collapse is a C/C++ based package for data transformation and statistical computing in R. It’s aims are:
This 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 addition help("collapse-package") provides a compact set of examples for quick-start.
Documentation and vignettes can also be viewed online.
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.
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 x 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
# # ... with 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 x 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
# # ... with 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.
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 x 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]
# # ... with 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
# List of 8
# $ 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 : logi [1:2] TRUE TRUE
# $ order : NULL
# $ call : language GRP.grouped_df(X = .)
# - attr(*, "class")= chr "GRP"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.
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 x 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
# # ... with 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 cld
# collapse 942.476 1033.066 1122.02 1059.394 1157.792 1947.874 100 a
# hybrid 12567.245 13084.000 14059.24 13524.893 14201.852 22570.792 100 b
# dplyr 59600.474 62732.691 66548.49 64481.761 69187.895 90369.739 100 cBenchmarks 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 x 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
# # ... with 5,017 more rows, and 2 more variables: OTH <dbl>, SUM <dbl>
#
# Grouped by: Variable, Country [85 | 59 (7.7)]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 x 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 x 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 x 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 6.86e3 3.55e4 19553. 1064. 1.17e4 1.93e4 8.03e3 5.60e3 NA 19986. 1.28e5
# 2 VA ZAF 1.64e4 4.29e4 87572. 13826. 1.64e4 6.83e4 4.53e4 6.64e4 7.58e4 30167. 4.63e5
# 3 VA ZMB 1.27e6 1.01e6 899510. 219164. 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 x 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 6.86e3 3.55e4 19553. 1064. 1.17e4 1.93e4 8.03e3 5.60e3 NA 19986. 1.28e5
# 2 VA ZAF 1.64e4 4.29e4 87572. 13826. 1.64e4 6.83e4 4.53e4 6.64e4 7.58e4 30167. 4.63e5
# 3 VA ZMB 1.27e6 1.01e6 899510. 219164. 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 x 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 x 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 x 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 x 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 x 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.
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 x 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.
# # ... with 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 x 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 x 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.
# # ... with 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 x 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~ 1980. 1325. 47.4 1988. 105. 782. 1855. 580. 464.
# 2 EMP BOL LAM Latin~ 1980 943. 53.5 167. 4.46 66.0 132. 97.0 15.3
# 3 EMP BRA LAM Latin~ 1980. 17481. 225. 7208. 376. 4055. 6455. 1581. 4355.
# # ... with 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 x 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 Ameri~ Latin Ameri~
# 2 EMP BOL LAM LAM LAM Latin Ameri~ Latin Ameri~
# 3 EMP BRA LAM LAM LAM Latin Ameri~ Latin Ameri~
# # ... with 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 x 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.
# # ... with 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 x 8
# Variable Country fmean.AGR fmean.MIN fmean.MAN fmedian.CON fmedian.WRT fmedian.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).
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 x 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 x 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 x 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.
# # ... with 4 more variables: TRA <dbl>, FIRE <dbl>, GOV <dbl>, OTH <dbl>collapse also provides some fast transformations that significantly extend the scope and speed of manipulations that can be performed with dplyr::mutate.
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 x 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 x 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…
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 transforms 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 x 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 x 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 x 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 61.3 21.7 23.1 6.31 23.2 26.7 8.98 11.3 27.0 10.1 220.
# 2 VA BWA 61.3 21.7 23.1 6.31 23.2 26.7 8.98 11.3 27.0 10.1 220.
# 3 VA BWA 61.3 21.7 23.1 6.31 23.2 26.7 8.98 11.3 27.0 10.1 220.
# Scaling sectoral data by Variable and Country
GGDC10S %>%
fselect(Variable, Country, AGR:SUM) %>%
fgroup_by(Variable, Country) %>% fsd(TRA = "/") %>% head
# # A tibble: 6 x 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 5.56e-4 5.23e-4 3.88e-4 5.11e-4 0.00194 0.00154 5.23e-4 0.00134
# 6 VA BWA 0.0260 3.97e-4 7.23e-4 5.03e-4 1.04e-3 0.00220 0.00180 5.83e-4 0.00158
# # ... with 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 x 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 Middl~ EMP 2010 5206. 29.0 2436. 307. 2733. 2977. 1992. 801. 5539.
# 2 EGY MENA Middl~ EMP 2011 5186. 27.6 2374. 318. 2795. 3020. 2048. 815. 5636.
# 3 EGY MENA Middl~ EMP 2012 5161. 24.8 2348. 325. 2931. 3110. 2065. 832. 5736.
# # ... with 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 x 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 Middl~ EMP 2010 8.41 2.28 4.32 3.56 3.62 3.75 3.75 3.14 3.80
# 2 EGY MENA Middl~ EMP 2011 8.38 2.17 4.21 3.68 3.70 3.81 3.86 3.19 3.86
# 3 EGY MENA Middl~ EMP 2012 8.34 1.95 4.17 3.76 3.88 3.92 3.89 3.26 3.93
# # ... with 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 x 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 x 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
# # ... with 5,017 more rows
#
# Grouped by: Variable, Country [85 | 59 (7.7)]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 x 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-s~ VA 1960 NA 47 NA 47 NA 47 NA 47 NA
# 2 BWA SSA Sub-s~ VA 1961 NA 47 NA 47 NA 47 NA 47 NA
# 3 BWA SSA Sub-s~ VA 1962 NA 47 NA 47 NA 47 NA 47 NA
# 4 BWA SSA Sub-s~ VA 1963 NA 47 NA 47 NA 47 NA 47 NA
# 5 BWA SSA Sub-s~ VA 1964 16.3 47 3.49 47 0.737 47 0.104 47 0.660
# 6 BWA SSA Sub-s~ VA 1965 15.7 47 2.50 47 1.02 47 0.135 47 1.35
# # ... with 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.
TRA FunctionTowards 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 x 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
# # ... with 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 x 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
# # ... with 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 x 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
# # ... with 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 x 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
# # ... with 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 x 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 8.80e4 3230. 1.20e5 6307. 4.60e4 1.23e5 4.02e4 3.89e4 1.27e5 6.15e4 6.54e5
# 2 EMP BOL 5.88e4 3418. 1.43e4 326. 7.49e3 1.72e4 7.04e3 2.72e3 NA 2.41e4 1.35e5
# 3 EMP BRA 1.07e6 12773. 4.33e5 22604. 2.19e5 5.28e5 1.27e5 2.74e5 3.29e5 3.54e5 3.36e6
# 4 EMP BWA 8.84e3 493. 8.49e2 145. 1.19e3 1.71e3 3.93e2 7.21e2 2.87e3 1.30e3 1.85e4
# 5 EMP CHL 4.42e4 6389. 3.94e4 1850. 1.86e4 4.38e4 1.63e4 1.72e4 NA 6.32e4 2.51e5
# 6 EMP CHN 1.73e7 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 x 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-s~ VA 1960 NA NA NA NA NA NA
# 2 BWA SSA Sub-s~ VA 1961 NA NA NA NA NA NA
# 3 BWA SSA Sub-s~ VA 1962 NA NA NA NA NA NA
# 4 BWA SSA Sub-s~ VA 1963 NA NA NA NA NA NA
# 5 BWA SSA Sub-s~ VA 1964 7.50e-4 1.65e-5 1.66e-5 1.03e-5 1.57e-5 6.82e-5
# 6 BWA SSA Sub-s~ VA 1965 7.24e-4 1.18e-5 2.30e-5 1.33e-5 3.20e-5 7.72e-5
# # ... with 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).
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 x 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 x 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 x 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 x 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 2.53e6 1.87e6 5.54e6 335856. 1.80e6 3.39e6 1.47e6 1.66e6 1.71e6 NA 2.16e7
# 2 EGY EMP 2.53e6 1.87e6 5.54e6 335867. 1.80e6 3.39e6 1.47e6 1.66e6 1.71e6 NA 2.16e7
# 3 EGY EMP 2.53e6 1.87e6 5.54e6 335873. 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 x 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. 4.29e8 3.70e8 7.38e8 2.73e7 2.83e8 4.33e8 1.97e8 1.55e8 2.10e8 NA
# 2 EGY EMP 22219. 4.29e8 3.70e8 7.38e8 2.73e7 2.83e8 4.33e8 1.97e8 1.55e8 2.10e8 NA
# 3 EGY EMP 22533. 4.29e8 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 x 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
# # ... with 5,017 more rows
#
# Grouped by: Variable, Country [85 | 59 (7.7)]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 x 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 x 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 x 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. 1. 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.
# 2 EMP BOL 1. 1.00 1. 1.00 1.00 1. 1. 1. NA 1. 1.
# 3 EMP BRA 1. 1. 1. 1.00 1. 1.00 1.00 1.00 1. 1.00 1.00
# 4 EMP BWA 1.00 1.00 1. 1. 1. 1.00 1. 1.00 1. 1.00 1.00
# 5 EMP CHL 1. 1. 1.00 1. 1. 1. 1.00 1. NA 1. 1.00
# 6 EMP CHN 1. 1. 1. 1.00 1.00 1. 1. 1. 1.00 1.00 1.One 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 x 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 4.50e7 4.01e7 7.56e7 3.06e6 3.08e7 4.41e7 2.07e7 1.60e7 2.04e7 1.88e7 3.06e8
# 2 BOL 4.50e7 4.01e7 7.56e7 3.06e6 3.08e7 4.41e7 2.07e7 1.60e7 NA 1.88e7 3.06e8
# 3 BRA 4.50e7 4.01e7 7.56e7 3.06e6 3.08e7 4.41e7 2.07e7 1.60e7 2.04e7 1.88e7 3.06e8
# 4 BWA 4.50e7 4.01e7 7.56e7 3.06e6 3.08e7 4.41e7 2.07e7 1.60e7 2.04e7 1.88e7 3.06e8
# 5 CHL 4.50e7 4.01e7 7.56e7 3.06e6 3.08e7 4.41e7 2.07e7 1.60e7 NA 1.88e7 3.06e8
# 6 CHN 4.50e7 4.01e7 7.56e7 3.06e6 3.08e7 4.41e7 2.07e7 1.60e7 2.04e7 1.88e7 3.06e8
# 7 COL 4.50e7 4.01e7 7.56e7 3.06e6 3.08e7 4.41e7 2.07e7 1.60e7 NA 1.88e7 3.06e8
# 8 CRI 4.50e7 4.01e7 7.56e7 3.06e6 3.08e7 4.41e7 2.07e7 1.60e7 2.04e7 1.88e7 3.06e8
# 9 DEW 4.50e7 4.01e7 7.56e7 3.06e6 3.08e7 4.41e7 2.07e7 1.60e7 2.04e7 1.88e7 3.06e8
# 10 DNK 4.50e7 4.01e7 7.56e7 3.06e6 3.08e7 4.41e7 2.07e7 1.60e7 2.04e7 1.88e7 3.06e8
# # ... with 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.
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 x 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
# # ... with 5,017 more rows, and 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)]If the time-variable passed does not exactly identify the data (i.e. because of gaps or repeated values in each group), all 3 functions will issue appropriate error messages. flag, fdiff and fgrowth support unbalanced panels with different start and end periods and duration of coverage for each individual, but not irregular panels. A workaround for such panels exists with the function seqid which generates a new panel-id identifying consecutive time-sequences at the sub-individual level, see ?seqid.
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 x 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
# # ... with 5,017 more rows
#
# Grouped by: Variable, Country [85 | 59 (7.7)]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 x 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
# # ... with 5,017 more rows, and 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>, L10D2.SUM <dbl>
#
# Grouped by: Variable, Country [85 | 59 (7.7)]Log-differences of the form \(log(x_t) - log(x_{t-s})\) are also easily computed.
GGDC10S %>%
fselect(-Region, -Regioncode) %>%
fgroup_by(Variable, Country) %>% fdiff(c(1, 10), 1, Year, log = TRUE)
# # A tibble: 5,027 x 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
# # ... with 5,017 more rows, and 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)]Finally, it is also possible to compute quasi-differences and quasi-log-differences of the form \(x_t - \rho x_{t-s}\) or \(log(x_t) - \rho log(x_{t-s})\):
GGDC10S %>%
fselect(-Region, -Regioncode) %>%
fgroup_by(Variable, Country) %>% fdiff(t = Year, rho = 0.95)
# # A tibble: 5,027 x 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
# # ... with 5,017 more rows, and 1 more variable: SUM <dbl>
#
# Grouped by: Variable, Country [85 | 59 (7.7)]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 \((x_t-x_{t-s}) / x_{t-s} \times 100\) (the default argument is scale = 100). The user can also request growth rates obtained by log-differencing using \(log(x_t/ x_{t-s}) \times 100\).
# 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 x 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 50.0 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.
# # ... with 5,017 more rows, and 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)]
# 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 x 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
# # ... with 5,017 more rows, and 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)]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 x 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
# # ... with 5,017 more rows, and 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>, G1.OTH <dbl>, L1.G1.OTH <dbl>, L10G1.OTH <dbl>,
# # L1.L10G1.OTH <dbl>, G1.SUM <dbl>, L1.G1.SUM <dbl>, L10G1.SUM <dbl>, L1.L10G1.SUM <dbl>
#
# Grouped by: Variable, Country [85 | 59 (7.7)]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 bechmarked 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.
Bechmarks 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 unordered
#
# 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 unordered
#
# 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) max used (Mb)
# Ncells 1941713 103.7 3719735 198.7 3719735 198.7
# Vcells 19911201 152.0 28373960 216.5 23085355 176.2## 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 cld
# dplyr 3131.771 3480.291 3652.60932 3664.8140 3817.43 4672.666 100 b
# collapse 10.711 16.288 28.84573 27.8905 39.27 90.142 100 a
# 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 cld
# dplyr 2795.300 2821.405 3039.02691 2948.5860 3174.387 3642.725 100 b
# collapse 12.049 15.619 27.15895 29.8985 35.700 109.331 100 a
## Subsetting columns
# Small
microbenchmark(dplyr = filter(GGDC10S, Variable == "VA"),
collapse = fsubset(GGDC10S, Variable == "VA"))
# Unit: microseconds
# expr min lq mean median uq max neval cld
# dplyr 2039.354 2304.426 2502.3374 2420.0045 2618.585 4196.519 100 b
# collapse 157.080 185.863 236.6948 210.8525 288.946 449.818 100 a
# Large
microbenchmark(dplyr = filter(data, Variable == "VA"),
collapse = fsubset(data, Variable == "VA"))
# Unit: milliseconds
# expr min lq mean median uq max neval cld
# dplyr 16.888713 17.218713 20.515368 17.792811 18.9207 57.01804 100 b
# collapse 6.448288 7.821841 8.897339 8.044964 8.6889 42.06024 100 a
## 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 cld
# dplyr 7357.296 7802.874 8374.6212 8376.0805 8695.8175 12976.454 100 b
# collapse 572.090 634.342 738.3358 684.9915 841.4015 1246.372 100 a
# 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 cld
# dplyr 2747.9010 2747.9010 2787.0271 2787.0271 2826.1533 2826.1533 2 b
# collapse 210.9429 210.9429 218.9627 218.9627 226.9824 226.9824 2 a
## 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 cld
# dplyr 2896.151 3045.645 3277.9081 3223.4745 3467.573 4052.827 100 b
# collapse 340.488 357.222 396.2643 393.5915 405.194 640.813 100 a
# 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 cld
# dplyr 70.91956 72.24626 78.50734 75.53265 80.80798 104.8246 10 b
# collapse 65.07817 65.23480 67.36426 67.12243 68.44467 72.2061 10 a
## 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 cld
# dplyr 3038.505 3206.0710 3471.43249 3373.414 3667.046 4836.439 100 b
# collapse 26.775 33.2455 46.61981 40.386 58.459 91.034 100 a
# Large
microbenchmark(dplyr = mutate(data, NEW = AGR+1),
collapse = ftransform(data, NEW = AGR+1))
# Unit: milliseconds
# expr min lq mean median uq max neval cld
# dplyr 3.936803 4.424775 6.327970 6.504293 6.945186 29.73799 100 b
# collapse 1.250388 1.551605 3.521283 3.676417 3.941042 33.47308 100 a
## 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 cld
# dplyr 16467.454 17059.849 17876.7955 17674.333 18234.37 23710.956 100 b
# collapse 697.486 767.324 865.2265 832.253 896.29 1863.533 100 a
# 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 cld
# dplyr 24.329902 25.566010 26.407991 25.744063 28.291248 29.071737 10 b
# collapse 6.918634 7.983828 8.220518 8.270543 8.671497 8.700949 10 a
gc()
# used (Mb) gc trigger (Mb) max used (Mb)
# Ncells 1947525 104.1 3719735 198.7 3719735 198.7
# Vcells 21427698 163.5 57613243 439.6 66848295 510.1## 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) max used (Mb)
# Ncells 1964529 105.0 3719735 198.7 3719735 198.7
# Vcells 20528287 156.7 57613243 439.6 66848295 510.1
## 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) 166.897 170.467 187.0318 172.6985 180.5075 443.571 100
# Large
microbenchmark(GRP(gdata))
# Unit: milliseconds
# expr min lq mean median uq max neval
# GRP(gdata) 31.06691 32.30324 34.0717 33.65069 35.22238 53.05223 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 cld
# dplyr 8360.015 8720.1375 9211.3590 8949.2865 9471.62 17006.522 100 b
# collapse 238.297 251.4615 291.3512 296.7555 302.78 485.519 100 a
# 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 cld
# dplyr 598.74203 603.34954 651.50459 629.12953 700.37954 764.99048 10 b
# collapse 40.13869 41.61845 43.07965 42.87554 44.06523 48.48621 10 a
## 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 cld
# dplyr 11301.238 11792.334 13179.5550 12139.738 12715.845 33178.56 100 b
# collapse 257.485 278.905 317.9387 315.274 324.423 561.38 100 a
# 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 cld
# dplyr 1359.61766 1398.07310 1543.02306 1558.3396 1615.48214 1748.97419 10 b
# collapse 43.21156 43.83541 45.03422 45.0356 46.34869 47.20191 10 a
## Median
# Small
microbenchmark(dplyr = summarise_all(gGGDC10S, median, na.rm = TRUE),
collapse = fmedian(cgGGDC10S))
# Unit: microseconds
# expr min lq mean median uq max neval cld
# dplyr 51165.489 52280.887 55266.225 53735.210 56140.7110 75017.013 100 b
# collapse 490.427 501.583 562.581 559.596 598.6415 811.726 100 a
# 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 cld
# dplyr 9785.20062 9785.20062 10103.21901 10103.21901 10421.23740 10421.23740 2 b
# collapse 92.81429 92.81429 93.39285 93.39285 93.97141 93.97141 2 a
## 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 cld
# dplyr 23908.64 24836.8405 26208.7552 25443.52 26458.06 34351.300 100 b
# collapse 427.06 444.0175 492.6495 484.18 504.93 835.377 100 a
# 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 cld
# dplyr 4195.77894 4195.77894 4259.9021 4259.9021 4324.02534 4324.02534 2 b
# collapse 81.48717 81.48717 82.4263 82.4263 83.36543 83.36543 2 a
## Maximum
# Small
microbenchmark(dplyr = summarise_all(gGGDC10S, max, na.rm = TRUE),
collapse = fmax(cgGGDC10S))
# Unit: microseconds
# expr min lq mean median uq max neval cld
# dplyr 10840.263 11216.674 11663.0739 11411.4615 11730.08 18719.67 100 b
# collapse 183.408 193.672 237.3552 240.7515 244.99 516.31 100 a
# 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 cld
# dplyr 1035.82526 1050.31806 1105.68453 1103.71926 1122.64331 1274.45251 10 b
# collapse 24.29153 24.84398 27.10525 25.21771 26.08901 43.95501 10 a
## 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 cld
# dplyr 10386.876 10866.816 11811.7102 11306.146 11918.6225 19031.597 100 b
# collapse 58.459 68.053 103.2532 119.818 127.6275 225.355 100 a
# Large
microbenchmark(dplyr = summarise_all(gdata, first),
collapse = ffirst(cgdata, na.rm = FALSE), times = 10)
# Unit: milliseconds
# expr min lq mean median uq max neval cld
# dplyr 1153.185432 1326.261042 1445.383896 1471.123943 1596.382711 1633.31243 10 b
# collapse 4.334856 4.570029 5.226371 4.774411 5.898064 6.83697 10 a
## Number of Distinct Values
# Small
microbenchmark(dplyr = summarise_all(gGGDC10S, n_distinct, na.rm = TRUE),
collapse = fNdistinct(cgGGDC10S))
# Unit: milliseconds
# expr min lq mean median uq max neval cld
# dplyr 68.530348 71.181732 75.602871 73.562244 78.482354 100.837385 100 b
# collapse 1.273592 1.339414 1.429775 1.375338 1.509435 2.041586 100 a
# 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 cld
# dplyr 13443.0170 13681.7897 14076.26 13824.7034 14275.9742 15155.8116 5 b
# collapse 312.2297 319.8538 329.89 331.7874 336.9509 348.6283 5 a
gc()
# used (Mb) gc trigger (Mb) max used (Mb)
# Ncells 1967244 105.1 3719735 198.7 3719735 198.7
# Vcells 20534540 156.7 57613243 439.6 66848295 510.1Below 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) 325.761 338.4795 412.8468 352.7595 489.9815 1034.85 100
# Large
microbenchmark(fmean(cgdata, SUM), times = 10)
# Unit: milliseconds
# expr min lq mean median uq max neval
# fmean(cgdata, SUM) 50.16411 55.41065 58.5007 56.05949 62.00754 71.00167 10
## Weighted Standard-Deviation
# Small
microbenchmark(fsd(cgGGDC10S, SUM))
# Unit: microseconds
# expr min lq mean median uq max neval
# fsd(cgGGDC10S, SUM) 438.662 445.3565 472.0684 459.636 462.537 776.472 100
# Large
microbenchmark(fsd(cgdata, SUM), times = 10)
# Unit: milliseconds
# expr min lq mean median uq max neval
# fsd(cgdata, SUM) 78.89134 79.89674 81.15476 81.07149 82.1851 84.39447 10
## Statistical Mode
# Small
microbenchmark(fmode(cgGGDC10S))
# Unit: milliseconds
# expr min lq mean median uq max neval
# fmode(cgGGDC10S) 1.579719 1.60694 1.726731 1.669638 1.818462 2.583332 100
# Large
microbenchmark(fmode(cgdata), times = 10)
# Unit: milliseconds
# expr min lq mean median uq max neval
# fmode(cgdata) 365.3667 366.6117 392.7847 367.7157 409.1356 478.1885 10
## Weighted Statistical Mode
# Small
microbenchmark(fmode(cgGGDC10S, SUM))
# Unit: milliseconds
# expr min lq mean median uq max neval
# fmode(cgGGDC10S, SUM) 1.773391 1.786555 1.88805 1.796819 2.01615 2.640898 100
# Large
microbenchmark(fmode(cgdata, SUM), times = 10)
# Unit: milliseconds
# expr min lq mean median uq max neval
# fmode(cgdata, SUM) 462.4471 464.0897 490.9401 473.4545 493.0575 582.1331 10
gc()
# used (Mb) gc trigger (Mb) max used (Mb)
# Ncells 1966698 105.1 3719735 198.7 3719735 198.7
# Vcells 20531165 156.7 72305010 551.7 72305007 551.7
## 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 cld
# dplyr 8766.994 9157.4615 9959.0079 9663.9530 10041.256 23563.248 100 b
# collapse 292.739 308.3575 350.5506 344.2805 355.437 529.697 100 a
# 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 cld
# dplyr 894.91344 906.01208 977.1793 931.67627 1050.9276 1203.0555 10 b
# collapse 53.80996 73.11912 143.7252 98.83864 247.6076 286.7542 10 a
## 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 cld
# dplyr 9078.475 9545.6970 10122.8167 9842.4525 10250.993 21063.811 100 b
# collapse 550.671 567.8515 616.4342 604.8895 648.399 800.124 100 a
# 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 cld
# dplyr 1167.2784 1535.0749 1500.3219 1560.0606 1586.4171 1623.8426 10 b
# collapse 108.0041 116.8019 133.9792 134.9087 144.0409 167.1521 10 a
## 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 cld
# dplyr 11938.481 12548.055 13547.9553 12717.630 13057.225 48706.66 100 b
# collapse 307.466 324.869 358.0074 362.131 367.485 539.96 100 a
# 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 cld
# dplyr 1999.81570 2716.63145 2655.66077 2749.2832 2777.8018 2875.7636 10 b
# collapse 64.89476 72.39709 91.01573 85.0933 104.5368 137.5435 10 a
## 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 cld
# dplyr 30282.855 31640.57 33557.79 32090.383 33465.497 50177.049 100 b
# collapse 494.444 504.93 556.57 544.423 563.389 969.251 100 a
# 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 cld
# dplyr 5954.8437 5954.8437 6147.7327 6147.7327 6340.6218 6340.6218 2 b
# collapse 106.3566 106.3566 117.1928 117.1928 128.0291 128.0291 2 a
## Lag
# Small
microbenchmark(dplyr_unordered = mutate_all(gGGDC10S, dplyr::lag),
collapse_unordered = flag(cgGGDC10S),
dplyr_ordered = mutate_all(gGGDC10S, dplyr::lag, order_by = "Year"),
collapse_ordered = flag(cgGGDC10S, t = Year))
# Unit: microseconds
# expr min lq mean median uq max neval cld
# dplyr_unordered 45658.786 47217.5305 49220.6008 48137.9180 49601.1660 79676.738 100 b
# collapse_unordered 340.488 402.9625 441.5808 444.2405 463.6520 664.018 100 a
# dplyr_ordered 110042.594 112531.3210 115768.3795 115080.0675 118492.5285 125884.854 100 c
# collapse_ordered 313.266 348.2975 382.0200 377.9730 388.6825 614.037 100 a
# Large
microbenchmark(dplyr_unordered = mutate_all(gdata, dplyr::lag),
collapse_unordered = flag(cgdata),
dplyr_ordered = mutate_all(gdata, dplyr::lag, order_by = "Year"),
collapse_ordered = flag(cgdata, t = Year), times = 2)
# Unit: milliseconds
# expr min lq mean median uq max neval
# dplyr_unordered 8805.61827 8805.61827 9302.45437 9302.45437 9799.29047 9799.29047 2
# collapse_unordered 50.92095 50.92095 60.38029 60.38029 69.83964 69.83964 2
# dplyr_ordered 23585.60849 23585.60849 27063.77245 27063.77245 30541.93641 30541.93641 2
# collapse_ordered 87.31785 87.31785 106.08147 106.08147 124.84510 124.84510 2
# cld
# a
# a
# b
# a
## 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 cld
# dplyr_unordered 59850.819 61307.820 66010.7816 63691.2320 68270.6320 109735.129 100 b
# collapse_unordered 369.493 422.374 485.4648 473.0235 496.8975 1885.399 100 a
# 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 cld
# dplyr_unordered 13885.45342 13885.45342 13896.288 13896.288 13907.12190 13907.12190 2 b
# collapse_unordered 41.58275 41.58275 50.468 50.468 59.35325 59.35325 2 a
gc()
# used (Mb) gc trigger (Mb) max used (Mb)
# Ncells 1969041 105.2 4900332 261.8 4900332 261.8
# Vcells 21580031 164.7 72305010 551.7 72305010 551.7Below 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") 64.03127 89.97258 100.3236 96.14308 104.1361 163.0997 10
# Weighted Centering
microbenchmark(fwithin(cgdata, SUM), times = 10)
# Unit: milliseconds
# expr min lq mean median uq max neval
# fwithin(cgdata, SUM) 60.98429 66.16523 82.76161 86.65271 97.8734 102.3403 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") 64.31062 71.64204 86.91975 86.67837 102.1663 107.515
# 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 = "/") 155.4559 170.5115 187.0186 174.3258 218.5894 237.1676 10
microbenchmark(fscale(cgdata, SUM), times = 10)
# Unit: milliseconds
# expr min lq mean median uq max neval
# fscale(cgdata, SUM) 98.63426 104.9522 150.7063 129.0923 158.1513 289.3277 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) 53.99247 117.4003 175.377 205.8782 236.3777 249.3649 10
# Iterated difference
microbenchmark(fdiff(cgdata, 1, 2), times = 10)
# Unit: milliseconds
# expr min lq mean median uq max neval
# fdiff(cgdata, 1, 2) 59.00473 64.41371 87.73701 93.595 101.7076 110.1796 10
# Growth Rate
microbenchmark(fgrowth(cgdata,1), times = 10)
# Unit: milliseconds
# expr min lq mean median uq max neval
# fgrowth(cgdata, 1) 62.5118 71.22524 89.1899 95.71914 100.5219 106.943 10Timmer, 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.
Row-wise operations are not supported by TRA.↩︎