Mixed-variables coefficient of distance

The mixed-variables coefficient of distance generalizes Gower's general coefficient of distance to allow the treatment of various statistical types of variables when calculating distances. This is especially important when measuring functional diversity. Indeed, most of the indices that measure functional diversity depend on variables (traits) that have various statistical types (e.g. circular, fuzzy, ordinal) and that go through a matrix of distances among species.

Usage

dist.ktab(x, type, option = c("scaledBYrange", "scaledBYsd", "noscale"),
scann = FALSE, tol = 1e-8)
ldist.ktab(x, type, option = c("scaledBYrange", "scaledBYsd",
"noscale"), scann = FALSE, tol = 1e-8)
kdist.cor(x, type, option = c("scaledBYrange", "scaledBYsd", "noscale"),
scann = FALSE, tol = 1e-8, squared = TRUE)
prep.fuzzy(df, col.blocks, row.w = rep(1, nrow(df)), labels = paste("F",
1:length(col.blocks), sep = ""))
prep.binary(df, col.blocks, labels = paste("B", 1:length(col.blocks), sep = "")) 
prep.circular(df, rangemin = apply(df, 2, min, na.rm = TRUE), rangemax =
apply(df, 2, max, na.rm = TRUE))

Arguments

x: Object of class ktab (see details)
type: Vector that provide the type of each table in x. The possible types are "Q" (quantitative), "O" (ordinal), "N" (nominal), "D" (dichotomous), "F" (fuzzy, or expressed as a proportion), "B" (multichoice nominal variables, coded by binary columns), "C" (circular). Values in type must be in the same order as in x.
option: A string that can have three values: either "scaledBYrange" if the quantitative variables must be scaled by their range, or "scaledBYsd" if they must be scaled by their standard deviation, or "noscale" if they should not be scaled. This last option can be useful if the the values have already been normalized by the known range of the whole population instead of the observed range measured on the sample. If x contains data from various types, then the option "scaledBYsd" is not suitable (a warning will appear if the option selected with that condition).
scann: A logical. If TRUE, then the user will have to choose among several possible functions of distances for the quantitative, ordinal, fuzzy and binary variables.
tol: A tolerance threshold: a value less than tol is considered as null.
squared: A logical, if TRUE, the squared distances are considered.
df: Objet of class data.frame
col.blocks: A vector that contains the number of levels per variable (in the same order as in df)
row.w: A vector of row weigths
labels: the names of the traits
rangemin: A numeric corresponding to the smallest level where the loop starts
rangemax: A numeric corresponding to the highest level where the loop closes

Value

The functions provide the following results:

dist.ktab: returns an object of class dist;
ldist.ktab: returns a list of objects of class dist that correspond to the distances between species calculated per trait;
kdist.cor: returns a list of three objects: "paircov" provides the covariance between traits in terms of (squared) distances between species; "paircor" provides the correlations between traits in terms of (squared) distances between species; "glocor" provides the correlations between the (squared) distances obtained for each trait and the global (squared) distances obtained by mixing all the traits (= contributions of traits to the global distances);
prep.binary and prep.fuzzy: returns a data frame with the following attributes: col.blocks specifies the number of columns per fuzzy variable; col.num specifies which variable each column belongs to;
prep.circular: returns a data frame with the following attributes: max specifies the number of levels in each circular variable.

References

Pavoine S., Vallet, J., Dufour, A.-B., Gachet, S. and Daniel, H. (2009) On the challenge of treating various types of variables: Application for improving the measurement of functional diversity. Oikos, 118, 391–402. doi:10.1111/j.1600-0706.2008.16668.x

Appendix available at: http://www.oikosjournal.org/sites/oikosjournal.org/files/appendix/o16668.pdf http://www.oikosjournal.org/sites/oikosjournal.org/files/appendix/o16668_files.zip

Author

Sandrine Pavoine pavoine@mnhn.fr

Details

When preparing the object of class ktab (object x), variables of type "Q", "O", "D", "F", "B" and "C" should be of class numeric (the class ordered is not yet considered by dist.ktab); variables of type "N" should be of class character or factor

Examples

# With fuzzy variables
data(bsetal97)

w <- prep.fuzzy(bsetal97$biol, bsetal97$biol.blo)
w[1:6, 1:10]
#>    size.1 size.2 size.3 size.4 size.5 size.6 size.7 egglen.1 egglen.2 egglen.3
#> E1      0      0      0      1      0   0.00   0.00        0        0        0
#> E2     NA     NA     NA     NA     NA     NA     NA        0        0        0
#> E3      0      1      0      0      0   0.00   0.00        0        0        0
#> E4      0      0      0      1      0   0.00   0.00        0        0        0
#> E5      0      0      0      0      0   0.25   0.75        0        0        0
#> E6      0      0      0      0      0   0.50   0.50        0        0        0
ktab1 <- ktab.list.df(list(w))
dis <- dist.ktab(ktab1, type = "F")
as.matrix(dis)[1:5, 1:5]
#>           E1        E2        E3        E4        E5
#> E1 0.0000000 0.6947589 0.5947593 0.4008332 0.6487069
#> E2 0.6947589 0.0000000 0.6401753 0.6689944 0.5623047
#> E3 0.5947593 0.6401753 0.0000000 0.7107262 0.6289859
#> E4 0.4008332 0.6689944 0.7107262 0.0000000 0.5244575
#> E5 0.6487069 0.5623047 0.6289859 0.5244575 0.0000000

if (FALSE) { # \dontrun{
# With ratio-scale and multichoice variables
data(ecomor)

wM <- log(ecomor$morpho + 1) # Quantitative variables
wD <- ecomor$diet
# wD is a data frame containing a multichoice nominal variable
# (diet habit), with 8 modalities (Granivorous, etc)
# We must prepare it by prep.binary
head(wD)
wD <- prep.binary(wD, col.blocks = 8, label = "diet")
wF <- ecomor$forsub
# wF is also a data frame containing a multichoice nominal variable
# (foraging substrat), with 6 modalities (Foliage, etc)
# We must prepare it by prep.binary
head(wF)
wF <- prep.binary(wF, col.blocks = 6, label = "foraging")
# Another possibility is to combine the two last data frames wD and wF as
# they contain the same type of variables
wB <- cbind.data.frame(ecomor$diet, ecomor$forsub)
head(wB)
wB <- prep.binary(wB, col.blocks = c(8, 6), label = c("diet", "foraging"))
# The results given by the two alternatives are identical
ktab2 <- ktab.list.df(list(wM, wD, wF))
disecomor <- dist.ktab(ktab2, type= c("Q", "B", "B"))
as.matrix(disecomor)[1:5, 1:5]
contrib2 <- kdist.cor(ktab2, type= c("Q", "B", "B"))
contrib2

ktab3 <- ktab.list.df(list(wM, wB))
disecomor2 <- dist.ktab(ktab3, type= c("Q", "B"))
as.matrix(disecomor2)[1:5, 1:5]
contrib3 <- kdist.cor(ktab3, type= c("Q", "B"))
contrib3

# With a range of variables
data(woangers)

traits <- woangers$traits
# Nominal variables 'li', 'pr', 'lp' and 'le'
# (see table 1 in the main text for the codes of the variables)
tabN <- traits[,c(1:2, 7, 8)]
# Circular variable 'fo'
tabC <- traits[3]
tabCp <- prep.circular(tabC, 1, 12)
# The levels of the variable lie between 1 (January) and 12 (December).
# Ordinal variables 'he', 'ae' and 'un'
tabO <- traits[, 4:6]
# Fuzzy variables 'mp', 'pe' and 'di'
tabF <- traits[, 9:19]
tabFp <- prep.fuzzy(tabF, c(3, 3, 5), labels = c("mp", "pe", "di"))
# 'mp' has 3 levels, 'pe' has 3 levels and 'di' has 5 levels.
# Quantitative variables 'lo' and 'lf'
tabQ <- traits[, 20:21]
ktab1 <- ktab.list.df(list(tabN, tabCp, tabO, tabFp, tabQ))
distrait <- dist.ktab(ktab1, c("N", "C", "O", "F", "Q"))
is.euclid(distrait)
contrib <- kdist.cor(ktab1, type = c("N", "C", "O", "F", "Q"))
contrib
dotchart(sort(contrib$glocor), labels = rownames(contrib$glocor)[order(contrib$glocor[, 1])])
} # }