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 938.46 1022.354 1130.047 1046.898 1097.324 7569.703 100 a
# hybrid 12165.16 12642.649 13353.758 12950.337 13519.303 20939.736 100 b
# dplyr 58681.15 60824.925 63850.124 62604.338 66157.140 81467.906 100 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. To avoid errors with these functions and print.grouped_df, [.grouped_df etc., the classes assigned after fgroup_by are reshuffled, so that the data.frame 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"In general fgroup_by first assigns the class GDP_df which is for printing grouping information, 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. 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). Thus 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)]:
head(fgroup_by(GGDC10S, Variable, Country))
# # 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 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
# # ... with 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.
#
# Grouped by: Variable, Country [85 | 59 (7.7)]
# 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>
#
# Grouped by: Variable, Country [85 | 59 (7.7)]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.
#
# Grouped by: Variable, Country [85 | 59 (7.7)]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>
#
# Grouped by: Variable, Country [85 | 59 (7.7)]
# 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>
#
# Grouped by: Variable, Country [85 | 59 (7.7)]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>
#
# Grouped by: Variable, Country [85 | 59 (7.7)]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>
#
# Grouped by: Variable, Country [85 | 59 (7.7)]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.
#
# Grouped by: Variable, Country [85 | 59 (7.7)]
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.
#
# Grouped by: Variable, Country [85 | 59 (7.7)]
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.
#
# Grouped by: Variable, Country [85 | 59 (7.7)]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 2.16e7
#
# Grouped by: Variable, Country [85 | 59 (7.7)]This 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 NA
#
# Grouped by: Variable, Country [85 | 59 (7.7)]Another 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 1940236 103.7 3717688 198.6 3717688 198.6
# Vcells 19908690 151.9 28370344 216.5 23082844 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 3061.707 3229.942 3340.91978 3326.7780 3465.7845 4142.519 100 b
# collapse 11.603 15.619 25.36942 23.8745 35.0305 56.227 100 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 2771.646 2847.285 3072.8900 3107.224 3194.9120 4258.99 100 b
# collapse 12.495 16.288 26.0611 28.783 34.3615 60.69 100 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 2046.047 2199.110 2389.479 2373.5925 2531.3415 2953.268 100 b
# collapse 173.144 197.688 241.938 218.8845 292.0695 382.881 100 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 16.687886 16.824215 19.049358 17.017886 17.842553 47.73067 100 b
# collapse 6.478627 7.755342 8.712829 7.850393 8.254694 46.17416 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 7402.806 7586.8840 8268.6522 8225.6870 8571.530 12362.405 100 b
# collapse 563.165 637.6885 742.6505 701.0555 845.194 1074.565 100 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 2385.8920 2385.8920 2400.7634 2400.7634 2415.6348 2415.6348 2 b
# collapse 178.9655 178.9655 191.7726 191.7726 204.5797 204.5797 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 2951.930 3089.3745 3234.075 3220.126 3343.959 3789.091 100 b
# collapse 354.322 372.1715 400.887 396.492 416.349 502.475 100 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 68.24201 69.36343 75.40416 73.60413 76.35837 101.41563 10 b
# collapse 64.51629 64.94290 67.42560 66.49741 69.54639 72.26315 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 3038.949 3177.285 3314.79642 3244.668 3424.283 4187.144 100 b
# collapse 28.113 33.915 46.62425 40.609 59.351 91.481 100 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 3.908239 4.282418 6.051429 6.376659 6.592421 26.69856 100 b
# collapse 1.265113 1.526390 3.426617 3.652093 3.759861 33.76178 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 15968.534 16537.947 17243.7636 16887.136 17721.3960 22449.839 100 b
# collapse 711.766 788.074 836.2107 835.822 863.9365 1039.311 100 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 23.080387 23.429353 24.995460 23.817811 28.121649 28.246153 10 b
# collapse 6.872664 7.004753 7.956109 8.225465 8.684431 9.260536 10 a
gc()
# used (Mb) gc trigger (Mb) max used (Mb)
# Ncells 1946045 104.0 3717688 198.6 3717688 198.6
# Vcells 21425190 163.5 57610832 439.6 66845873 510.0## 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 1963051 104.9 3717688 198.6 3717688 198.6
# Vcells 20525803 156.6 57610832 439.6 66845873 510.0
## 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) 166.897 169.128 174.2155 170.021 172.475 260.609 100
# Large
microbenchmark(GRP(gdata))
# Unit: milliseconds
# expr min lq mean median uq max neval
# GRP(gdata) 30.59297 32.09169 33.24536 32.70618 34.7076 37.20012 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 8332.340 8654.086 9140.232 8870.069 9343.3150 16933.768 100 b
# collapse 240.082 266.187 295.635 301.441 309.2495 409.656 100 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 554.04039 558.6305 572.88754 572.61591 577.02841 616.51064 10 b
# collapse 39.87983 40.1632 42.23696 42.53389 43.58458 44.49181 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 11151.289 11524.352 12388.270 11807.719 12031.959 31118.65 100 b
# collapse 260.609 274.442 304.975 316.167 323.753 405.64 100 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 1297.2944 1438.65988 1518.14667 1520.49527 1656.09684 1702.34151 10 b
# collapse 43.1959 43.56049 44.67526 44.88919 45.46507 46.20808 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 49193.474 50737.4920 53360.0773 51968.2435 53670.2325 76091.065 100 b
# collapse 491.319 505.1525 558.5509 557.5865 586.8155 759.514 100 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 9448.74285 9448.74285 9555.37111 9555.37111 9661.99936 9661.99936 2 b
# collapse 87.67387 87.67387 88.16765 88.16765 88.66142 88.66142 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 23062.091 23747.5280 25054.2217 24247.549 25451.3025 32090.132 100 b
# collapse 428.844 440.0005 473.3309 485.518 489.0875 622.962 100 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 4005.86147 4005.86147 4090.09343 4090.09343 4174.3254 4174.3254 2 b
# collapse 80.23403 80.23403 80.94357 80.94357 81.6531 81.6531 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 10950.923 11278.469 11854.4592 11534.6155 12198.4095 20697.869 100 b
# collapse 183.408 213.753 243.8971 245.4365 251.9075 600.204 100 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 1043.28961 1053.34804 1081.87716 1061.95773 1087.9202 1238.50209 10 b
# collapse 24.16298 24.23438 24.95289 24.97449 25.1657 27.24656 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 10229.340 10669.118 11194.4586 10828.206 11343.1755 18912.431 100 b
# collapse 59.797 79.209 105.7833 97.951 128.7425 193.672 100 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 1148.937016 1243.711587 1329.5020 1346.93653 1390.871643 1528.336071 10 b
# collapse 4.257652 4.352256 4.4457 4.38684 4.513351 4.694974 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 65.389148 67.188865 71.079318 68.63940 71.151994 219.626696 100 b
# collapse 1.246817 1.292334 1.370013 1.33272 1.417061 1.988927 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 12713.3442 13077.167 13102.5746 13167.2314 13199.612 13355.5185 5 b
# collapse 305.4437 307.343 313.8839 308.1359 316.446 332.0508 5 a
gc()
# used (Mb) gc trigger (Mb) max used (Mb)
# Ncells 1965766 105.0 3717688 198.6 3717688 198.6
# Vcells 20532054 156.7 57610832 439.6 66845873 510.0Below 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) 288.276 325.761 336.1944 344.727 347.627 432.415 100
# Large
microbenchmark(fmean(cgdata, SUM), times = 10)
# Unit: milliseconds
# expr min lq mean median uq max neval
# fmean(cgdata, SUM) 48.38978 49.62633 50.98619 50.54627 52.10435 55.63328 10
## Weighted Standard-Deviation
# Small
microbenchmark(fsd(cgGGDC10S, SUM))
# Unit: microseconds
# expr min lq mean median uq max neval
# fsd(cgGGDC10S, SUM) 440.001 447.587 461.4876 460.9745 462.9825 585.031 100
# Large
microbenchmark(fsd(cgdata, SUM), times = 10)
# Unit: milliseconds
# expr min lq mean median uq max neval
# fsd(cgdata, SUM) 77.75602 78.2451 79.50143 79.19427 80.87663 81.94852 10
## Statistical Mode
# Small
microbenchmark(fmode(cgGGDC10S))
# Unit: milliseconds
# expr min lq mean median uq max neval
# fmode(cgGGDC10S) 2.094242 2.109414 2.186535 2.123247 2.215844 2.797529 100
# Large
microbenchmark(fmode(cgdata), times = 10)
# Unit: milliseconds
# expr min lq mean median uq max neval
# fmode(cgdata) 458.2787 464.5704 500.8933 493.9852 531.8195 569.1526 10
## Weighted Statistical Mode
# Small
microbenchmark(fmode(cgGGDC10S, SUM))
# Unit: milliseconds
# expr min lq mean median uq max neval
# fmode(cgGGDC10S, SUM) 1.764465 1.785215 1.937573 1.849028 2.015925 3.221464 100
# Large
microbenchmark(fmode(cgdata, SUM), times = 10)
# Unit: milliseconds
# expr min lq mean median uq max neval
# fmode(cgdata, SUM) 424.7289 450.3931 463.624 459.4651 465.009 527.9559 10
gc()
# used (Mb) gc trigger (Mb) max used (Mb)
# Ncells 1965220 105.0 3717688 198.6 3717688 198.6
# Vcells 20528687 156.7 72302159 551.7 72302156 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 8737.087 9149.867 9878.1031 9567.778 9981.896 22892.517 100 b
# collapse 296.755 341.603 362.2688 356.775 373.287 514.524 100 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 865.10150 908.00154 990.0571 955.10077 1070.63078 1210.0101 10 b
# collapse 52.86966 55.18569 108.0811 65.81353 83.25022 296.2899 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 9015.546 9481.429 10103.7975 9736.9060 10344.695 22450.731 100 b
# collapse 556.918 584.585 621.4183 612.6985 649.291 778.702 100 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 1096.4123 1297.9954 1425.3915 1494.1336 1549.1326 1562.5218 10 b
# collapse 102.6977 104.9513 119.0727 115.3647 136.1957 144.4036 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 12090.640 12434.6970 13523.1362 12739.038 13131.960 46424.51 100 b
# collapse 320.406 347.1815 371.0375 370.609 383.104 593.51 100 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 1958.9166 2646.70064 2589.65285 2668.9113 2728.9593 2767.7784 10 b
# collapse 63.8188 74.85987 87.06073 80.4431 97.5895 129.7327 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 29549.196 30809.177 34210.6659 31922.120 34752.223 60542.004 100 b
# collapse 498.012 528.804 582.1931 553.124 596.634 896.958 100 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 6215.2593 6215.2593 6445.2813 6445.2813 6675.3033 6675.3033 2 b
# collapse 103.7727 103.7727 107.9616 107.9616 112.1506 112.1506 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 43906.329 45347.4865 46894.3694 46259.1710 47563.7770 59132.307 100 b
# collapse_unordered 338.702 403.6315 435.3017 443.3475 469.4525 630.994 100 a
# dplyr_ordered 107641.683 112130.4900 114552.2151 114408.5860 116274.5715 136275.178 100 c
# collapse_ordered 312.820 349.4125 373.1706 373.7330 387.5660 641.705 100 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 8486.05989 8486.05989 8627.22839 8627.22839 8768.39690 8768.39690 2
# collapse_unordered 28.62323 28.62323 34.22855 34.22855 39.83387 39.83387 2
# dplyr_ordered 21386.81079 21386.81079 21700.49069 21700.49069 22014.17060 22014.17060 2
# collapse_ordered 65.01832 65.01832 76.41236 76.41236 87.80641 87.80641 2
# cld
# b
# a
# c
# 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 57758.310 59035.917 61826.3411 60604.7015 62783.730 99087.557 100 b
# collapse_unordered 376.187 402.962 461.1171 473.4695 495.558 631.887 100 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
# dplyr_unordered 11651.41704 11651.41704 11826.30738 11826.30738 12001.19773 12001.19773 2
# collapse_unordered 29.34303 29.34303 46.95733 46.95733 64.57162 64.57162 2
# cld
# b
# a
gc()
# used (Mb) gc trigger (Mb) max used (Mb)
# Ncells 1967585 105.1 4756390 254.1 4756390 254.1
# Vcells 21577603 164.7 72302159 551.7 72302159 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") 61.23413 66.18972 89.89963 96.50244 101.4866 117.7398 10
# Weighted Centering
microbenchmark(fwithin(cgdata, SUM), times = 10)
# Unit: milliseconds
# expr min lq mean median uq max neval
# fwithin(cgdata, SUM) 66.09958 71.73078 87.59395 84.45821 106.51 111.4044 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") 61.82943 65.92108 80.93767 83.51217 94.47782 100.267
# 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 = "/") 132.0657 132.5013 159.288 160.8864 168.5987 204.8095 10
microbenchmark(fscale(cgdata, SUM), times = 10)
# Unit: milliseconds
# expr min lq mean median uq max neval
# fscale(cgdata, SUM) 92.93291 96.53502 114.9687 112.6562 126.1337 158.3511 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) 46.03493 82.18324 117.1779 108.0114 141.2433 214.1945 10
# Iterated difference
microbenchmark(fdiff(cgdata, 1, 2), times = 10)
# Unit: milliseconds
# expr min lq mean median uq max neval
# fdiff(cgdata, 1, 2) 59.08768 76.45476 97.38677 106.7711 114.4867 122.7601 10
# Growth Rate
microbenchmark(fgrowth(cgdata,1), times = 10)
# Unit: milliseconds
# expr min lq mean median uq max neval
# fgrowth(cgdata, 1) 65.57345 70.42996 100.6642 94.74601 97.94427 228.3125 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.↩︎