) %>% select_at(6:16) %>% tail(3)
# # A tibble: 3 × 13
# # Groups: Variable, Country [1]
# Variable Country AGR MIN MAN PU CON WRT TRA FIRE GOV OTH SUM
# <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
# 1 EMP EGY 5206. 29.0 2436. 307. 2733. 2977. 1992. 801. 5539. NA 22020.
# 2 EMP EGY 5186. 27.6 2374. 318. 2795. 3020. 2048. 815. 5636. NA 22219.
# 3 EMP EGY 5161. 24.8 2348. 325. 2931. 3110. 2065. 832. 5736. NA 22533.
GGDC10S %>% group_by(Variable, Country) %>% get_vars(6:16) %>% tail(3)
# # A tibble: 3 × 11
# AGR MIN MAN PU CON WRT TRA FIRE GOV OTH SUM
# <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
# 1 5206. 29.0 2436. 307. 2733. 2977. 1992. 801. 5539. NA 22020.
# 2 5186. 27.6 2374. 318. 2795. 3020. 2048. 815. 5636. NA 22219.
# 3 5161. 24.8 2348. 325. 2931. 3110. 2065. 832. 5736. NA 22533.Since by default keep.group_vars = TRUE in the Fast
Statistical Functions, the end result is nevertheless the same:
GGDC10S %>% group_by(Variable, Country) %>% select_at(6:16) %>% fmean %>% tail(3)
# # A tibble: 3 × 13
# Variable Country AGR MIN MAN PU CON WRT TRA FIRE GOV OTH SUM
# <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
# 1 VA VEN 6860. 35478. 1.96e4 1.06e3 1.17e4 1.93e4 8.03e3 5.60e3 NA 19986. 1.28e5
# 2 VA ZAF 16419. 42928. 8.76e4 1.38e4 1.64e4 6.83e4 4.53e4 6.64e4 7.58e4 30167. 4.63e5
# 3 VA ZMB 1268849. 1006099. 9.00e5 2.19e5 8.66e5 2.10e6 7.05e5 9.10e5 1.10e6 81871. 9.16e6
GGDC10S %>% group_by(Variable, Country) %>% get_vars(6:16) %>% fmean %>% tail(3)
# # A tibble: 3 × 13
# Variable Country AGR MIN MAN PU CON WRT TRA FIRE GOV OTH SUM
# <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
# 1 VA VEN 6860. 35478. 1.96e4 1.06e3 1.17e4 1.93e4 8.03e3 5.60e3 NA 19986. 1.28e5
# 2 VA ZAF 16419. 42928. 8.76e4 1.38e4 1.64e4 6.83e4 4.53e4 6.64e4 7.58e4 30167. 4.63e5
# 3 VA ZMB 1268849. 1006099. 9.00e5 2.19e5 8.66e5 2.10e6 7.05e5 9.10e5 1.10e6 81871. 9.16e6Another useful verb introduced by collapse is
fgroup_vars, which can be used to efficiently obtain the
grouping columns or grouping variables from a grouped tibble:
# fgroup_by fully supports grouped tibbles created with group_by or fgroup_by:
GGDC10S %>% group_by(Variable, Country) %>% fgroup_vars %>% head(3)
# # A tibble: 3 × 2
# Variable Country
# <chr> <chr>
# 1 VA BWA
# 2 VA BWA
# 3 VA BWA
GGDC10S %>% fgroup_by(Variable, Country) %>% fgroup_vars %>% head(3)
# # A tibble: 3 × 2
# Variable Country
# <chr> <chr>
# 1 VA BWA
# 2 VA BWA
# 3 VA BWA
# The other possibilities:
GGDC10S %>% group_by(Variable, Country) %>% fgroup_vars("unique") %>% head(3)
# # A tibble: 3 × 2
# Variable Country
# <chr> <chr>
# 1 EMP ARG
# 2 EMP BOL
# 3 EMP BRA
GGDC10S %>% group_by(Variable, Country) %>% fgroup_vars("names")
# [1] "Variable" "Country"
GGDC10S %>% group_by(Variable, Country) %>% fgroup_vars("indices")
# [1] 4 1
GGDC10S %>% group_by(Variable, Country) %>% fgroup_vars("named_indices")
# Variable Country
# 4 1
GGDC10S %>% group_by(Variable, Country) %>% fgroup_vars("logical")
# [1] TRUE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
GGDC10S %>% group_by(Variable, Country) %>% fgroup_vars("named_logical")
# Country Regioncode Region Variable Year AGR MIN MAN PU
# TRUE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
# CON WRT TRA FIRE GOV OTH SUM
# FALSE FALSE FALSE FALSE FALSE FALSE FALSEAnother collapse verb to mention here is
fsubset, a faster alternative to dplyr::filter
which also provides an option to flexibly subset columns after the
select argument:
# Two equivalent calls, the first is substantially faster
GGDC10S %>% fsubset(Variable == "VA" & Year > 1990, Country, Year, AGR:GOV) %>% head(3)
# # A tibble: 3 × 11
# Country Year AGR MIN MAN PU CON WRT TRA FIRE GOV
# <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
# 1 BWA 1991 303. 2647. 473. 161. 580. 807. 233. 433. 1073.
# 2 BWA 1992 333. 2691. 537. 178. 679. 725. 285. 517. 1234.
# 3 BWA 1993 405. 2625. 567. 219. 634. 772. 350. 673. 1487.
GGDC10S %>% filter(Variable == "VA" & Year > 1990) %>% select(Country, Year, AGR:GOV) %>% head(3)
# # A tibble: 3 × 11
# Country Year AGR MIN MAN PU CON WRT TRA FIRE GOV
# <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
# 1 BWA 1991 303. 2647. 473. 161. 580. 807. 233. 433. 1073.
# 2 BWA 1992 333. 2691. 537. 178. 679. 725. 285. 517. 1234.
# 3 BWA 1993 405. 2625. 567. 219. 634. 772. 350. 673. 1487.collapse also offers roworder,
frename, colorder and
ftransform/TRA as fast replacements for
dplyr::arrange, dplyr::rename,
dplyr::relocate and dplyr::mutate.
1.3 Multi-Function Aggregations
One can also aggregate with multiple functions at the same time. For
such operations it is often necessary to use curly braces {
to prevent first argument injection so that
%>% cbind(FUN1(.), FUN2(.)) does not evaluate as
%>% cbind(., FUN1(.), FUN2(.)):
GGDC10S %>%
fgroup_by(Variable, Country) %>%
get_vars(6:16) %>% {
cbind(fmedian(.),
add_stub(fmean(., keep.group_vars = FALSE), "mean_"))
} %>% head(3)
# Variable Country AGR MIN MAN PU CON WRT TRA
# 1 EMP ARG 1324.5255 47.35255 1987.5912 104.738825 782.40283 1854.612 579.93982
# 2 EMP BOL 943.1612 53.53538 167.1502 4.457895 65.97904 132.225 96.96828
# 3 EMP BRA 17480.9810 225.43693 7207.7915 375.851832 4054.66103 6454.523 1580.81120
# FIRE GOV OTH SUM mean_AGR mean_MIN mean_MAN mean_PU mean_CON
# 1 464.39920 1738.836 866.1119 9743.223 1419.8013 52.08903 1931.7602 101.720936 742.4044
# 2 15.34259 NA 384.0678 1842.055 964.2103 56.03295 235.0332 5.346433 122.7827
# 3 4354.86210 4449.942 4478.6927 51881.110 17191.3529 206.02389 6991.3710 364.573404 3524.7384
# mean_WRT mean_TRA mean_FIRE mean_GOV mean_OTH mean_SUM
# 1 1982.1775 648.5119 627.79291 2043.471 992.4475 10542.177
# 2 281.5164 115.4728 44.56442 NA 395.5650 2220.524
# 3 8509.4612 2054.3731 4413.54448 5307.280 5710.2665 54272.985The function add_stub used above is a collapse
function adding a prefix (default) or suffix to variables names. The
collapse predicate add_vars provides a more
efficient alternative to cbind.data.frame. The idea here is
‘adding’ variables to the data.frame in the first argument i.e. the
attributes of the first argument are preserved, so the expression below
still gives a tibble instead of a data.frame:
GGDC10S %>%
fgroup_by(Variable, Country) %>% {
add_vars(get_vars(., "Reg", regex = TRUE) %>% ffirst, # Regular expression matching column names
num_vars(.) %>% fmean(keep.group_vars = FALSE) %>% add_stub("mean_"), # num_vars selects all numeric variables
fselect(., PU:TRA) %>% fmedian(keep.group_vars = FALSE) %>% add_stub("median_"),
fselect(., PU:CON) %>% fmin(keep.group_vars = FALSE) %>% add_stub("min_"))
} %>% head(3)
# # A tibble: 3 × 22
# Variable Country Regioncode Region mean_Year mean_AGR mean_MIN mean_MAN mean_PU mean_CON mean_WRT
# <chr> <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
# 1 EMP ARG LAM Latin … 1980. 1420. 52.1 1932. 102. 742. 1982.
# 2 EMP BOL LAM Latin … 1980 964. 56.0 235. 5.35 123. 282.
# 3 EMP BRA LAM Latin … 1980. 17191. 206. 6991. 365. 3525. 8509.
# # ℹ 11 more variables: mean_TRA <dbl>, mean_FIRE <dbl>, mean_GOV <dbl>, mean_OTH <dbl>,
# # mean_SUM <dbl>, median_PU <dbl>, median_CON <dbl>, median_WRT <dbl>, median_TRA <dbl>,
# # min_PU <dbl>, min_CON <dbl>Another nice feature of add_vars is that it can also
very efficiently reorder columns i.e. bind columns in a different order
than they are passed. This can be done by simply specifying the
positions the added columns should have in the final data frame, and
then add_vars shifts the first argument columns to the
right to fill in the gaps.
GGDC10S %>%
fsubset(Variable == "VA", Country, AGR, SUM) %>%
fgroup_by(Country) %>% {
add_vars(fgroup_vars(.,"unique"),
fmean(., keep.group_vars = FALSE) %>% add_stub("mean_"),
fsd(., keep.group_vars = FALSE) %>% add_stub("sd_"),
pos = c(2,4,3,5))
} %>% head(3)
# # A tibble: 3 × 5
# Country mean_AGR sd_AGR mean_SUM sd_SUM
# <chr> <dbl> <dbl> <dbl> <dbl>
# 1 ARG 14951. 33061. 152534. 301316.
# 2 BOL 3300. 4456. 22619. 33173.
# 3 BRA 76870. 59442. 1200563. 976963.A much more compact solution to multi-function and multi-type aggregation is offered by the function collapg:
# This aggregates numeric colums using the mean (fmean) and categorical columns with the mode (fmode)
GGDC10S %>% fgroup_by(Variable, Country) %>% collapg %>% head(3)
# # A tibble: 3 × 16
# Variable Country Regioncode Region Year AGR MIN MAN PU CON WRT TRA FIRE GOV
# <chr> <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
# 1 EMP ARG LAM Latin … 1980. 1420. 52.1 1932. 102. 742. 1982. 649. 628. 2043.
# 2 EMP BOL LAM Latin … 1980 964. 56.0 235. 5.35 123. 282. 115. 44.6 NA
# 3 EMP BRA LAM Latin … 1980. 17191. 206. 6991. 365. 3525. 8509. 2054. 4414. 5307.
# # ℹ 2 more variables: OTH <dbl>, SUM <dbl>By default it aggregates numeric columns using the fmean
and categorical columns using fmode, and preserves the
order of all columns. Changing these defaults is very easy:
# This aggregates numeric colums using the median and categorical columns using the first value
GGDC10S %>% fgroup_by(Variable, Country) %>% collapg(fmedian, flast) %>% head(3)
# # A tibble: 3 × 16
# Variable Country Regioncode Region Year AGR MIN MAN PU CON WRT TRA FIRE
# <chr> <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
# 1 EMP ARG LAM Latin Amer… 1980. 1325. 47.4 1988. 105. 782. 1855. 580. 464.
# 2 EMP BOL LAM Latin Amer… 1980 943. 53.5 167. 4.46 66.0 132. 97.0 15.3
# 3 EMP BRA LAM Latin Amer… 1980. 17481. 225. 7208. 376. 4055. 6455. 1581. 4355.
# # ℹ 3 more variables: GOV <dbl>, OTH <dbl>, SUM <dbl>One can apply multiple functions to both numeric and/or categorical data:
GGDC10S %>% fgroup_by(Variable, Country) %>%
collapg(list(fmean, fmedian), list(first, fmode, flast)) %>% head(3)
# # A tibble: 3 × 32
# Variable Country first.Regioncode fmode.Regioncode flast.Regioncode first.Region fmode.Region
# <chr> <chr> <chr> <chr> <chr> <chr> <chr>
# 1 EMP ARG LAM LAM LAM Latin America Latin America
# 2 EMP BOL LAM LAM LAM Latin America Latin America
# 3 EMP BRA LAM LAM LAM Latin America Latin America
# # ℹ 25 more variables: flast.Region <chr>, fmean.Year <dbl>, fmedian.Year <dbl>, fmean.AGR <dbl>,
# # fmedian.AGR <dbl>, fmean.MIN <dbl>, fmedian.MIN <dbl>, fmean.MAN <dbl>, fmedian.MAN <dbl>,
# # fmean.PU <dbl>, fmedian.PU <dbl>, fmean.CON <dbl>, fmedian.CON <dbl>, fmean.WRT <dbl>,
# # fmedian.WRT <dbl>, fmean.TRA <dbl>, fmedian.TRA <dbl>, fmean.FIRE <dbl>, fmedian.FIRE <dbl>,
# # fmean.GOV <dbl>, fmedian.GOV <dbl>, fmean.OTH <dbl>, fmedian.OTH <dbl>, fmean.SUM <dbl>,
# # fmedian.SUM <dbl>Applying multiple functions to only numeric (or only categorical) data allows return in a long format:
GGDC10S %>% fgroup_by(Variable, Country) %>%
collapg(list(fmean, fmedian), cols = is.numeric, return = "long") %>% head(3)
# # A tibble: 3 × 15
# Function Variable Country Year AGR MIN MAN PU CON WRT TRA FIRE GOV OTH
# <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
# 1 fmean EMP ARG 1980. 1420. 52.1 1932. 102. 742. 1982. 649. 628. 2043. 992.
# 2 fmean EMP BOL 1980 964. 56.0 235. 5.35 123. 282. 115. 44.6 NA 396.
# 3 fmean EMP BRA 1980. 17191. 206. 6991. 365. 3525. 8509. 2054. 4414. 5307. 5710.
# # ℹ 1 more variable: SUM <dbl>Finally, collapg also makes it very easy to apply
aggregator functions to certain columns only:
GGDC10S %>% fgroup_by(Variable, Country) %>%
collapg(custom = list(fmean = 6:8, fmedian = 10:12)) %>% head(3)
# # A tibble: 3 × 8
# Variable Country AGR MIN MAN CON WRT TRA
# <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
# 1 EMP ARG 1420. 52.1 1932. 782. 1855. 580.
# 2 EMP BOL 964. 56.0 235. 66.0 132. 97.0
# 3 EMP BRA 17191. 206. 6991. 4055. 6455. 1581.To understand more about collapg, look it up in the
documentation (?collapg).
1.4 Weighted Aggregations
Weighted aggregations are possible with the functions
fsum, fprod, fmean, fmedian, fnth, fmode, fvar and
fsd. The implementation is such that by default (option
keep.w = TRUE) these functions also aggregate the weights,
so that further weighted computations can be performed on the aggregated
data. fprod saves the product of the weights, whereas the
other functions save the sum of the weights in a column next to the
grouping variables. If na.rm = TRUE (the default), rows
with missing weights are omitted from the computation.
# This computes a frequency-weighted grouped standard-deviation, taking the total EMP / VA as weight
GGDC10S %>%
fgroup_by(Variable, Country) %>%
fselect(AGR:SUM) %>% fsd(SUM) %>% head(3)
# # A tibble: 3 × 13
# Variable Country sum.SUM AGR MIN MAN PU CON WRT TRA FIRE GOV OTH
# <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
# 1 EMP ARG 653615. 225. 22.2 176. 20.5 285. 856. 195. 493. 1123. 506.
# 2 EMP BOL 135452. 99.7 17.1 168. 4.87 123. 324. 98.1 69.8 NA 258.
# 3 EMP BRA 3364925. 1587. 73.8 2952. 93.8 1861. 6285. 1306. 3003. 3621. 4257.
# This computes a weighted grouped mode, taking the total EMP / VA as weight
GGDC10S %>%
fgroup_by(Variable, Country) %>%
fselect(AGR:SUM) %>% fmode(SUM) %>% head(3)
# # A tibble: 3 × 13
# Variable Country sum.SUM AGR MIN MAN PU CON WRT TRA FIRE GOV OTH
# <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
# 1 EMP ARG 653615. 1162. 127. 2164. 152. 1415. 3768. 1060. 1748. 4336. 1999.
# 2 EMP BOL 135452. 819. 37.6 604. 10.8 433. 893. 333. 321. NA 1057.
# 3 EMP BRA 3364925. 16451. 313. 11841. 388. 8154. 21860. 5169. 12011. 12149. 14235.The weighted variance / standard deviation is currently only implemented with frequency weights.
Weighted aggregations may also be performed with
collapg. By default fsum is used to compute a
sum of the weights, but it is also possible here to aggregate the
weights with other functions:
# This aggregates numeric colums using the weighted mean (the default) and categorical columns using the weighted mode (the default).
# Weights (column SUM) are aggregated using both the sum and the maximum.
GGDC10S %>% group_by(Variable, Country) %>%
collapg(w = SUM, wFUN = list(fsum, fmax)) %>% head(3)
# # A tibble: 3 × 17
# Variable Country fsum.SUM fmax.SUM Regioncode Region Year AGR MIN MAN PU CON WRT
# <chr> <chr> <dbl> <dbl> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
# 1 EMP ARG 653615. 17929. LAM Latin … 1985. 1361. 56.5 1935. 105. 811. 2217.
# 2 EMP BOL 135452. 4508. LAM Latin … 1987. 977. 57.9 296. 7.07 167. 400.
# 3 EMP BRA 3364925. 102572. LAM Latin … 1989. 17746. 238. 8466. 389. 4436. 11376.
# # ℹ 4 more variables: TRA <dbl>, FIRE <dbl>, GOV <dbl>, OTH <dbl>2. Fast Transformations
collapse also provides some fast transformations that
significantly extend the scope and speed of manipulations that can be
performed with dplyr::mutate.
2.1 Fast Transform and Compute Variables
The function ftransform can be used to manipulate
columns in the same ways as mutate:
GGDC10S %>% fsubset(Variable == "VA", Country, Year, AGR, SUM) %>%
ftransform(AGR_perc = AGR / SUM * 100, # Computing % of VA in Agriculture
AGR_mean = fmean(AGR), # Average Agricultural VA
AGR = NULL, SUM = NULL) %>% # Deleting columns AGR and SUM
head
# # A tibble: 6 × 4
# Country Year AGR_perc AGR_mean
# <chr> <dbl> <dbl> <dbl>
# 1 BWA 1960 NA 5137561.
# 2 BWA 1961 NA 5137561.
# 3 BWA 1962 NA 5137561.
# 4 BWA 1963 NA 5137561.
# 5 BWA 1964 43.5 5137561.
# 6 BWA 1965 40.0 5137561.The modification brought by ftransformv enables
transformations of groups of columns like dplyr::mutate_at
and dplyr::mutate_if:
# This replaces variables mpg, carb and wt by their log (.c turns expressions into character vectors)
mtcars %>% ftransformv(.c(mpg, carb, wt), log) %>% head
# mpg cyl disp hp drat wt qsec vs am gear carb
# Mazda RX4 3.044522 6 160 110 3.90 0.9631743 16.46 0 1 4 1.3862944
# Mazda RX4 Wag 3.044522 6 160 110 3.90 1.0560527 17.02 0 1 4 1.3862944
# Datsun 710 3.126761 4 108 93 3.85 0.8415672 18.61 1 1 4 0.0000000
# Hornet 4 Drive 3.063391 6 258 110 3.08 1.1678274 19.44 1 0 3 0.0000000
# Hornet Sportabout 2.928524 8 360 175 3.15 1.2354715 17.02 0 0 3 0.6931472
# Valiant 2.895912 6 225 105 2.76 1.2412686 20.22 1 0 3 0.0000000
# Logging numeric variables
iris %>% ftransformv(is.numeric, log) %>% head
# Sepal.Length Sepal.Width Petal.Length Petal.Width Species
# 1 1.629241 1.252763 0.3364722 -1.6094379 setosa
# 2 1.589235 1.098612 0.3364722 -1.6094379 setosa
# 3 1.547563 1.163151 0.2623643 -1.6094379 setosa
# 4 1.526056 1.131402 0.4054651 -1.6094379 setosa
# 5 1.609438 1.280934 0.3364722 -1.6094379 setosa
# 6 1.686399 1.360977 0.5306283 -0.9162907 setosaInstead of column = value type arguments, it is also
possible to pass a single list of transformed variables to
ftransform, which will be regarded in the same way as an
evaluated list of column = value arguments. It can be used
for more complex transformations:
# Logging values and replacing generated Inf values
mtcars %>% ftransform(fselect(., mpg, cyl, vs:gear) %>% lapply(log) %>% replace_Inf) %>% head
# mpg cyl disp hp drat wt qsec vs am gear carb
# Mazda RX4 3.044522 1.791759 160 110 3.90 2.620 16.46 NA 0 1.386294 4
# Mazda RX4 Wag 3.044522 1.791759 160 110 3.90 2.875 17.02 NA 0 1.386294 4
# Datsun 710 3.126761 1.386294 108 93 3.85 2.320 18.61 0 0 1.386294 1
# Hornet 4 Drive 3.063391 1.791759 258 110 3.08 3.215 19.44 0 NA 1.098612 1
# Hornet Sportabout 2.928524 2.079442 360 175 3.15 3.440 17.02 NA NA 1.098612 2
# Valiant 2.895912 1.791759 225 105 2.76 3.460 20.22 0 NA 1.098612 1If only the computed columns need to be returned,
fcompute provides an efficient alternative:
GGDC10S %>% fsubset(Variable == "VA", Country, Year, AGR, SUM) %>%
fcompute(AGR_perc = AGR / SUM * 100,
AGR_mean = fmean(AGR)) %>% head
# # A tibble: 6 × 2
# AGR_perc AGR_mean
# <dbl> <dbl>
# 1 NA 5137561.
# 2 NA 5137561.
# 3 NA 5137561.
# 4 NA 5137561.
# 5 43.5 5137561.
# 6 40.0 5137561.ftransform and fcompute are an order of
magnitude faster than mutate, but they do not support
grouped computations using arbitrary functions. We will see that this is
hardly a limitation as collapse provides very efficient and
elegant alternative programming mechanisms…
2.2 Replacing and Sweeping out Statistics
All statistical (scalar-valued) functions in the collapse package
(fsum, fprod, fmean, fmedian, fmode, fvar, fsd, fmin, fmax, fnth, ffirst, flast, fnobs, fndistinct)
have a TRA argument which can be used to efficiently
transform data by either (column-wise) replacing data values with
computed statistics or sweeping the statistics out of the data.
Operations can be specified using either an integer or quoted operator /
string. The 10 operations supported by TRA are:
1 - “replace_fill” : replace and overwrite missing values (same as
mutate)2 - “replace” : replace but preserve missing values
3 - “-” : subtract (center)
4 - “-+” : subtract group-statistics but add average of group statistics
5 - “/” : divide (scale)
6 - “%” : compute percentages (divide and multiply by 100)
7 - “+” : add
8 - “*” : multiply
9 - “%%” : modulus
10 - “-%%” : subtract modulus
Simple transformations are again straightforward to specify:
# This subtracts the median value from all data points i.e. centers on the median
GGDC10S %>% num_vars %>% fmedian(TRA = "-") %>% head
# # A tibble: 6 × 12
# Year AGR MIN MAN PU CON WRT TRA FIRE GOV OTH SUM
# <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
# 1 -22 NA NA NA NA NA NA NA NA NA NA NA
# 2 -21 NA NA NA NA NA NA NA NA NA NA NA
# 3 -20 NA NA NA NA NA NA NA NA NA NA NA
# 4 -19 NA NA NA NA NA NA NA NA NA NA NA
# 5 -18 -4378. -170. -3717. -168. -1473. -3767. -1173. -959. -3924. -1431. -23149.
# 6 -17 -4379. -171. -3717. -168. -1472. -3767. -1173. -959. -3923. -1430. -23147.
# This replaces all data points with the mode
GGDC10S %>% char_vars %>% fmode(TRA = "replace") %>% head
# # A tibble: 6 × 4
# Country Regioncode Region Variable
# <chr> <chr> <chr> <chr>
# 1 USA ASI Asia EMP
# 2 USA ASI Asia EMP
# 3 USA ASI Asia EMP
# 4 USA ASI Asia EMP
# 5 USA ASI Asia EMP
# 6 USA ASI Asia EMPSimilarly for grouped transformations:
# Replacing data with the 2nd quartile (25%)
GGDC10S %>%
fselect(Variable, Country, AGR:SUM) %>%
fgroup_by(Variable, Country) %>% fnth(0.25, TRA = "replace_fill") %>% head(3)
# # A tibble: 3 × 13
# Variable Country AGR MIN MAN PU CON WRT TRA FIRE GOV OTH SUM
# <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
# 1 VA BWA 63.5 33.1 27.3 7.36 26.8 31.1 13.2 12.0 33.6 11.5 262.
# 2 VA BWA 63.5 33.1 27.3 7.36 26.8 31.1 13.2 12.0 33.6 11.5 262.
# 3 VA BWA 63.5 33.1 27.3 7.36 26.8 31.1 13.2 12.0 33.6 11.5 262.
# Scaling sectoral data by Variable and Country
GGDC10S %>%
fselect(Variable, Country, AGR:SUM) %>%
fgroup_by(Variable, Country) %>% fsd(TRA = "/") %>% head
# # A tibble: 6 × 13
# Variable Country AGR MIN MAN PU CON WRT TRA FIRE GOV
# <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
# 1 VA BWA NA NA NA NA NA NA NA NA NA
# 2 VA BWA NA NA NA NA NA NA NA NA NA
# 3 VA BWA NA NA NA NA NA NA NA NA NA
# 4 VA BWA NA NA NA NA NA NA NA NA NA
# 5 VA BWA 0.0270 0.000556 0.000523 3.88e-4 5.11e-4 0.00194 0.00154 5.23e-4 0.00134
# 6 VA BWA 0.0260 0.000397 0.000723 5.03e-4 1.04e-3 0.00220 0.00180 5.83e-4 0.00158
# # ℹ 2 more variables: OTH <dbl>, SUM <dbl>The benchmarks below will demonstrate that these internal sweeping
and replacement operations fully performed in C++ compute significantly
faster than using dplyr::mutate, especially as the number
of groups grows large. The S3 generic nature of the Fast Statistical
Functions further allows us to perform grouped mutations on the fly
(together with ftransform or fcompute),
without the need of first creating a grouped tibble:
# AGR_gmed = TRUE if AGR is greater than it's median value, grouped by Variable and Country
# Note: This calls fmedian.default
settransform(GGDC10S, AGR_gmed = AGR > fmedian(AGR, list(Variable, Country), TRA = "replace"))
tail(GGDC10S, 3)
# # A tibble: 3 × 17
# Country Regioncode Region Variable Year AGR MIN MAN PU CON WRT TRA FIRE GOV
# <chr> <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
# 1 EGY MENA Middle Ea… EMP 2010 5206. 29.0 2436. 307. 2733. 2977. 1992. 801. 5539.
# 2 EGY MENA Middle Ea… EMP 2011 5186. 27.6 2374. 318. 2795. 3020. 2048. 815. 5636.
# 3 EGY MENA Middle Ea… EMP 2012 5161. 24.8 2348. 325. 2931. 3110. 2065. 832. 5736.
# # ℹ 3 more variables: OTH <dbl>, SUM <dbl>, AGR_gmed <lgl>
# Dividing (scaling) the sectoral data (columns 6 through 16) by their grouped standard deviation
settransformv(GGDC10S, 6:16, fsd, list(Variable, Country), TRA = "/", apply = FALSE)
tail(GGDC10S, 3)
# # A tibble: 3 × 17
# Country Regioncode Region Variable Year AGR MIN MAN PU CON WRT TRA FIRE GOV
# <chr> <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
# 1 EGY MENA Middle Ea… EMP 2010 8.41 2.28 4.32 3.56 3.62 3.75 3.75 3.14 3.80
# 2 EGY MENA Middle Ea… EMP 2011 8.38 2.17 4.21 3.68 3.70 3.81 3.86 3.19 3.86
# 3 EGY MENA Middle Ea… EMP 2012 8.34 1.95 4.17 3.76 3.88 3.92 3.89 3.26 3.93
# # ℹ 3 more variables: OTH <dbl>, SUM <dbl>, AGR_gmed <lgl>
rm(GGDC10S)Weights are easily added to any grouped transformation:
# This subtracts weighted group means from the data, using SUM column as weights..
GGDC10S %>%
fselect(Variable, Country, AGR:SUM) %>%
fgroup_by(Variable, Country) %>% fmean(SUM, "-") %>% head
# # A tibble: 6 × 13
# Variable Country SUM AGR MIN MAN PU CON WRT TRA FIRE GOV OTH
# <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
# 1 VA BWA NA NA NA NA NA NA NA NA NA NA NA
# 2 VA BWA NA NA NA NA NA NA NA NA NA NA NA
# 3 VA BWA NA NA NA NA NA NA NA NA NA NA NA
# 4 VA BWA NA NA NA NA NA NA NA NA NA NA NA
# 5 VA BWA 37.5 -1301. -13317. -2965. -529. -2746. -6540. -2157. -4431. -7551. -2613.
# 6 VA BWA 39.3 -1302. -13318. -2964. -529. -2745. -6540. -2156. -4431. -7550. -2613.Sequential operations are also easily performed:
# This scales and then subtracts the median
GGDC10S %>%
fselect(Variable, Country, AGR:SUM) %>%
fgroup_by(Variable, Country) %>% fsd(TRA = "/") %>% fmedian(TRA = "-")
# # A tibble: 5,027 × 13
# Variable Country AGR MIN MAN PU CON WRT TRA FIRE GOV OTH SUM
# * <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
# 1 VA BWA NA NA NA NA NA NA NA NA NA NA NA
# 2 VA BWA NA NA NA NA NA NA NA NA NA NA NA
# 3 VA BWA NA NA NA NA NA NA NA NA NA NA NA
# 4 VA BWA NA NA NA NA NA NA NA NA NA NA NA
# 5 VA BWA -0.182 -0.235 -0.183 -0.245 -0.118 -0.0820 -0.0724 -0.0661 -0.108 -0.0848 -0.146
# 6 VA BWA -0.183 -0.235 -0.183 -0.245 -0.117 -0.0817 -0.0722 -0.0660 -0.108 -0.0846 -0.146
# 7 VA BWA -0.180 -0.235 -0.183 -0.245 -0.117 -0.0813 -0.0720 -0.0659 -0.107 -0.0843 -0.145
# 8 VA BWA -0.177 -0.235 -0.183 -0.245 -0.117 -0.0826 -0.0724 -0.0659 -0.107 -0.0841 -0.146
# 9 VA BWA -0.174 -0.235 -0.183 -0.245 -0.117 -0.0823 -0.0717 -0.0661 -0.108 -0.0848 -0.146
# 10 VA BWA -0.173 -0.234 -0.182 -0.243 -0.115 -0.0821 -0.0715 -0.0660 -0.108 -0.0846 -0.145
# # ℹ 5,017 more rows
#
# Grouped by: Variable, Country [85 | 59 (7.7) 4-65]Of course it is also possible to combine multiple functions as in the aggregation section, or to add variables to existing data:
# This adds a groupwise observation count next to each column
add_vars(GGDC10S, seq(7,27,2)) <- GGDC10S %>%
fgroup_by(Variable, Country) %>% fselect(AGR:SUM) %>%
fnobs("replace_fill") %>% add_stub("N_")
head(GGDC10S)
# # A tibble: 6 × 27
# Country Regioncode Region Variable Year AGR N_AGR MIN N_MIN MAN N_MAN PU N_PU CON
# <chr> <chr> <chr> <chr> <dbl> <dbl> <int> <dbl> <int> <dbl> <int> <dbl> <int> <dbl>
# 1 BWA SSA Sub-sa… VA 1960 NA 47 NA 47 NA 47 NA 47 NA
# 2 BWA SSA Sub-sa… VA 1961 NA 47 NA 47 NA 47 NA 47 NA
# 3 BWA SSA Sub-sa… VA 1962 NA 47 NA 47 NA 47 NA 47 NA
# 4 BWA SSA Sub-sa… VA 1963 NA 47 NA 47 NA 47 NA 47 NA
# 5 BWA SSA Sub-sa… VA 1964 16.3 47 3.49 47 0.737 47 0.104 47 0.660
# 6 BWA SSA Sub-sa… VA 1965 15.7 47 2.50 47 1.02 47 0.135 47 1.35
# # ℹ 13 more variables: N_CON <int>, WRT <dbl>, N_WRT <int>, TRA <dbl>, N_TRA <int>, FIRE <dbl>,
# # N_FIRE <int>, GOV <dbl>, N_GOV <int>, OTH <dbl>, N_OTH <int>, SUM <dbl>, N_SUM <int>
rm(GGDC10S)There are lots of other examples one could construct using the 10
operations and 14 functions listed above, the examples provided just
outline the suggested programming basics. Performance considerations
make it very much worthwhile to spend some time and think how complex
operations can be implemented in this programming framework, before
defining some function in R and applying it to data using
dplyr::mutate.
2.3 More Control using the TRA Function
Towards this end, calling TRA() directly also
facilitates more complex and customized operations. Behind the scenes of
the TRA = ... argument, the Fast Statistical
Functions first compute the grouped statistics on all columns of
the data, and these statistics are then directly fed into a C++ function
that uses them to replace or sweep them out of data points in one of the
10 ways described above. This function can also be called directly by
the name of TRA.
Fundamentally, TRA is a generalization of
base::sweep for column-wise grouped operations1. Direct
calls to TRA enable more control over inputs and
outputs.
The two operations below are equivalent, although the first is slightly more efficient as it only requires one method dispatch and one check of the inputs:
# This divides by the product
GGDC10S %>%
fgroup_by(Variable, Country) %>%
get_vars(6:16) %>% fprod(TRA = "/") %>% head
# # A tibble: 6 × 11
# AGR MIN MAN PU CON WRT TRA FIRE GOV
# <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
# 1 NA NA NA NA NA NA NA NA NA
# 2 NA NA NA NA NA NA NA NA NA
# 3 NA NA NA NA NA NA NA NA NA
# 4 NA NA NA NA NA NA NA NA NA
# 5 1.29e-105 2.81e-127 1.40e-101 4.44e-74 4.19e-102 3.97e-113 6.91e-92 1.01e-97 2.51e-117
# 6 1.24e-105 2.00e-127 1.94e-101 5.75e-74 8.55e-102 4.49e-113 8.08e-92 1.13e-97 2.96e-117
# # ℹ 2 more variables: OTH <dbl>, SUM <dbl>
# Same thing
GGDC10S %>%
fgroup_by(Variable, Country) %>%
get_vars(6:16) %>%
TRA(fprod(., keep.group_vars = FALSE), "/") %>% head # [same as TRA(.,fprod(., keep.group_vars = FALSE),"/")]
# # A tibble: 6 × 11
# AGR MIN MAN PU CON WRT TRA FIRE GOV
# <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
# 1 NA NA NA NA NA NA NA NA NA
# 2 NA NA NA NA NA NA NA NA NA
# 3 NA NA NA NA NA NA NA NA NA
# 4 NA NA NA NA NA NA NA NA NA
# 5 1.29e-105 2.81e-127 1.40e-101 4.44e-74 4.19e-102 3.97e-113 6.91e-92 1.01e-97 2.51e-117
# 6 1.24e-105 2.00e-127 1.94e-101 5.75e-74 8.55e-102 4.49e-113 8.08e-92 1.13e-97 2.96e-117
# # ℹ 2 more variables: OTH <dbl>, SUM <dbl>TRA.grouped_df was designed such that it matches the
columns of the statistics (aggregated columns) to those of the original
data, and only transforms matching columns while returning the whole
data frame. Thus it is easily possible to only apply a transformation to
the first two sectors:
# This only demeans Agriculture (AGR) and Mining (MIN)
GGDC10S %>%
fgroup_by(Variable, Country) %>%
TRA(fselect(., AGR, MIN) %>% fmean(keep.group_vars = FALSE), "-") %>% head
# # A tibble: 6 × 16
# Country Regioncode Region Variable Year AGR MIN MAN PU CON WRT TRA FIRE GOV
# <chr> <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
# 1 BWA SSA Sub-s… VA 1960 NA NA NA NA NA NA NA NA NA
# 2 BWA SSA Sub-s… VA 1961 NA NA NA NA NA NA NA NA NA
# 3 BWA SSA Sub-s… VA 1962 NA NA NA NA NA NA NA NA NA
# 4 BWA SSA Sub-s… VA 1963 NA NA NA NA NA NA NA NA NA
# 5 BWA SSA Sub-s… VA 1964 -446. -4505. 0.737 0.104 0.660 6.24 1.66 1.12 4.82
# 6 BWA SSA Sub-s… VA 1965 -446. -4506. 1.02 0.135 1.35 7.06 1.94 1.25 5.70
# # ℹ 2 more variables: OTH <dbl>, SUM <dbl>Since TRA is already built into all Fast Statistical
Functions as an argument, it is best used in computations where
grouped statistics are computed using some other function.
# Same as above, with one line of code using fmean.data.frame and ftransform...
GGDC10S %>% ftransform(fmean(list(AGR = AGR, MIN = MIN), list(Variable, Country), TRA = "-")) %>% head
# # A tibble: 6 × 16
# Country Regioncode Region Variable Year AGR MIN MAN PU CON WRT TRA FIRE GOV
# <chr> <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
# 1 BWA SSA Sub-s… VA 1960 NA NA NA NA NA NA NA NA NA
# 2 BWA SSA Sub-s… VA 1961 NA NA NA NA NA NA NA NA NA
# 3 BWA SSA Sub-s… VA 1962 NA NA NA NA NA NA NA NA NA
# 4 BWA SSA Sub-s… VA 1963 NA NA NA NA NA NA NA NA NA
# 5 BWA SSA Sub-s… VA 1964 -446. -4505. 0.737 0.104 0.660 6.24 1.66 1.12 4.82
# 6 BWA SSA Sub-s… VA 1965 -446. -4506. 1.02 0.135 1.35 7.06 1.94 1.25 5.70
# # ℹ 2 more variables: OTH <dbl>, SUM <dbl>Another potential use of TRA is to do computations in
two- or more steps, for example if both aggregated and transformed data
are needed, or if computations are more complex and involve other
manipulations in-between the aggregating and sweeping part:
# Get grouped tibble
gGGDC <- GGDC10S %>% fgroup_by(Variable, Country)
# Get aggregated data
gsumGGDC <- gGGDC %>% fselect(AGR:SUM) %>% fsum
head(gsumGGDC)
# # A tibble: 6 × 13
# Variable Country AGR MIN MAN PU CON WRT TRA FIRE GOV OTH SUM
# <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
# 1 EMP ARG 88028. 3230. 1.20e5 6307. 4.60e4 1.23e5 4.02e4 3.89e4 1.27e5 6.15e4 6.54e5
# 2 EMP BOL 58817. 3418. 1.43e4 326. 7.49e3 1.72e4 7.04e3 2.72e3 NA 2.41e4 1.35e5
# 3 EMP BRA 1065864. 12773. 4.33e5 22604. 2.19e5 5.28e5 1.27e5 2.74e5 3.29e5 3.54e5 3.36e6
# 4 EMP BWA 8839. 493. 8.49e2 145. 1.19e3 1.71e3 3.93e2 7.21e2 2.87e3 1.30e3 1.85e4
# 5 EMP CHL 44220. 6389. 3.94e4 1850. 1.86e4 4.38e4 1.63e4 1.72e4 NA 6.32e4 2.51e5
# 6 EMP CHN 17264654. 422972. 4.03e6 96364. 1.25e6 1.73e6 8.36e5 2.96e5 1.36e6 1.86e6 2.91e7
# Get transformed (scaled) data
head(TRA(gGGDC, gsumGGDC, "/"))
# # A tibble: 6 × 16
# Country Regioncode Region Variable Year AGR MIN MAN PU CON WRT
# <chr> <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
# 1 BWA SSA Sub-sahar… VA 1960 NA NA NA NA NA NA
# 2 BWA SSA Sub-sahar… VA 1961 NA NA NA NA NA NA
# 3 BWA SSA Sub-sahar… VA 1962 NA NA NA NA NA NA
# 4 BWA SSA Sub-sahar… VA 1963 NA NA NA NA NA NA
# 5 BWA SSA Sub-sahar… VA 1964 7.50e-4 1.65e-5 1.66e-5 1.03e-5 1.57e-5 6.82e-5
# 6 BWA SSA Sub-sahar… VA 1965 7.24e-4 1.18e-5 2.30e-5 1.33e-5 3.20e-5 7.72e-5
# # ℹ 5 more variables: TRA <dbl>, FIRE <dbl>, GOV <dbl>, OTH <dbl>, SUM <dbl>As discussed, whether using the argument to fast statistical
functions or TRA directly, these data transformations are
essentially a two-step process: Statistics are first computed and then
used to transform the original data.
Although both steps are efficiently done in C++, it would be even more efficient to do them in a single step without materializing all the statistics before transforming the data. Such slightly more efficient functions are provided for the very commonly applied tasks of centering and averaging data by groups (widely known as ‘between’-group and ‘within’-group transformations), and scaling and centering data by groups (also known as ‘standardizing’ data).
2.4 Faster Centering, Averaging and Standardizing
The functions fbetween and fwithin are
slightly more memory efficient implementations of fmean
invoked with different TRA options:
GGDC10S %>% # Same as ... %>% fmean(TRA = "replace")
fgroup_by(Variable, Country) %>% get_vars(6:16) %>% fbetween %>% tail(2)
# # A tibble: 2 × 11
# AGR MIN MAN PU CON WRT TRA FIRE GOV OTH SUM
# <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
# 1 4444. 34.9 1614. 131. 997. 1307. 799. 320. 2958. NA 12605.
# 2 4444. 34.9 1614. 131. 997. 1307. 799. 320. 2958. NA 12605.
GGDC10S %>% # Same as ... %>% fmean(TRA = "replace_fill")
fgroup_by(Variable, Country) %>% get_vars(6:16) %>% fbetween(fill = TRUE) %>% tail(2)
# # A tibble: 2 × 11
# AGR MIN MAN PU CON WRT TRA FIRE GOV OTH SUM
# <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
# 1 4444. 34.9 1614. 131. 997. 1307. 799. 320. 2958. NA 12605.
# 2 4444. 34.9 1614. 131. 997. 1307. 799. 320. 2958. NA 12605.
GGDC10S %>% # Same as ... %>% fmean(TRA = "-")
fgroup_by(Variable, Country) %>% get_vars(6:16) %>% fwithin %>% tail(2)
# # A tibble: 2 × 11
# AGR MIN MAN PU CON WRT TRA FIRE GOV OTH SUM
# <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
# 1 742. -7.35 760. 187. 1798. 1713. 1249. 495. 2678. NA 9614.
# 2 717. -10.1 734. 194. 1934. 1803. 1266. 512. 2778. NA 9928.Apart from higher speed, fwithin has a mean
argument to assign an arbitrary mean to centered data, the default being
mean = 0. A very common choice for such an added mean is
just the overall mean of the data, which can be added in by invoking
mean = "overall.mean":
GGDC10S %>%
fgroup_by(Variable, Country) %>%
fselect(Country, Variable, AGR:SUM) %>% fwithin(mean = "overall.mean") %>% tail(3)
# # A tibble: 3 × 13
# Country Variable AGR MIN MAN PU CON WRT TRA FIRE GOV OTH SUM
# <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
# 1 EGY EMP 2527458. 1867903. 5539313. 3.36e5 1.80e6 3.39e6 1.47e6 1.66e6 1.71e6 NA 2.16e7
# 2 EGY EMP 2527439. 1867902. 5539251. 3.36e5 1.80e6 3.39e6 1.47e6 1.66e6 1.71e6 NA 2.16e7
# 3 EGY EMP 2527413. 1867899. 5539226. 3.36e5 1.80e6 3.39e6 1.47e6 1.66e6 1.72e6 NA 2.16e7This can also be done using weights. The code below uses the
SUM column as weights, and then for each variable and each
group subtracts out the weighted mean, and then adds the overall
weighted column mean back to the centered columns. The SUM
column is just kept as it is and added after the grouping columns.
GGDC10S %>%
fgroup_by(Variable, Country) %>%
fselect(Country, Variable, AGR:SUM) %>% fwithin(SUM, mean = "overall.mean") %>% tail(3)
# # A tibble: 3 × 13
# Country Variable SUM AGR MIN MAN PU CON WRT TRA FIRE GOV OTH
# <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
# 1 EGY EMP 22020. 429066006. 3.70e8 7.38e8 2.73e7 2.83e8 4.33e8 1.97e8 1.55e8 2.10e8 NA
# 2 EGY EMP 22219. 429065986. 3.70e8 7.38e8 2.73e7 2.83e8 4.33e8 1.97e8 1.55e8 2.10e8 NA
# 3 EGY EMP 22533. 429065961. 3.70e8 7.38e8 2.73e7 2.83e8 4.33e8 1.97e8 1.55e8 2.10e8 NAAnother argument to fwithin is the theta
parameter, allowing partial- or quasi-demeaning operations,
e.g. fwithin(gdata, theta = theta) is equal to
gdata - theta * fbetween(gdata). This is particularly
useful to prepare data for variance components (also known as
‘random-effects’) estimation.
Apart from fbetween and fwithin, the
function fscale exists to efficiently scale and center
data, to avoid sequential calls such as
... %>% fsd(TRA = "/") %>% fmean(TRA = "-").
# This efficiently scales and centers (i.e. standardizes) the data
GGDC10S %>%
fgroup_by(Variable, Country) %>%
fselect(Country, Variable, AGR:SUM) %>% fscale
# # A tibble: 5,027 × 13
# Country Variable AGR MIN MAN PU CON WRT TRA FIRE GOV OTH SUM
# * <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
# 1 BWA VA NA NA NA NA NA NA NA NA NA NA NA
# 2 BWA VA NA NA NA NA NA NA NA NA NA NA NA
# 3 BWA VA NA NA NA NA NA NA NA NA NA NA NA
# 4 BWA VA NA NA NA NA NA NA NA NA NA NA NA
# 5 BWA VA -0.738 -0.717 -0.668 -0.805 -0.692 -0.603 -0.589 -0.635 -0.656 -0.596 -0.676
# 6 BWA VA -0.739 -0.717 -0.668 -0.805 -0.692 -0.603 -0.589 -0.635 -0.656 -0.596 -0.676
# 7 BWA VA -0.736 -0.717 -0.668 -0.805 -0.692 -0.603 -0.589 -0.635 -0.656 -0.595 -0.676
# 8 BWA VA -0.734 -0.717 -0.668 -0.805 -0.692 -0.604 -0.589 -0.635 -0.655 -0.595 -0.676
# 9 BWA VA -0.730 -0.717 -0.668 -0.805 -0.692 -0.604 -0.588 -0.635 -0.656 -0.596 -0.676
# 10 BWA VA -0.729 -0.716 -0.667 -0.803 -0.690 -0.603 -0.588 -0.635 -0.656 -0.596 -0.675
# # ℹ 5,017 more rows
#
# Grouped by: Variable, Country [85 | 59 (7.7) 4-65]fscale also has additional mean and
sd arguments allowing the user to (group-) scale data to an
arbitrary mean and standard deviation. Setting mean = FALSE
just scales the data but preserves the means, and is thus different from
fsd(..., TRA = "/") which simply divides all values by the
standard deviation:
# Saving grouped tibble
gGGDC <- GGDC10S %>%
fgroup_by(Variable, Country) %>%
fselect(Country, Variable, AGR:SUM)
# Original means
head(fmean(gGGDC))
# # A tibble: 6 × 13
# Variable Country AGR MIN MAN PU CON WRT TRA FIRE GOV OTH SUM
# <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
# 1 EMP ARG 1420. 52.1 1932. 102. 742. 1.98e3 6.49e2 628. 2043. 9.92e2 1.05e4
# 2 EMP BOL 964. 56.0 235. 5.35 123. 2.82e2 1.15e2 44.6 NA 3.96e2 2.22e3
# 3 EMP BRA 17191. 206. 6991. 365. 3525. 8.51e3 2.05e3 4414. 5307. 5.71e3 5.43e4
# 4 EMP BWA 188. 10.5 18.1 3.09 25.3 3.63e1 8.36e0 15.3 61.1 2.76e1 3.94e2
# 5 EMP CHL 702. 101. 625. 29.4 296. 6.95e2 2.58e2 272. NA 1.00e3 3.98e3
# 6 EMP CHN 287744. 7050. 67144. 1606. 20852. 2.89e4 1.39e4 4929. 22669. 3.10e4 4.86e5
# Mean Preserving Scaling
head(fmean(fscale(gGGDC, mean = FALSE)))
# # A tibble: 6 × 13
# Variable Country AGR MIN MAN PU CON WRT TRA FIRE GOV OTH SUM
# <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
# 1 EMP ARG 1420. 52.1 1932. 102. 742. 1.98e3 6.49e2 628. 2043. 9.92e2 1.05e4
# 2 EMP BOL 964. 56.0 235. 5.35 123. 2.82e2 1.15e2 44.6 NA 3.96e2 2.22e3
# 3 EMP BRA 17191. 206. 6991. 365. 3525. 8.51e3 2.05e3 4414. 5307. 5.71e3 5.43e4
# 4 EMP BWA 188. 10.5 18.1 3.09 25.3 3.63e1 8.36e0 15.3 61.1 2.76e1 3.94e2
# 5 EMP CHL 702. 101. 625. 29.4 296. 6.95e2 2.58e2 272. NA 1.00e3 3.98e3
# 6 EMP CHN 287744. 7050. 67144. 1606. 20852. 2.89e4 1.39e4 4929. 22669. 3.10e4 4.86e5
head(fsd(fscale(gGGDC, mean = FALSE)))
# # A tibble: 6 × 13
# Variable Country AGR MIN MAN PU CON WRT TRA FIRE GOV OTH SUM
# <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
# 1 EMP ARG 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
# 2 EMP BOL 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 NA 1.00 1.00
# 3 EMP BRA 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
# 4 EMP BWA 1.00 1.00 1.00 1 1.00 1.00 1.00 1 1.00 1.00 1.00
# 5 EMP CHL 1.00 1 1.00 1.00 1.00 1.00 1.00 1.00 NA 1.00 1.00
# 6 EMP CHN 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00One can also set mean = "overall.mean", which
group-centers columns on the overall mean as illustrated with
fwithin. Another interesting option is setting
sd = "within.sd". This group-scales data such that every
group has a standard deviation equal to the within-standard deviation of
the data:
# Just using VA data for this example
gGGDC <- GGDC10S %>%
fsubset(Variable == "VA", Country, AGR:SUM) %>%
fgroup_by(Country)
# This calculates the within- standard deviation for all columns
fsd(num_vars(ungroup(fwithin(gGGDC))))
# AGR MIN MAN PU CON WRT TRA FIRE GOV OTH
# 45046972 40122220 75608708 3062688 30811572 44125207 20676901 16030868 20358973 18780869
# SUM
# 306429102
# This scales all groups to take on the within- standard deviation while preserving group means
fsd(fscale(gGGDC, mean = FALSE, sd = "within.sd"))
# # A tibble: 43 × 12
# Country AGR MIN MAN PU CON WRT TRA FIRE GOV OTH SUM
# <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
# 1 ARG 45046972. 40122220. 75608708. 3062688. 3.08e7 4.41e7 2.07e7 1.60e7 2.04e7 1.88e7 3.06e8
# 2 BOL 45046972. 40122220. 75608708. 3062688. 3.08e7 4.41e7 2.07e7 1.60e7 NA 1.88e7 3.06e8
# 3 BRA 45046972. 40122220. 75608708. 3062688. 3.08e7 4.41e7 2.07e7 1.60e7 2.04e7 1.88e7 3.06e8
# 4 BWA 45046972. 40122220. 75608708. 3062688. 3.08e7 4.41e7 2.07e7 1.60e7 2.04e7 1.88e7 3.06e8
# 5 CHL 45046972. 40122220. 75608708. 3062688. 3.08e7 4.41e7 2.07e7 1.60e7 NA 1.88e7 3.06e8
# 6 CHN 45046972. 40122220. 75608708. 3062688. 3.08e7 4.41e7 2.07e7 1.60e7 2.04e7 1.88e7 3.06e8
# 7 COL 45046972. 40122220. 75608708. 3062688. 3.08e7 4.41e7 2.07e7 1.60e7 NA 1.88e7 3.06e8
# 8 CRI 45046972. 40122220. 75608708. 3062688. 3.08e7 4.41e7 2.07e7 1.60e7 2.04e7 1.88e7 3.06e8
# 9 DEW 45046972. 40122220. 75608708. 3062688. 3.08e7 4.41e7 2.07e7 1.60e7 2.04e7 1.88e7 3.06e8
# 10 DNK 45046972. 40122220. 75608708. 3062688. 3.08e7 4.41e7 2.07e7 1.60e7 2.04e7 1.88e7 3.06e8
# # ℹ 33 more rowsA grouped scaling operation with both
mean = "overall.mean" and sd = "within.sd"
thus efficiently achieves a harmonization of all groups in the first two
moments without changing the fundamental properties (in terms of level
and scale) of the data.
2.5 Lags / Leads, Differences and Growth Rates
This section introduces 3 further powerful collapse
functions: flag, fdiff and
fgrowth. The first function, flag, efficiently
computes sequences of fully identified lags and leads on time series and
panel data. The following code computes 1 fully-identified panel-lag and
1 fully identified panel-lead of each variable in the data:
GGDC10S %>%
fselect(-Region, -Regioncode) %>%
fgroup_by(Variable, Country) %>% flag(-1:1, Year)
# # A tibble: 5,027 × 36
# Country Variable Year F1.AGR AGR L1.AGR F1.MIN MIN L1.MIN F1.MAN MAN L1.MAN F1.PU PU
# * <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
# 1 BWA VA 1960 NA NA NA NA NA NA NA NA NA NA NA
# 2 BWA VA 1961 NA NA NA NA NA NA NA NA NA NA NA
# 3 BWA VA 1962 NA NA NA NA NA NA NA NA NA NA NA
# 4 BWA VA 1963 16.3 NA NA 3.49 NA NA 0.737 NA NA 0.104 NA
# 5 BWA VA 1964 15.7 16.3 NA 2.50 3.49 NA 1.02 0.737 NA 0.135 0.104
# 6 BWA VA 1965 17.7 15.7 16.3 1.97 2.50 3.49 0.804 1.02 0.737 0.203 0.135
# 7 BWA VA 1966 19.1 17.7 15.7 2.30 1.97 2.50 0.938 0.804 1.02 0.203 0.203
# 8 BWA VA 1967 21.1 19.1 17.7 1.84 2.30 1.97 0.750 0.938 0.804 0.203 0.203
# 9 BWA VA 1968 21.9 21.1 19.1 5.24 1.84 2.30 2.14 0.750 0.938 0.578 0.203
# 10 BWA VA 1969 23.1 21.9 21.1 10.2 5.24 1.84 4.15 2.14 0.750 1.12 0.578
# # ℹ 5,017 more rows
# # ℹ 22 more variables: L1.PU <dbl>, F1.CON <dbl>, CON <dbl>, L1.CON <dbl>, F1.WRT <dbl>, WRT <dbl>,
# # L1.WRT <dbl>, F1.TRA <dbl>, TRA <dbl>, L1.TRA <dbl>, F1.FIRE <dbl>, FIRE <dbl>, L1.FIRE <dbl>,
# # F1.GOV <dbl>, GOV <dbl>, L1.GOV <dbl>, F1.OTH <dbl>, OTH <dbl>, L1.OTH <dbl>, F1.SUM <dbl>,
# # SUM <dbl>, L1.SUM <dbl>
#
# Grouped by: Variable, Country [85 | 59 (7.7) 4-65]If the time-variable passed does not exactly identify the data
(i.e. because of repeated values in each group), all 3 functions will
issue appropriate error messages. flag, fdiff
and fgrowth support irregular time series and unbalanced
panels.
It is also possible to omit the time-variable if one is certain that the data is sorted:
GGDC10S %>%
fselect(Variable, Country,AGR:SUM) %>%
fgroup_by(Variable, Country) %>% flag
# # A tibble: 5,027 × 13
# Variable Country AGR MIN MAN PU CON WRT TRA FIRE GOV OTH SUM
# * <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
# 1 VA BWA NA NA NA NA NA NA NA NA NA NA NA
# 2 VA BWA NA NA NA NA NA NA NA NA NA NA NA
# 3 VA BWA NA NA NA NA NA NA NA NA NA NA NA
# 4 VA BWA NA NA NA NA NA NA NA NA NA NA NA
# 5 VA BWA NA NA NA NA NA NA NA NA NA NA NA
# 6 VA BWA 16.3 3.49 0.737 0.104 0.660 6.24 1.66 1.12 4.82 2.34 37.5
# 7 VA BWA 15.7 2.50 1.02 0.135 1.35 7.06 1.94 1.25 5.70 2.68 39.3
# 8 VA BWA 17.7 1.97 0.804 0.203 1.35 8.27 2.15 1.36 6.37 2.99 43.1
# 9 VA BWA 19.1 2.30 0.938 0.203 0.897 4.31 1.72 1.54 7.04 3.31 41.4
# 10 VA BWA 21.1 1.84 0.750 0.203 1.22 5.17 2.44 1.03 5.03 2.36 41.1
# # ℹ 5,017 more rows
#
# Grouped by: Variable, Country [85 | 59 (7.7) 4-65]fdiff computes sequences of lagged-leaded and iterated
differences as well as quasi-differences and log-differences on time
series and panel data. The code below computes the 1 and 10 year first
and second differences of each variable in the data:
GGDC10S %>%
fselect(-Region, -Regioncode) %>%
fgroup_by(Variable, Country) %>% fdiff(c(1, 10), 1:2, Year)
# # A tibble: 5,027 × 47
# Country Variable Year D1.AGR D2.AGR L10D1.AGR L10D2.AGR D1.MIN D2.MIN L10D1.MIN L10D2.MIN D1.MAN
# * <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
# 1 BWA VA 1960 NA NA NA NA NA NA NA NA NA
# 2 BWA VA 1961 NA NA NA NA NA NA NA NA NA
# 3 BWA VA 1962 NA NA NA NA NA NA NA NA NA
# 4 BWA VA 1963 NA NA NA NA NA NA NA NA NA
# 5 BWA VA 1964 NA NA NA NA NA NA NA NA NA
# 6 BWA VA 1965 -0.575 NA NA NA -0.998 NA NA NA 0.282
# 7 BWA VA 1966 1.95 2.53 NA NA -0.525 0.473 NA NA -0.214
# 8 BWA VA 1967 1.47 -0.488 NA NA 0.328 0.854 NA NA 0.134
# 9 BWA VA 1968 1.95 0.488 NA NA -0.460 -0.788 NA NA -0.188
# 10 BWA VA 1969 0.763 -1.19 NA NA 3.41 3.87 NA NA 1.39
# # ℹ 5,017 more rows
# # ℹ 35 more variables: D2.MAN <dbl>, L10D1.MAN <dbl>, L10D2.MAN <dbl>, D1.PU <dbl>, D2.PU <dbl>,
# # L10D1.PU <dbl>, L10D2.PU <dbl>, D1.CON <dbl>, D2.CON <dbl>, L10D1.CON <dbl>, L10D2.CON <dbl>,
# # D1.WRT <dbl>, D2.WRT <dbl>, L10D1.WRT <dbl>, L10D2.WRT <dbl>, D1.TRA <dbl>, D2.TRA <dbl>,
# # L10D1.TRA <dbl>, L10D2.TRA <dbl>, D1.FIRE <dbl>, D2.FIRE <dbl>, L10D1.FIRE <dbl>,
# # L10D2.FIRE <dbl>, D1.GOV <dbl>, D2.GOV <dbl>, L10D1.GOV <dbl>, L10D2.GOV <dbl>, D1.OTH <dbl>,
# # D2.OTH <dbl>, L10D1.OTH <dbl>, L10D2.OTH <dbl>, D1.SUM <dbl>, D2.SUM <dbl>, L10D1.SUM <dbl>, …
#
# Grouped by: Variable, Country [85 | 59 (7.7) 4-65]Log-differences of the form are also easily computed.
GGDC10S %>%
fselect(-Region, -Regioncode) %>%
fgroup_by(Variable, Country) %>% fdiff(c(1, 10), 1, Year, log = TRUE)
# # A tibble: 5,027 × 25
# Country Variable Year Dlog1.AGR L10Dlog1.AGR Dlog1.MIN L10Dlog1.MIN Dlog1.MAN L10Dlog1.MAN
# * <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
# 1 BWA VA 1960 NA NA NA NA NA NA
# 2 BWA VA 1961 NA NA NA NA NA NA
# 3 BWA VA 1962 NA NA NA NA NA NA
# 4 BWA VA 1963 NA NA NA NA NA NA
# 5 BWA VA 1964 NA NA NA NA NA NA
# 6 BWA VA 1965 -0.0359 NA -0.336 NA 0.324 NA
# 7 BWA VA 1966 0.117 NA -0.236 NA -0.236 NA
# 8 BWA VA 1967 0.0796 NA 0.154 NA 0.154 NA
# 9 BWA VA 1968 0.0972 NA -0.223 NA -0.223 NA
# 10 BWA VA 1969 0.0355 NA 1.05 NA 1.05 NA
# # ℹ 5,017 more rows
# # ℹ 16 more variables: Dlog1.PU <dbl>, L10Dlog1.PU <dbl>, Dlog1.CON <dbl>, L10Dlog1.CON <dbl>,
# # Dlog1.WRT <dbl>, L10Dlog1.WRT <dbl>, Dlog1.TRA <dbl>, L10Dlog1.TRA <dbl>, Dlog1.FIRE <dbl>,
# # L10Dlog1.FIRE <dbl>, Dlog1.GOV <dbl>, L10Dlog1.GOV <dbl>, Dlog1.OTH <dbl>, L10Dlog1.OTH <dbl>,
# # Dlog1.SUM <dbl>, L10Dlog1.SUM <dbl>
#
# Grouped by: Variable, Country [85 | 59 (7.7) 4-65]Finally, it is also possible to compute quasi-differences and quasi-log-differences of the form or :
GGDC10S %>%
fselect(-Region, -Regioncode) %>%
fgroup_by(Variable, Country) %>% fdiff(t = Year, rho = 0.95)
# # A tibble: 5,027 × 14
# Country Variable Year AGR MIN MAN PU CON WRT TRA FIRE GOV OTH
# * <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
# 1 BWA VA 1960 NA NA NA NA NA NA NA NA NA NA
# 2 BWA VA 1961 NA NA NA NA NA NA NA NA NA NA
# 3 BWA VA 1962 NA NA NA NA NA NA NA NA NA NA
# 4 BWA VA 1963 NA NA NA NA NA NA NA NA NA NA
# 5 BWA VA 1964 NA NA NA NA NA NA NA NA NA NA
# 6 BWA VA 1965 0.241 -0.824 0.318 0.0359 0.719 1.13 0.363 0.184 1.11 0.454
# 7 BWA VA 1966 2.74 -0.401 -0.163 0.0743 0.0673 1.56 0.312 0.174 0.955 0.449
# 8 BWA VA 1967 2.35 0.427 0.174 0.0101 -0.381 -3.55 -0.323 0.246 0.988 0.465
# 9 BWA VA 1968 2.91 -0.345 -0.141 0.0101 0.365 1.08 0.804 -0.427 -1.66 -0.780
# 10 BWA VA 1969 1.82 3.50 1.43 0.385 2.32 0.841 0.397 0.252 0.818 0.385
# # ℹ 5,017 more rows
# # ℹ 1 more variable: SUM <dbl>
#
# Grouped by: Variable, Country [85 | 59 (7.7) 4-65]The quasi-differencing feature was added to fdiff to
facilitate the preparation of time series and panel data for
least-squares estimations suffering from serial correlation following
Cochrane & Orcutt (1949).
Finally, fgrowth computes growth rates in the same way.
By default exact growth rates are computed in percentage terms using
(the default argument is scale = 100). The user can also
request growth rates obtained by log-differencing using
.
# Exact growth rates, computed as: (x/lag(x) - 1) * 100
GGDC10S %>%
fselect(-Region, -Regioncode) %>%
fgroup_by(Variable, Country) %>% fgrowth(c(1, 10), 1, Year)
# # A tibble: 5,027 × 25
# Country Variable Year G1.AGR L10G1.AGR G1.MIN L10G1.MIN G1.MAN L10G1.MAN G1.PU L10G1.PU G1.CON
# * <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
# 1 BWA VA 1960 NA NA NA NA NA NA NA NA NA
# 2 BWA VA 1961 NA NA NA NA NA NA NA NA NA
# 3 BWA VA 1962 NA NA NA NA NA NA NA NA NA
# 4 BWA VA 1963 NA NA NA NA NA NA NA NA NA
# 5 BWA VA 1964 NA NA NA NA NA NA NA NA NA
# 6 BWA VA 1965 -3.52 NA -28.6 NA 38.2 NA 29.4 NA 104.
# 7 BWA VA 1966 12.4 NA -21.1 NA -21.1 NA 50 NA 0
# 8 BWA VA 1967 8.29 NA 16.7 NA 16.7 NA 0 NA -33.3
# 9 BWA VA 1968 10.2 NA -20 NA -20 NA 0 NA 35.7
# 10 BWA VA 1969 3.61 NA 185. NA 185. NA 185. NA 185.
# # ℹ 5,017 more rows
# # ℹ 13 more variables: L10G1.CON <dbl>, G1.WRT <dbl>, L10G1.WRT <dbl>, G1.TRA <dbl>,
# # L10G1.TRA <dbl>, G1.FIRE <dbl>, L10G1.FIRE <dbl>, G1.GOV <dbl>, L10G1.GOV <dbl>, G1.OTH <dbl>,
# # L10G1.OTH <dbl>, G1.SUM <dbl>, L10G1.SUM <dbl>
#
# Grouped by: Variable, Country [85 | 59 (7.7) 4-65]
# Log-difference growth rates, computed as: log(x / lag(x)) * 100
GGDC10S %>%
fselect(-Region, -Regioncode) %>%
fgroup_by(Variable, Country) %>% fgrowth(c(1, 10), 1, Year, logdiff = TRUE)
# # A tibble: 5,027 × 25
# Country Variable Year Dlog1.AGR L10Dlog1.AGR Dlog1.MIN L10Dlog1.MIN Dlog1.MAN L10Dlog1.MAN
# * <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
# 1 BWA VA 1960 NA NA NA NA NA NA
# 2 BWA VA 1961 NA NA NA NA NA NA
# 3 BWA VA 1962 NA NA NA NA NA NA
# 4 BWA VA 1963 NA NA NA NA NA NA
# 5 BWA VA 1964 NA NA NA NA NA NA
# 6 BWA VA 1965 -3.59 NA -33.6 NA 32.4 NA
# 7 BWA VA 1966 11.7 NA -23.6 NA -23.6 NA
# 8 BWA VA 1967 7.96 NA 15.4 NA 15.4 NA
# 9 BWA VA 1968 9.72 NA -22.3 NA -22.3 NA
# 10 BWA VA 1969 3.55 NA 105. NA 105. NA
# # ℹ 5,017 more rows
# # ℹ 16 more variables: Dlog1.PU <dbl>, L10Dlog1.PU <dbl>, Dlog1.CON <dbl>, L10Dlog1.CON <dbl>,
# # Dlog1.WRT <dbl>, L10Dlog1.WRT <dbl>, Dlog1.TRA <dbl>, L10Dlog1.TRA <dbl>, Dlog1.FIRE <dbl>,
# # L10Dlog1.FIRE <dbl>, Dlog1.GOV <dbl>, L10Dlog1.GOV <dbl>, Dlog1.OTH <dbl>, L10Dlog1.OTH <dbl>,
# # Dlog1.SUM <dbl>, L10Dlog1.SUM <dbl>
#
# Grouped by: Variable, Country [85 | 59 (7.7) 4-65]fdiff and fgrowth can also perform leaded
(forward) differences and growth rates
(i.e. ... %>% fgrowth(-c(1, 10), 1:2, Year) would
compute one and 10-year leaded first and second differences). Again it
is possible to perform sequential operations:
# This computes the 1 and 10-year growth rates, for the current period and lagged by one period
GGDC10S %>%
fselect(-Region, -Regioncode) %>%
fgroup_by(Variable, Country) %>% fgrowth(c(1, 10), 1, Year) %>% flag(0:1, Year)
# # A tibble: 5,027 × 47
# Country Variable Year G1.AGR L1.G1.AGR L10G1.AGR L1.L10G1.AGR G1.MIN L1.G1.MIN L10G1.MIN
# * <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
# 1 BWA VA 1960 NA NA NA NA NA NA NA
# 2 BWA VA 1961 NA NA NA NA NA NA NA
# 3 BWA VA 1962 NA NA NA NA NA NA NA
# 4 BWA VA 1963 NA NA NA NA NA NA NA
# 5 BWA VA 1964 NA NA NA NA NA NA NA
# 6 BWA VA 1965 -3.52 NA NA NA -28.6 NA NA
# 7 BWA VA 1966 12.4 -3.52 NA NA -21.1 -28.6 NA
# 8 BWA VA 1967 8.29 12.4 NA NA 16.7 -21.1 NA
# 9 BWA VA 1968 10.2 8.29 NA NA -20 16.7 NA
# 10 BWA VA 1969 3.61 10.2 NA NA 185. -20 NA
# # ℹ 5,017 more rows
# # ℹ 37 more variables: L1.L10G1.MIN <dbl>, G1.MAN <dbl>, L1.G1.MAN <dbl>, L10G1.MAN <dbl>,
# # L1.L10G1.MAN <dbl>, G1.PU <dbl>, L1.G1.PU <dbl>, L10G1.PU <dbl>, L1.L10G1.PU <dbl>,
# # G1.CON <dbl>, L1.G1.CON <dbl>, L10G1.CON <dbl>, L1.L10G1.CON <dbl>, G1.WRT <dbl>,
# # L1.G1.WRT <dbl>, L10G1.WRT <dbl>, L1.L10G1.WRT <dbl>, G1.TRA <dbl>, L1.G1.TRA <dbl>,
# # L10G1.TRA <dbl>, L1.L10G1.TRA <dbl>, G1.FIRE <dbl>, L1.G1.FIRE <dbl>, L10G1.FIRE <dbl>,
# # L1.L10G1.FIRE <dbl>, G1.GOV <dbl>, L1.G1.GOV <dbl>, L10G1.GOV <dbl>, L1.L10G1.GOV <dbl>, …
#
# Grouped by: Variable, Country [85 | 59 (7.7) 4-65]3. Benchmarks
This section seeks to demonstrate that the functionality introduced in the preceding 2 sections indeed produces code that evaluates substantially faster than native dplyr.
To do this properly, the different components of a typical piped call (selecting / subsetting, ordering, grouping, and performing some computation) are benchmarked separately on 2 different data sizes.
All benchmarks are run on a Windows 8.1 laptop with a 2x 2.2 GHZ Intel i5 processor, 8GB DDR3 RAM and a Samsung 850 EVO SSD hard drive.
3.1 Data
Benchmarks are run on the original GGDC10S data used
throughout this vignette and a larger dataset with approx. 1 million
observations, obtained by replicating and row-binding
GGDC10S 200 times while maintaining unique groups.
# This shows the groups in GGDC10S
GRP(GGDC10S, ~ Variable + Country)
# collapse grouping object of length 5027 with 85 ordered groups
#
# Call: GRP.default(X = GGDC10S, by = ~Variable + Country), X is unsorted
#
# Distribution of group sizes:
# Min. 1st Qu. Median Mean 3rd Qu. Max.
# 4.00 53.00 62.00 59.14 63.00 65.00
#
# Groups with sizes:
# EMP.ARG EMP.BOL EMP.BRA EMP.BWA EMP.CHL EMP.CHN
# 62 61 62 52 63 62
# ---
# VA.TWN VA.TZA VA.USA VA.VEN VA.ZAF VA.ZMB
# 63 52 65 63 52 52
# This replicates the data 200 times
data <- replicate(200, GGDC10S, simplify = FALSE)
# This function adds a number i to the country and variable columns of each dataset
uniquify <- function(x, i) ftransform(x, lapply(unclass(x)[c(1,4)], paste0, i))
# Making datasets unique and row-binding them
data <- unlist2d(Map(uniquify, data, as.list(1:200)), idcols = FALSE)
fdim(data)
# [1] 1005400 16
# This shows the groups in the replicated data
GRP(data, ~ Variable + Country)
# collapse grouping object of length 1005400 with 17000 ordered groups
#
# Call: GRP.default(X = data, by = ~Variable + Country), X is unsorted
#
# Distribution of group sizes:
# Min. 1st Qu. Median Mean 3rd Qu. Max.
# 4.00 53.00 62.00 59.14 63.00 65.00
#
# Groups with sizes:
# EMP1.ARG1 EMP1.BOL1 EMP1.BRA1 EMP1.BWA1 EMP1.CHL1 EMP1.CHN1
# 62 61 62 52 63 62
# ---
# VA99.TWN99 VA99.TZA99 VA99.USA99 VA99.VEN99 VA99.ZAF99 VA99.ZMB99
# 63 52 65 63 52 52
gc()
# used (Mb) gc trigger (Mb) limit (Mb) max used (Mb)
# Ncells 3184710 170.1 8862174 473.3 NA 8862174 473.3
# Vcells 23965820 182.9 147787078 1127.6 16384 445825141 3401.43.1 Selecting, Subsetting, Ordering and Grouping
## Selecting columns
# Small
microbenchmark(dplyr = select(GGDC10S, Country, Variable, AGR:SUM),
collapse = fselect(GGDC10S, Country, Variable, AGR:SUM))
# Unit: microseconds
# expr min lq mean median uq max neval
# dplyr 400.775 410.7585 425.43117 416.396 424.637 820.041 100
# collapse 2.911 3.4645 4.59856 4.469 5.412 15.293 100
# Large
microbenchmark(dplyr = select(data, Country, Variable, AGR:SUM),
collapse = fselect(data, Country, Variable, AGR:SUM))
# Unit: microseconds
# expr min lq mean median uq max neval
# dplyr 388.926 396.429 412.67730 402.9890 411.0455 728.734 100
# collapse 2.870 3.280 4.44686 3.8335 5.3300 12.669 100
## Subsetting columns
# Small
microbenchmark(dplyr = filter(GGDC10S, Variable == "VA"),
collapse = fsubset(GGDC10S, Variable == "VA"))
# Unit: microseconds
# expr min lq mean median uq max neval
# dplyr 374.084 394.4405 409.23986 401.0005 414.3050 716.475 100
# collapse 39.278 48.2775 55.85307 55.5550 60.4545 103.320 100
# Large
microbenchmark(dplyr = filter(data, Variable == "VA"),
collapse = fsubset(data, Variable == "VA"))
# Unit: milliseconds
# expr min lq mean median uq max neval
# dplyr 4.487409 5.242752 8.352270 5.653223 6.434048 159.13658 100
# collapse 2.840808 3.082359 3.469128 3.163478 3.302714 16.56047 100
## Ordering rows
# Small
microbenchmark(dplyr = arrange(GGDC10S, desc(Country), Variable, Year),
collapse = roworder(GGDC10S, -Country, Variable, Year))
# Unit: microseconds
# expr min lq mean median uq max neval
# dplyr 1715.112 1867.4270 1983.4726 2015.109 2080.7500 2367.791 100
# collapse 192.495 232.4085 256.3878 247.968 258.7715 1055.381 100
# Large
microbenchmark(dplyr = arrange(data, desc(Country), Variable, Year),
collapse = roworder(data, -Country, Variable, Year), times = 2)
# Unit: milliseconds
# expr min lq mean median uq max neval
# dplyr 89.37512 89.37512 101.05180 101.05180 112.72848 112.72848 2
# collapse 66.46703 66.46703 67.45254 67.45254 68.43806 68.43806 2
## Grouping
# Small
microbenchmark(dplyr = group_by(GGDC10S, Country, Variable),
collapse = fgroup_by(GGDC10S, Country, Variable))
# Unit: microseconds
# expr min lq mean median uq max neval
# dplyr 778.713 815.1825 911.3484 874.2225 960.3840 1529.874 100
# collapse 146.534 157.6245 198.5921 165.0660 177.3455 1484.241 100
# Large
microbenchmark(dplyr = group_by(data, Country, Variable),
collapse = fgroup_by(data, Country, Variable), times = 10)
# Unit: milliseconds
# expr min lq mean median uq max neval
# dplyr 34.20294 34.62839 34.88041 34.88432 35.07821 35.48279 10
# collapse 27.89972 28.03211 28.55175 28.36954 29.32283 29.54206 10
## Computing a new column
# Small
microbenchmark(dplyr = mutate(GGDC10S, NEW = AGR+1),
collapse = ftransform(GGDC10S, NEW = AGR+1))
# Unit: microseconds
# expr min lq mean median uq max neval
# dplyr 317.463 321.7270 333.38822 324.9660 333.7810 631.564 100
# collapse 8.897 11.0495 12.95354 12.4435 14.2065 38.991 100
# Large
microbenchmark(dplyr = mutate(data, NEW = AGR+1),
collapse = ftransform(data, NEW = AGR+1))
# Unit: microseconds
# expr min lq mean median uq max neval
# dplyr 637.878 1084.225 1330.006 1164.6665 1291.2335 15869.05 100
# collapse 210.740 657.025 1021.434 698.3735 781.7675 16725.09 100
## All combined with pipes
# Small
microbenchmark(dplyr = filter(GGDC10S, Variable == "VA") %>%
select(Country, Year, AGR:SUM) %>%
arrange(desc(Country), Year) %>%
mutate(NEW = AGR+1) %>%
group_by(Country),
collapse = fsubset(GGDC10S, Variable == "VA", Country, Year, AGR:SUM) %>%
roworder(-Country, Year) %>%
ftransform(NEW = AGR+1) %>%
fgroup_by(Country))
# Unit: microseconds
# expr min lq mean median uq max neval
# dplyr 2982.340 3416.325 3525.7983 3538.464 3668.516 5034.021 100
# collapse 136.858 186.632 214.4681 211.683 243.130 314.470 100
# Large
microbenchmark(dplyr = filter(data, Variable == "VA") %>%
select(Country, Year, AGR:SUM) %>%
arrange(desc(Country), Year) %>%
mutate(NEW = AGR+1) %>%
group_by(Country),
collapse = fsubset(data, Variable == "VA", Country, Year, AGR:SUM) %>%
roworder(-Country, Year) %>%
ftransform(NEW = AGR+1) %>%
fgroup_by(Country), times = 10)
# Unit: milliseconds
# expr min lq mean median uq max neval
# dplyr 7.917182 7.997378 8.142653 8.109943 8.292291 8.423163 10
# collapse 3.080289 3.104028 3.150153 3.140969 3.188365 3.251259 10
gc()
# used (Mb) gc trigger (Mb) limit (Mb) max used (Mb)
# Ncells 3184728 170.1 8862174 473.3 NA 8862174 473.3
# Vcells 23970594 182.9 75772825 578.2 16384 445825141 3401.43.1 Aggregation
## Grouping the data
cgGGDC10S <- fgroup_by(GGDC10S, Variable, Country) %>% fselect(-Region, -Regioncode)
gGGDC10S <- group_by(GGDC10S, Variable, Country) %>% fselect(-Region, -Regioncode)
cgdata <- fgroup_by(data, Variable, Country) %>% fselect(-Region, -Regioncode)
gdata <- group_by(data, Variable, Country) %>% fselect(-Region, -Regioncode)
rm(data, GGDC10S)
gc()
# used (Mb) gc trigger (Mb) limit (Mb) max used (Mb)
# Ncells 3201723 171 8862174 473.3 NA 8862174 473.3
# Vcells 23589381 180 75772825 578.2 16384 445825141 3401.4
## Conversion of Grouping object: This time would be required extra in all hybrid calls
## i.e. when calling collapse functions on data grouped with dplyr::group_by
# Small
microbenchmark(GRP(gGGDC10S))
# Unit: microseconds
# expr min lq mean median uq max neval
# GRP(gGGDC10S) 8.692 9.2455 10.16021 9.4915 10.086 39.196 100
# Large
microbenchmark(GRP(gdata))
# Unit: microseconds
# expr min lq mean median uq max neval
# GRP(gdata) 885.641 1160.915 1248.258 1237.236 1323.234 1651.398 100
## Sum
# Small
microbenchmark(dplyr = summarise_all(gGGDC10S, sum, na.rm = TRUE),
collapse = fsum(cgGGDC10S))
# Unit: microseconds
# expr min lq mean median uq max neval
# dplyr 3017.723 3354.1895 3733.4739 3620.9560 3738.441 22135.736 100
# collapse 218.120 227.3655 236.7693 235.1965 244.852 270.805 100
# Large
microbenchmark(dplyr = summarise_all(gdata, sum, na.rm = TRUE),
collapse = fsum(cgdata), times = 10)
# Unit: milliseconds
# expr min lq mean median uq max neval
# dplyr 272.9737 279.91024 305.02067 283.59737 303.57122 448.07629 10
# collapse 41.5330 41.63214 41.88717 41.77062 41.96059 42.78662 10
## Mean
# Small
microbenchmark(dplyr = summarise_all(gGGDC10S, mean.default, na.rm = TRUE),
collapse = fmean(cgGGDC10S))
# Unit: microseconds
# expr min lq mean median uq max neval
# dplyr 4360.104 4596.6740 5125.4194 4754.791 5005.710 37144.852 100
# collapse 169.084 174.3935 185.4594 183.434 194.832 221.933 100
# Large
microbenchmark(dplyr = summarise_all(gdata, mean.default, na.rm = TRUE),
collapse = fmean(cgdata), times = 10)
# Unit: milliseconds
# expr min lq mean median uq max neval
# dplyr 623.5123 642.83748 704.39836 681.32260 786.82731 829.74435 10
# collapse 31.7636 31.88037 32.00222 31.99445 32.08209 32.43875 10
## Median
# Small
microbenchmark(dplyr = summarise_all(gGGDC10S, median, na.rm = TRUE),
collapse = fmedian(cgGGDC10S))
# Unit: microseconds
# expr min lq mean median uq max neval
# dplyr 14399.118 14849.933 16170.3500 14982.5685 15145.892 33613.235 100
# collapse 137.596 164.902 189.2056 178.1245 214.676 248.624 100
# Large
microbenchmark(dplyr = summarise_all(gdata, median, na.rm = TRUE),
collapse = fmedian(cgdata), times = 2)
# Unit: milliseconds
# expr min lq mean median uq max neval
# dplyr 2826.83036 2826.83036 2828.12912 2828.12912 2829.42788 2829.42788 2
# collapse 19.95564 19.95564 19.98524 19.98524 20.01485 20.01485 2
## Standard Deviation
# Small
microbenchmark(dplyr = summarise_all(gGGDC10S, sd, na.rm = TRUE),
collapse = fsd(cgGGDC10S))
# Unit: microseconds
# expr min lq mean median uq max neval
# dplyr 8332.635 8612.5215 9365.1216 8712.766 8989.086 25087.982 100
# collapse 242.228 251.0225 269.7849 273.552 282.326 321.891 100
# Large
microbenchmark(dplyr = summarise_all(gdata, sd, na.rm = TRUE),
collapse = fsd(cgdata), times = 2)
# Unit: milliseconds
# expr min lq mean median uq max neval
# dplyr 1375.80363 1375.80363 1409.60358 1409.60358 1443.40352 1443.40352 2
# collapse 46.21713 46.21713 56.88205 56.88205 67.54697 67.54697 2
## Maximum
# Small
microbenchmark(dplyr = summarise_all(gGGDC10S, max, na.rm = TRUE),
collapse = fmax(cgGGDC10S))
# Unit: microseconds
# expr min lq mean median uq max neval
# dplyr 39964.504 41008.8560 43577.92707 41448.273 44195.1095 58816.550 100
# collapse 68.798 74.7225 87.83389 77.572 100.9215 129.519 100
# Large
microbenchmark(dplyr = summarise_all(gdata, max, na.rm = TRUE),
collapse = fmax(cgdata), times = 10)
# Unit: milliseconds
# expr min lq mean median uq max neval
# dplyr 480.83804 490.9982 540.7374 517.86136 533.85723 687.14713 10
# collapse 11.40116 11.7745 11.9366 11.85156 11.94908 13.18318 10
## First Value
# Small
microbenchmark(dplyr = summarise_all(gGGDC10S, first),
collapse = ffirst(cgGGDC10S, na.rm = FALSE))
# Unit: microseconds
# expr min lq mean median uq max neval
# dplyr 4147.888 4242.249 4801.88966 4383.248 4701.532 19254.215 100
# collapse 11.685 14.227 26.25476 24.764 35.301 137.514 100
# Large
microbenchmark(dplyr = summarise_all(gdata, first),
collapse = ffirst(cgdata, na.rm = FALSE), times = 10)
# Unit: microseconds
# expr min lq mean median uq max neval
# dplyr 530327.66 558767.393 637499.226 596503.08 672801.103 969373.660 10
# collapse 872.89 999.088 1087.845 1068.87 1204.416 1289.327 10
## Number of Distinct Values
# Small
microbenchmark(dplyr = summarise_all(gGGDC10S, n_distinct, na.rm = TRUE),
collapse = fndistinct(cgGGDC10S))
# Unit: microseconds
# expr min lq mean median uq max neval
# dplyr 11316.574 11600.847 12573.1010 11759.435 11939.487 31659.667 100
# collapse 189.051 205.164 226.0933 235.422 239.604 443.661 100
# Large
microbenchmark(dplyr = summarise_all(gdata, n_distinct, na.rm = TRUE),
collapse = fndistinct(cgdata), times = 5)
# Unit: milliseconds
# expr min lq mean median uq max neval
# dplyr 2044.13376 2110.16926 2133.91960 2138.07456 2154.39797 2222.82246 5
# collapse 30.65443 30.94582 31.51081 31.17123 31.17972 33.60286 5
gc()
# used (Mb) gc trigger (Mb) limit (Mb) max used (Mb)
# Ncells 3972309 212.2 8862174 473.3 NA 8862174 473.3
# Vcells 24857303 189.7 75772825 578.2 16384 445825141 3401.4Below are some additional benchmarks for weighted aggregations and aggregations using the statistical mode, which cannot easily or efficiently be performed with dplyr.
## Weighted Mean
# Small
microbenchmark(fmean(cgGGDC10S, SUM))
# Unit: microseconds
# expr min lq mean median uq max neval
# fmean(cgGGDC10S, SUM) 195.488 200.4285 218.2836 211.1295 218.8375 444.276 100
# Large
microbenchmark(fmean(cgdata, SUM), times = 10)
# Unit: milliseconds
# expr min lq mean median uq max neval
# fmean(cgdata, SUM) 34.73516 35.28276 35.66689 35.32257 36.44802 36.80722 10
## Weighted Standard-Deviation
# Small
microbenchmark(fsd(cgGGDC10S, SUM))
# Unit: microseconds
# expr min lq mean median uq max neval
# fsd(cgGGDC10S, SUM) 243.048 244.606 249.2181 246.9635 249.444 323.9 100
# Large
microbenchmark(fsd(cgdata, SUM), times = 10)
# Unit: milliseconds
# expr min lq mean median uq max neval
# fsd(cgdata, SUM) 44.905 44.93116 45.15391 45.01095 45.22677 46.14689 10
## Statistical Mode
# Small
microbenchmark(fmode(cgGGDC10S))
# Unit: microseconds
# expr min lq mean median uq max neval
# fmode(cgGGDC10S) 245.098 248.3575 253.4809 250.6945 253.9335 420.619 100
# Large
microbenchmark(fmode(cgdata), times = 10)
# Unit: milliseconds
# expr min lq mean median uq max neval
# fmode(cgdata) 40.26151 41.82082 41.63019 41.88382 42.0232 42.0587 10
## Weighted Statistical Mode
# Small
microbenchmark(fmode(cgGGDC10S, SUM))
# Unit: microseconds
# expr min lq mean median uq max neval
# fmode(cgGGDC10S, SUM) 330.993 333.535 337.7744 334.5395 337.3685 447.187 100
# Large
microbenchmark(fmode(cgdata, SUM), times = 10)
# Unit: milliseconds
# expr min lq mean median uq max neval
# fmode(cgdata, SUM) 57.69815 57.78466 57.98187 57.84567 58.09942 58.81835 10
gc()
# used (Mb) gc trigger (Mb) limit (Mb) max used (Mb)
# Ncells 3971768 212.2 8862174 473.3 NA 8862174 473.3
# Vcells 24853915 189.7 75772825 578.2 16384 445825141 3401.43.2 Transformation
## Replacing with group sum
# Small
microbenchmark(dplyr = mutate_all(gGGDC10S, sum, na.rm = TRUE),
collapse = fsum(cgGGDC10S, TRA = "replace_fill"))
# Unit: microseconds
# expr min lq mean median uq max neval
# dplyr 13088.102 13223.340 14388.9000 13359.7680 14380.05 29060.554 100
# collapse 238.456 273.757 292.1693 293.9905 312.01 388.106 100
# Large
microbenchmark(dplyr = mutate_all(gdata, sum, na.rm = TRUE),
collapse = fsum(cgdata, TRA = "replace_fill"), times = 10)
# Unit: milliseconds
# expr min lq mean median uq max neval
# dplyr 391.63618 679.62609 662.91807 716.40975 729.7527 749.4973 10
# collapse 49.63788 50.24189 61.77658 55.18416 63.4596 111.6039 10
## Dividing by group sum
# Small
microbenchmark(dplyr = mutate_all(gGGDC10S, function(x) x/sum(x, na.rm = TRUE)),
collapse = fsum(cgGGDC10S, TRA = "/"))
# Unit: microseconds
# expr min lq mean median uq max neval
# dplyr 13058.992 13203.8450 14294.3733 13321.41 13880.796 42300.028 100
# collapse 242.884 268.5295 278.8541 274.29 294.585 330.255 100
# Large
microbenchmark(dplyr = mutate_all(gdata, function(x) x/sum(x, na.rm = TRUE)),
collapse = fsum(cgdata, TRA = "/"), times = 10)
# Unit: milliseconds
# expr min lq mean median uq max neval
# dplyr 474.9046 654.6199 796.14248 907.32863 942.32567 999.2501 10
# collapse 49.3542 50.9056 84.66647 52.05635 74.51705 325.4319 10
## Centering
# Small
microbenchmark(dplyr = mutate_all(gGGDC10S, function(x) x-mean.default(x, na.rm = TRUE)),
collapse = fwithin(cgGGDC10S))
# Unit: microseconds
# expr min lq mean median uq max neval
# dplyr 14460.04 14769.4095 15977.4942 14859.815 15013.421 37113.077 100
# collapse 203.77 229.7845 246.5043 242.638 266.664 293.191 100
# Large
microbenchmark(dplyr = mutate_all(gdata, function(x) x-mean.default(x, na.rm = TRUE)),
collapse = fwithin(cgdata), times = 10)
# Unit: milliseconds
# expr min lq mean median uq max neval
# dplyr 893.06503 925.50231 1217.2225 1259.34620 1445.254 1545.5490 10
# collapse 43.90731 56.97093 143.4797 73.39498 152.872 429.3341 10
## Centering and Scaling (Standardizing)
# Small
microbenchmark(dplyr = mutate_all(gGGDC10S, function(x) (x-mean.default(x, na.rm = TRUE))/sd(x, na.rm = TRUE)),
collapse = fscale(cgGGDC10S))
# Unit: microseconds
# expr min lq mean median uq max neval
# dplyr 20275.033 21145.524 24976.1242 22214.190 25194.0285 79869.435 100
# collapse 277.775 304.958 323.3613 314.388 338.2705 437.388 100
# Large
microbenchmark(dplyr = mutate_all(gdata, function(x) (x-mean.default(x, na.rm = TRUE))/sd(x, na.rm = TRUE)),
collapse = fscale(cgdata), times = 2)
# Unit: milliseconds
# expr min lq mean median uq max neval
# dplyr 2118.97696 2118.97696 2315.9282 2315.9282 2512.87938 2512.87938 2
# collapse 60.17144 60.17144 60.6284 60.6284 61.08537 61.08537 2
## Lag
# Small
microbenchmark(dplyr_unordered = mutate(gGGDC10S, across(everything(), dplyr::lag)),
collapse_unordered = flag(cgGGDC10S),
dplyr_ordered = mutate(gGGDC10S, across(everything(), \(x) dplyr::lag(x, order_by = Year))),
collapse_ordered = flag(cgGGDC10S, t = Year))
# Unit: microseconds
# expr min lq mean median uq max neval
# dplyr_unordered 14495.386 14796.101 17579.85413 15265.3250 15889.7550 49137.721 100
# collapse_unordered 48.544 75.071 90.29225 86.6330 109.6545 225.377 100
# dplyr_ordered 24893.437 25327.607 27521.59809 25904.9275 27136.2190 51312.074 100
# collapse_ordered 80.196 107.953 120.85160 117.5675 131.6715 189.051 100
# Large
microbenchmark(dplyr_unordered = mutate(gdata, across(everything(), dplyr::lag)),
collapse_unordered = flag(cgdata),
dplyr_ordered = mutate(gdata, across(everything(), \(x) dplyr::lag(x, order_by = Year))),
collapse_ordered = flag(cgdata, t = Year), times = 2)
# Unit: milliseconds
# expr min lq mean median uq max neval
# dplyr_unordered 3461.11500 3461.11500 3471.95821 3471.95821 3482.80142 3482.80142 2
# collapse_unordered 13.71897 13.71897 211.59809 211.59809 409.47721 409.47721 2
# dplyr_ordered 5786.57522 5786.57522 6291.90389 6291.90389 6797.23256 6797.23256 2
# collapse_ordered 25.14399 25.14399 35.36102 35.36102 45.57806 45.57806 2
## First-Difference (unordered)
# Small
microbenchmark(dplyr_unordered = mutate_all(gGGDC10S, function(x) x - dplyr::lag(x)),
collapse_unordered = fdiff(cgGGDC10S))
# Unit: microseconds
# expr min lq mean median uq max neval
# dplyr_unordered 25613.274 25878.0725 27951.41954 26257.3225 27226.808 43048.893 100
# collapse_unordered 56.539 72.3035 95.72147 91.6965 102.664 254.077 100
# Large
microbenchmark(dplyr_unordered = mutate_all(gdata, function(x) x - dplyr::lag(x)),
collapse_unordered = fdiff(cgdata), times = 2)
# Unit: milliseconds
# expr min lq mean median uq max neval
# dplyr_unordered 3287.88487 3287.88487 3425.69703 3425.69703 3563.509 3563.509 2
# collapse_unordered 16.58971 16.58971 23.36885 23.36885 30.148 30.148 2
gc()
# used (Mb) gc trigger (Mb) limit (Mb) max used (Mb)
# Ncells 3978800 212.5 8862175 473.3 NA 8862175 473.3
# Vcells 24870572 189.8 72805912 555.5 16384 445825141 3401.4Below again some benchmarks for transformations not easily of efficiently performed with dplyr, such as centering on the overall mean, mean-preserving scaling, weighted scaling and centering, sequences of lags / leads, (iterated) panel-differences and growth rates.
# Centering on overall mean
microbenchmark(fwithin(cgdata, mean = "overall.mean"), times = 10)
# Unit: milliseconds
# expr min lq mean median uq max neval
# fwithin(cgdata, mean = "overall.mean") 44.66782 48.03445 52.04073 50.07953 53.67134 71.13221 10
# Weighted Centering
microbenchmark(fwithin(cgdata, SUM), times = 10)
# Unit: milliseconds
# expr min lq mean median uq max neval
# fwithin(cgdata, SUM) 40.45204 42.86833 46.55326 46.18277 47.28202 57.82673 10
microbenchmark(fwithin(cgdata, SUM, mean = "overall.mean"), times = 10)
# Unit: milliseconds
# expr min lq mean median uq max
# fwithin(cgdata, SUM, mean = "overall.mean") 39.99279 40.32256 43.0638 40.60269 41.34366 54.45542
# neval
# 10
# Weighted Scaling and Standardizing
microbenchmark(fsd(cgdata, SUM, TRA = "/"), times = 10)
# Unit: milliseconds
# expr min lq mean median uq max neval
# fsd(cgdata, SUM, TRA = "/") 50.19536 50.9145 55.12553 53.23862 56.27094 67.46816 10
microbenchmark(fscale(cgdata, SUM), times = 10)
# Unit: milliseconds
# expr min lq mean median uq max neval
# fscale(cgdata, SUM) 54.14792 57.64584 60.83251 59.88025 61.16425 72.31928 10
# Sequence of lags and leads
microbenchmark(flag(cgdata, -1:1), times = 10)
# Unit: milliseconds
# expr min lq mean median uq max neval
# flag(cgdata, -1:1) 26.03902 48.02695 194.8518 257.0652 264.5479 276.5348 10
# Iterated difference
microbenchmark(fdiff(cgdata, 1, 2), times = 10)
# Unit: milliseconds
# expr min lq mean median uq max neval
# fdiff(cgdata, 1, 2) 38.76001 39.83896 44.93731 41.08887 48.98348 63.42528 10
# Growth Rate
microbenchmark(fgrowth(cgdata,1), times = 10)
# Unit: milliseconds
# expr min lq mean median uq max neval
# fgrowth(cgdata, 1) 11.58627 13.81528 18.05776 14.03489 22.34279 31.15811 10References
Timmer, M. P., de Vries, G. J., & de Vries, K. (2015). “Patterns of Structural Change in Developing Countries.” . In J. Weiss, & M. Tribe (Eds.), Routledge Handbook of Industry and Development. (pp. 65-83). Routledge.
Cochrane, D. & Orcutt, G. H. (1949). “Application of Least Squares Regression to Relationships Containing Auto-Correlated Error Terms”. Journal of the American Statistical Association. 44 (245): 32–61.
Prais, S. J. & Winsten, C. B. (1954). “Trend Estimators and Serial Correlation”. Cowles Commission Discussion Paper No. 383. Chicago.