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Type:	Package
Title:	A Basic Set of Functions for Compositional Data Analysis
Version:	1.0.3
Date:	2025-07-02
Description:	A minimum set of functions to perform compositional data analysis using the log-ratio approach introduced by John Aitchison (1982). Main functions have been implemented in c++ for better performance.
URL:	https://mcomas.net/coda.base/,https://github.com/mcomas/coda.base
Depends:	R (≥ 3.5)
Imports:	Rcpp (≥ 0.12.12), stats, Matrix
LinkingTo:	Rcpp, RcppArmadillo
License:	GPL-2 |GPL-3 [expanded from: GPL]
Encoding:	UTF-8
LazyData:	true
NeedsCompilation:	yes
RoxygenNote:	7.3.2
Suggests:	knitr, rmarkdown, testthat (≥ 2.1.0), ggplot2, jsonlite
VignetteBuilder:	knitr
Packaged:	2025-07-02 20:50:41 UTC; marc
Author:	Marc Comas-Cufí [aut, cre]
Maintainer:	Marc Comas-Cufí <mcomas@imae.udg.edu>
Repository:	CRAN
Date/Publication:	2025-07-02 22:10:09 UTC

coda.base

Description

A minimum set of functions to perform compositional data analysisusing the log-ratio approach introduced by John Aitchison (1982)<https://www.jstor.org/stable/2345821>. Main functionshave been implemented in c++ for better performance.

Author(s)

Marc Comas-Cufí

See Also

Useful links:

• https://mcomas.net/coda.base/

• https://github.com/mcomas/coda.base

Food consumption in European countries

Description

The alimentation data set contains the percentages of consumption of severaltypes of food in 25 European countries during the 80s. The categories are:* RM: red meat (pork, veal, beef),* WM: white meat (chicken),* E: eggs,* M: milk,* F: fish,* C: cereals,* S: starch (potatoes),* N: nuts, and* FV: fruits and vegetables.

Usage

alimentation

Format

An object of classdata.frame with 25 rows and 13 columns.

Details

Moreover, the dataset contains a categorical variable thatshows if the country is from the North or a Southern Mediterranean country. Inaddition, the countries are classified as Eastern European or as Western European.

Additive log-ratio basis

Description

Compute the transformation matrix to express a composition using the oblique additive log-ratiocoordinates.

Usage

alr_basis(dim, denominator = NULL, numerator = NULL)

Arguments

Value

matrix

References

Aitchison, J. (1986)The Statistical Analysis of Compositional Data.Monographs on Statistics and Applied Probability. Chapman & Hall Ltd., London (UK). 416p.

Examples

alr_basis(5)# Third part is used as denominatoralr_basis(5, 3)# Third part is used as denominator, and# other parts are rearrangedalr_basis(5, 3, c(1,5,2,4))

Arctic lake sediments at different depths

Description

The arctic lake data set records the [sand, silt, clay] compositions of 39 sediment

Usage

arctic_lake

Format

An object of classdata.frame with 39 rows and 5 columns.

The MN blood system

Description

In humans the main blood group systems are the ABO system, the Rh system andthe MN system. The MN blood system is a system of blood antigens also relatedto proteins of the red blood cell plasma membrane. The inheritance pattern of theMN blood system is autosomal with codominance, a type of lack of dominance inwhich the heterozygous manifests a phenotype totally distinct from the homozygous.The possible phenotypical forms are three blood types: type M blood, typeN blood and type MN blood. The frequencies of M, N and MN blood types varywidely depending on the ethnic population. However, the Hardy-Weinbergprinciple states that allele and genotype frequencies in a population willremain constant from generation to generation in the absence of otherevolutionary influences. This implies that, in the long run, it holds that

\frac{x_{MM}x_{NN}}{x_{MN}} = \frac{1}{4}

where xM M and xN N are the genotype relative frequencies of MM and NNhomozygotes, respectively, and xM N is the genotype relative frequencyof MN heterozygotes. This principle was named after G.H. Hardy and W.Weinberg demonstrated it mathematically.

Usage

blood_mn

Format

An object of classdata.frame with 49 rows and 5 columns.

Physical activity and body mass index

Description

The 'bmi_activity' data set records the proportion of daily time spent to sleep(sleep), sedentary behaviour (sedent), light physical activity (Lpa), moderatephysical activity (Mpa) and vigorous physical activity (Vpa) measured on a smallpopulation of 393 children. Moreover the standardized body mass index (zBMI) ofeach child was also registered.

This data set was used in the example of the article (Dumuid et al. 2019) to examine theexpected differences in zBMI for reallocations of daily time between sleep, physicalactivity and sedentary behaviour. Because the original data is confidential, thedata set BMIPhisActi includes simulated data that mimics the main features of theoriginal data.

Usage

bmi_activity

Format

An object of classdata.frame with 393 rows and 8 columns.

References

D. Dumuid, Z. Pedisic, T.E. Stanford, J.A. Martín-Fernández, K. Hron, C.Maher, L.K. Lewis and T.S. Olds,The Compositional Isotemporal Sub-stitution Model: a Method for Estimating Changes in a Health Outcomefor Reallocation of Time between Sleep, Sedentary Behaviour, and PhysicalActivity. Statistical Methods in Medical Research28(3) (2019), 846–857

Isometric Log-Ratio Basis Based on Canonical Correlations

Description

Constructs an isometric log-ratio (ilr) basis for a compositional dataset,optimized with respect to canonical correlations with an explanatory dataset.

Usage

cc_basis(Y, X)

Arguments

Value

A matrix representing the isometric log-ratio basis.

CoDaPack's default binary partition

Description

Compute the default binary partition used in CoDaPack's software

Usage

cdp_partition(ncomp)

Arguments

Value

matrix

Examples

cdp_partition(4)

Dataset center

Description

Generic function to calculate the center of a compositional dataset

Usage

center(X, zero.rm = FALSE, na.rm = FALSE)

Arguments

Examples

X = matrix(exp(rnorm(5*100)), nrow=100, ncol=5)g = rep(c('a','b','c','d'), 25)center(X)(by_g <- by(X, g, center))center(t(simplify2array(by_g)))

Centered log-ratio basis

Description

Compute the transformation matrix to express a composition usingthe linearly dependant centered log-ratio coordinates.

Usage

clr_basis(dim)

Arguments

Value

matrix

References

Aitchison, J. (1986)The Statistical Analysis of Compositional Data.Monographs on Statistics and Applied Probability. Chapman & Hall Ltd., London (UK). 416p.

Examples

(B <- clr_basis(5))# CLR coordinates are linearly dependant coordinates.(clr_coordinates <- coordinates(c(1,2,3,4,5), B))# The sum of all coordinates equal to zerosum(clr_coordinates) < 1e-15

Replacement of Missing Values and Below-Detection Zeros in Compositional Data

Description

Performs imputation (replacement) of missing values and/or values below the detection limit (BDL) in compositional datasets using the EM-algorithm assuming normality on the Simplex.This function is designed to prepare compositional data for subsequent log-ratio transformations.

Usage

coda_replacement(  X,  DL = NULL,  dl_prop = 0.65,  eps = 1e-04,  parameters = FALSE,  debug = FALSE)

Arguments

Details

- Missing values are imputed based on a multivariate normal model on the simplex.- Zeros are treated as censored values and replaced accordingly.- The EM algorithm iteratively estimates the missing parts and model parameters.- To initialize the EM algorithm, zero values (considered below the detection limit) are replaced with a small positive value. Specifically, each zero is replaced bydl_prop times the detection limit of that part (column). This restrictions is imposed in the geometric mean of the parts with zeros against the non-missing positive values, helping to preserve the compositional structure in the simplex.

Value

Ifparameters = FALSE, returns a numeric matrix with imputed values.Ifparameters = TRUE, returns a list with two components:

X_imp

The imputed compositional data matrix.

info

A list containing information about the EM algorithm parameters and convergence diagnostics.

Examples

# Simulate compositional data with zerosset.seed(123)X <- abs(matrix(rnorm(100), ncol = 5))X[sample(length(X), 10)] <- 0  # Introduce some zerosX[sample(length(X), 10)] <- NA  # Introduce some NAs# Apply replacementsummary(X/rowSums(X, na.rm=TRUE))summary(coda_replacement(X))

Get composition from coordinates w.r.t. an specific basis

Description

Calculate a composition from coordinates with respect a given basis

Usage

composition(H, basis = "ilr")comp(H, basis = "ilr")

Arguments

Value

coordinates with respect the given basis

See Also

See functionsilr_basis,alr_basis,clr_basis,sbp_basisto define different compositional basis.See functioncoordinates to obtain details on how to calculatecoordinates of a given composition.

Get coordinates from compositions w.r.t. an specific basis

Description

Calculate the coordinates of a composition with respect a given basis

Usage

coordinates(X, basis = "ilr")coord(..., basis = "ilr")alr_c(X)clr_c(X)ilr_c(X)olr_c(X)

Arguments

Details

coordinates function calculates the coordinates of a compositiona w.r.t. a given basis. 'basis' parameter isused to set the basis, it can be either a matrix defining the log-contrasts in columns or a string defining some well-knownlog-contrast: 'alr' 'clr', 'ilr', 'pw', 'pc', 'pb' and 'cdp', for the additive log-ratio, centered log-ratio, isometric log-ratio,pairwise log-ratio, clr principal components, clr principal balances or default's CoDaPack balances respectively.

Value

Coordinates of compositionX with respect the givenbasis.

See Also

See functionsilr_basis,alr_basis,clr_basis,sbp_basisto define different compositional basis.See functioncomposition to obtain details on how to calculatea compositions from given coordinates.

Examples

# Default ilr given by ilr_basis(5) is givencoordinates(1:5)B = ilr_basis(5)coordinates(1:5, B)

Distance Matrix Computation (including Aitchison distance)

Description

This function overwritesdist function to contain Aitchison distance betweencompositions.

Usage

dist(x, method = "euclidean", ...)

Arguments

Value

dist returns an object of class "dist".

See Also

See functionsdist.

Examples

X = exp(matrix(rnorm(10*50), ncol=50, nrow=10))(d <- dist(X, method = 'aitchison'))plot(hclust(d))# In contrast to Euclidean distancedist(rbind(c(1,1,1), c(100, 100, 100)), method = 'euc') # method = 'euclidean'# using Aitchison distance, only relative information is of importancedist(rbind(c(1,1,1), c(100, 100, 100)), method = 'ait') # method = 'aitchison'

Employment distribution in EUROSTAT countries

Description

According to the three–sector theory, as a country’s economy develops, employmentshifts from the primary sector (raw material extraction: farming, hunting, fishing,mining) to the secondary sector (industry, energy and construction) and finally tothe tertiary sector (services). Thus, a country’s employment distribution can beused as a predictor of economic wealth.

The 'eurostat_employment' data set contains EUROSTAT data on employmentaggregated for both sexes, and all ages distributed by economic activity(classification 1983-2008, NACE Rev. 1.1) in 2008 for the 29 EUROSTAT membercountries, thus reflecting reality just before the 2008 financial crisis.Country codes in alphabetical order according to the country name in itsown language are: Belgium (BE), Cyprus (CY), Czechia (CZ), Denmark (DK),Deutchland–Germany (DE), Eesti–Estonia (EE), Eire–Ireland (IE),España–Spain (ES), France (FR), Hellas-Greece (GR), Hrvatska–Croatia (HR),Iceland (IS), Italy (IT), Latvia (LV), Lithuania (LT), Luxembourg (LU),Macedonia (MK), Magyarország-Hungary (HU), Malta (MT), Netherlands (NL),Norway (NO), Österreich–Austria (AT), Portugal (PT), Romania (RO),Slovakia (SK), Suomi–Finland (FI), Switzerland (CH), Turkey (TR),United Kingdom (GB).

A key related variable is the logarithm of gross domestic product per person inEUR at current prices (“logGDP”). For the purposes of exploratory data analysesit has also been categorised as a binary variable indicating values higher or lowerthan the median (“Binary GDP”). The employment composition (D = 11) is:

* Primary sector (agriculture, hunting, forestry, fishing, mining, quarrying)* Manufacturing* Energy (electricity, gas and water supply)* Construction* Trade repair transport (wholesale and retail trade, repair, transport,storage, communications)* Hotels restaurants* Financial intermediation* Real estate (real estate, renting and business activities)* Educ admin defense soc sec (education, public administration, defence,social security)* Health social work* Other services (other community, social and personal service activities)

Usage

eurostat_employment

Format

An object of classdata.frame with 29 rows and 17 columns.

Paleocological compositions

Description

The foraminiferal data set (Aitchison, 1986) is a typical example ofpaleocological data. It contains compositions of 4 different fossils(Neogloboquadrina atlantica, Neogloboquadrina pachyderma, Globorotaliaobesa, and Globigerinoides triloba) at 30 different depths. Due to therounded zeros present in the data set we will apply some zero replacementtechniques to impute these values in advance. After data preprocessing,the analysis that should be undertaken is the association betweenthe composition and the depth.

Usage

foraminiferals

Format

An object of classdata.frame with 30 rows and 5 columns.

Geometric Mean

Description

Generic function for the (trimmed) geometric mean.

Usage

gmean(x, zero.rm = FALSE, trim = 0, na.rm = FALSE)

Arguments

See Also

center

Household expenditures

Description

From Eurostat (the European Union’s statistical information service) thehouseexpend data set records the composition on proportions of meanconsumption expenditure of households expenditures on 12 domestic yearcosts in 27 states of the European Union. Some values in the data set arerounded zeros. In addition the data set contains the gross domesticproduct (GDP05) and (GDP14) in years 2005 and 2014, respectively. Aninteresting analysis is the potential association between expenditurescompositions and GDP. Once a linear regression model is established,predictions can be provided.

Usage

house_expend

Format

An object of classdata.frame with 27 rows and 15 columns.

Household budget patterns

Description

In a sample survey of single persons living alone in rented accommodation, twentymen and twenty women were randomly selected and asked to record over a period ofone month their expenditures on the following four mutually exclusive andexhaustive commodity groups:* Hous: Housing, including fuel and light.* Food: Foodstuffs, including alcohol and tobacco.* Serv: Services, including transport and vehicles.* Other: Other goods, including clothing, footwear and durable goods.

Usage

household_budget

Format

An object of classdata.frame with 40 rows and 6 columns.

Isometric/Orthonormal Log-Ratio Basis for Log-Transformed Compositions

Description

Builds an isometric log-ratio (ilr) basis for a composition withk+1 parts, also called orthonormal log-ratio (olr) basis.

Usage

ilr_basis(dim, type = "default")olr_basis(dim, type = "default")

Arguments

Details

The basis vectors are constructed as:

h_i = \sqrt{\frac{i}{i+1}} \log\frac{\sqrt[i]{\prod_{j=1}^i x_j}}{x_{i+1}}

fori = 1, \ldots, k.

Setting thetype parameter to"pivot" (pivot balances) or"cdp" (codapack balances) allows generating alternative ilr/olr bases.

Value

A matrix representing the orthonormal basis.

References

Egozcue, J.J., Pawlowsky-Glahn, V., Mateu-Figueras, G., & Barceló-Vidal, C. (2003).Isometric logratio transformations for compositional data analysis.Mathematical Geology,35(3), 279–300.

Examples

ilr_basis(5)ilr_basis(alimentation[,1:9])

Chemical Composition of Volcanic Rocks from Kilauea Iki

Description

This dataset contains the chemical composition of volcanic rocks sampled from the lava lake at Kilauea Iki (Hawaii). The data represents major oxide concentrations in fractional form.

Usage

kilauea_iki

Format

A data frame with 17 observations and 11 variables:

SiO2

Silicon dioxide (fraction)

TiO2

Titanium dioxide (fraction)

Al2O3

Aluminium oxide (fraction)

Fe2O3

Ferric oxide (fraction)

FeO

Ferrous oxide (fraction)

MnO

Manganese oxide (fraction)

MgO

Magnesium oxide (fraction)

CaO

Calcium oxide (fraction)

Na2O

Sodium oxide (fraction)

K2O

Potassium oxide (fraction)

P2O5

Phosphorus pentoxide (fraction)

Details

The variability in the oxide concentrations is attributed to magnesic olivine fractionation, starting from a single magmatic mass as suggested by Richter & Moore (1966).

Source

Richter, D.H., & Moore, J.G. (1966). Petrology of Kilauea Iki lava lake, Hawaii. *Geological Survey Professional Paper* 537-B.

Mammal’s milk

Description

The mammalsmilk data set contains the percentages of five constituents (W: water,P: protein, F: fat, L: lactose, and A: ash) of the milk of 24 mammals. The data aretaken from [Har75].

Usage

mammals_milk

Format

An object of classdata.frame with 24 rows and 6 columns.

Milk composition study

Description

In an attempt to improve the quality of cow milk, milk from each of thirty cowswas assessed by dietary composition before and after a strictly controlled dietaryand hormonal regime over a period of eight weeks. Although seasonal variations inmilk quality might have been regarded as negligible over this period, it was decidedto have a control group of thirty cows kept under the same conditions but on aregular established regime. The sixty cows were of course allocated to control andtreatment groups at random. The 'milk_cows' data set provides the complete set ofbefore and after milk compositions for the sixty cows, showing the protein (pr),milk fat (mf), carbohydrate (ch), calcium (Ca), sodium (Na) and potassium (K)proportions by weight of total dietary content.

Usage

milk_cows

Format

An object of classtbl_df (inherits fromtbl,data.frame) with 116 rows and 10 columns.

Concentration of minor elements in carbon ashes

Description

The montana data set consists of 229 samples of the concentration (in ppm) ofminor elements [Cr, Cu, Hg, U, V] in carbon ashes from the Fort Unionformation (Montana, USA), side of the Powder River Basin. The formation ismostly Palaeocene in age, and the coal is the result of deposition inconditions ranging from fluvial to lacustrine. All samples were taken fromthe same seam at different sites over an area of 430 km by 300 km, whichimplies that on average, the sampling spacing is 24 km. Using the spatialcoordinates of the data, a semivariogram analysis was conducted for eachchemical element in order to check for a potential spatial dependencestructure in the data (not shown here). No spatial dependence patternswere observed for any component, which allowed us to assume an independenceof the chemical samples at different locations.

The aforementioned chemical components actually represent a fully observedsubcomposition of a much larger chemical composition. The five elements arenot closed to a constant sum. Note that, as the samples are expressed inparts per million and all concentrations were originally measured, a residualelement could be defined to fill up the gap to 10^6.

Usage

montana

Format

An object of classdata.frame with 229 rows and 6 columns.

Pairwise log-ratio generator system

Description

The function returns all combinations of pairs of log-ratios.

Usage

pairwise_basis(dim)

Arguments

Value

matrix

Results of catalan parliament elections in 2017 by regions.

Description

Results of catalan parliament elections in 2017 by regions.

Usage

parliament2017

Format

A data frame with 42 rows and 9 variables:

com

Region

cs

Votes to Ciutadans party

jxcat

Votes to Junts per Catalunya party

erc

Votes to Esquerra republicana de Catalunya party

psc

Votes to Partit socialista de Catalunya party

catsp

Votes to Catalunya si que es pot party

cup

Votes to Candidatura d'unitat popular party

pp

Votes to Partit popular party

other

Votes to other parties

Source

https://www.idescat.cat/tema/elecc

Isometric log-ratio basis based on Principal Balances.

Description

Exact method to calculate the principal balances of a compositional dataset. Different methods to approximate the principal balances of a compositional dataset are also included.

Usage

pb_basis(  X,  method,  constrained.criterion = "variance",  cluster.method = "ward.D2",  ordering = TRUE,  ...)

Arguments

Value

matrix

References

Martín-Fernández, J.A., Pawlowsky-Glahn, V., Egozcue, J.J., Tolosana-Delgado R. (2018).Advances in Principal Balances for Compositional Data.Mathematical Geosciencies, 50, 273-298.

Examples

set.seed(1)X = matrix(exp(rnorm(5*100)), nrow=100, ncol=5)# Optimal variance obtained with Principal components(v1 <- apply(coordinates(X, 'pc'), 2, var))# Optimal variance obtained with Principal balances(v2 <- apply(coordinates(X,pb_basis(X, method='exact')), 2, var))# Solution obtained using constrained method(v3 <- apply(coordinates(X,pb_basis(X, method='constrained')), 2, var))# Solution obtained using Ward method(v4 <- apply(coordinates(X,pb_basis(X, method='cluster')), 2, var))# Plotting the variancesbarplot(rbind(v1,v2,v3,v4), beside = TRUE, ylim = c(0,2),        legend = c('Principal Components','PB (Exact method)',                   'PB (Constrained)','PB (Ward approximation)'),        names = paste0('Comp.', 1:4), args.legend = list(cex = 0.8), ylab = 'Variance')

Isometric log-ratio basis based on Principal Components.

Description

Different approximations to approximate the principal balances of a compositional dataset.

Usage

pc_basis(X)

Arguments

Value

matrix

Calc-alkaline and tholeiitic volcanic rocks

Description

This petrafm data set is formed by 100 classified volcanic rock samples fromOntario (Canada). The three parts are:

[A: {Na}_2 O + K_2 O; F: Fe O + 0.8998 Fe_2 O_3 ; M: Mg O]

Rocks from the calc-alkaline magma series (25) can be well distinguished fromsamples from the tholeiitic magma series (75) on an AFM diagram.

Usage

petrafm

Format

An object of classdata.frame with 100 rows and 4 columns.

Plot a balance

Description

Plot a balance

Usage

plot_balance(B, data = NULL, main = "Balance dendrogram", ...)

Arguments

Value

Balance plot

Pollen composition in fossils

Description

The pollen data set is formed by 30 fossil pollen samples from three differentlocations (recorded in variable group) . The samples were analysed and the 3-partcomposition [pinus, abies, quercus] was measured.

Usage

pollen

Format

An object of classdata.frame with 30 rows and 4 columns.

Chemical compositions of Romano-British pottery

Description

The pottery data set consists of data pertaining to the chemical composition of 45specimens of Romano-British pottery. The method used to generate these data isatomic absorption spectophotometry, and readings for nine oxides(Al2O3, Fe2O3, MgO, CaO, Na2O, K2O, TiO2 , MnO, BaO) are provided. These samples comefrom five different kiln sites.

Usage

pottery

Format

An object of classdata.frame with 45 rows and 11 columns.

Import data from a codapack workspace

Description

Import data from a codapack workspace

Usage

read_cdp(fname)

Arguments

Isometric log-ratio basis based on Balances

Description

Build anilr_basis using a sequential binary partition ora generic coordinate system based on balances.

Usage

sbp_basis(sbp, data = NULL, fill = FALSE, silent = FALSE)

Arguments

Value

matrix

Examples

X = data.frame(a=1:2, b=2:3, c=4:5, d=5:6, e=10:11, f=100:101, g=1:2)sbp_basis(list(b1 = a~b+c+d+e+f+g,               b2 = b~c+d+e+f+g,               b3 = c~d+e+f+g,               b4 = d~e+f+g,               b5 = e~f+g,               b6 = f~g), data = X)sbp_basis(list(b1 = a~b,               b2 = b1~c,               b3 = b2~d,               b4 = b3~e,               b5 = b4~f,               b6 = b5~g), data = X)# A non-orthogonal basis can also be calculated.sbp_basis(list(b1 = a+b+c~e+f+g,              b2 = d~a+b+c,              b3 = d~e+g,              b4 = a~e+b,              b5 = b~f,              b6 = c~g), data = X)

Serum proteins

Description

The 'serprot' data set records the percentages of the four serum proteinsfrom the blood samples of 30 patients. Fourteen patients have onedisease (1) and sixteen are known to have another different disease (2).The 4-compositions are formed by the proteins [albumin, pre-albumin,globulin A, globulin B].

Usage

serprot

Format

An object of classdata.frame with 36 rows and 7 columns.

A statistician’s time budget

Description

Time budgets –how a day or a period of work is divided up into differentactivities have become a popular source of data in psychology andsociology. To illustrate such problems we consider six daily activitiesundertaken by an academic statistician: teaching (T); consultation (C);administration (A); research (R); other wakeful activities (O); and sleep (S).

The 'statistician_time' data set records the daily time (in hours) devotedto each activity, recorded on each of 20 days, selected randomly from working daysin alternate weeks so as to avoid possible carry-over effects such as a short-sleepday being compensated by make-up sleep on the succeeding day. The six activitiesmay be divided into two categories: 'work' comprising activities T, C, A, and R, and'leisure', comprising activities O and S. Our analysis may then be directed towardsthe work pattern consisting of the relative times spent in the four work activities,the leisure pattern, and the division of the day into work time and leisure time.Two obvious questions are as follows. To what extent, if any, do the patterns ofwork and of leisure depend on the times allocated to these major divisions of theday? Is the ratio of sleep to other wakeful activities dependent on the times spentin the various work activities?

Usage

statistitian_time

Format

An object of classdata.frame with 20 rows and 7 columns.

Variation array is returned.

Description

Variation array is returned.

Usage

variation_array(X, include_means = FALSE)

Arguments

Value

variation array matrix

Examples

set.seed(1)X = matrix(exp(rnorm(5*100)), nrow=100, ncol=5)variation_array(X)variation_array(X, include_means = TRUE)

The waste composition in Catalonia

Description

The actual population residing in a municipality of Catalonia is composed by thecensus count and the so-called floating population (tourists, seasonal visitors,hostel students, short-time employees, and the like). Since actual populationcombines long and short term residents it is convenient to express it asequivalent full-time residents. Floating population may be positive if the +municipality is receiving more short term residents than it is sending elsewhere,or negative if the opposite holds (expressed as a percentage above –if positive–or below –if negative– the census count). The waste data set includes thisinformation in the variable floating population. Floating population has alarge impact on solid waste generation and thus waste can be used to predictfloating population which is a hard to estimate demographic variable. Thiscase study was presented in

Usage

waste

Format

An object of classdata.frame with 215 rows and 10 columns.

Details

Tourists and census population do not generate the same volume of waste and havedifferent consumption and recycling patterns (waste composition). The CatalanStatistical Institute (IDESCAT) publishes official floating population data for allmunicipalities in Catalonia (Spain) above 5000 census habitants. The compositionof urban solid waste is classified into D = 5 parts:* x1 : non recyclable (grey waste container in Catalonia),* x2 : glass (bottles and jars of any colour: green waste container),* x3 : light containers (plastic packaging, cans and tetra packs: yellow container),* x4 : paper and cardboard (blue container), and* x5 : biodegradable waste (brown container).

References

G. Coenders, J.A.Martín-Fernández and B. Ferrer-Rosell,When relative andabsolute information matter: compositional predictor with a total in generalizedlinear models. Statistical Modelling17(6) (2017), 494–512.

Hotel posts in social media

Description

The 'weibo_hotels' data set aims at comparing the use of Weibo (Facebookequivalent in China) in hospitality e-marketing between small and mediumaccommodation establishments (private hostels, small hotels) and big andwell-established business (such as international hotel chains or large hotels)in China. The 50 latest posts of the Weibo pages of each hotel (n = 10) arecontent-analyzed and coded regarding the count of posts featuring informationon a 4-part composition [facilities, food, events, promotions]. Hotels werecoded as large “L” or small “S” in the hotel size categorical variable.

Usage

weibo_hotels

Format

An object of classdata.frame with 10 rows and 5 columns.