StatMatch (version 1.2.0)

gower.dist: Computes the Gower's Distance

Description

This function computes the Gower's distance (dissimilarity) among units in a dataset or among observations in two distinct datasets.

Usage

gower.dist(data.x, data.y=data.x, rngs=NULL, KR.corr=TRUE)

Arguments

data.x

A matrix or a data frame containing variables that should be used in the computation of the distance. Columns of mode numeric will be considered as interval scaled variables; columns of mode character or class fact

data.y

A numeric matrix or data frame with the same variables, of the same type, as those in data.x. Dissimilarities between rows of data.x and rows of data.y will be computed. If not provided, by default it is assumed equa

rngs

A vector with the ranges to scale the variables. Its length must be equal to number of variables in data.x. In correspondence of nonnumeric variables, just put 1 or NA. When rngs=NULL (default) the range of a numeric

KR.corr

When TRUE (default) the extension of the Gower's dissimilarity measure proposed by Kaufman and Rousseeuw (1990) is used. Otherwise, when KR.corr=FALSE, the Gower's (1971) formula is considered.

Value

• A matrix object with distances among rows of data.x and those of data.y.

Details

This function computes distances among records when variables of different type (categorical and continuous) have been observed. In order to handle different types of variables, the Gower's dissimilarity coefficient (Gower, 1971) is used. By default (KR.corr=TRUE) the Kaufman and Rousseeuw (1990) extension of the Gower's dissimilarity coefficient is used.

The final dissimilarity between the ith and jth unit is obtained as a weighted sum of dissimilarities for each variable: $$d(i,j) = \frac{\sum_k{\delta_{ijk} d_{ijk}}}{\sum_k{\delta_{ijk}}}$$

In particular, $d_{ijk}$ represents the distance between the ith and jth unit computed considering the kth variable. It depends on the nature of the variable:

• logicalcolumns are considered as asymmetric binary variables, for such case$d_{ijk}=0$if$x_{ik} = x_{jk} = \code{TRUE}$, 1 otherwise;
• factororcharactercolumns are considered as categorical nominal variables and$d_{ijk}=0$if$x_{ik}=x_{jk}$, 1 otherwise;
• numericcolumns are considered as interval-scaled variables and$$d_{ijk}=\frac{\left|x_{ik}-x_{jk}\right|}{R_k}$$being$R_k$the range of thekth variable. The range is the one supplied with the argumentrngs(rngs[k]) or the one computed on available data (whenrngs=NULL);
• orderedcolumns are considered as categorical ordinal variables and the values are substituted with the corresponding position index,$r_{ik}$in the factor levels. WhenKR.corr=FALSEthese position indexes (that are different from the output of the R functionrank) are transformed in the following manner$$z_{ik}=\frac{(r_{ik}-1)}{max\left(r_{ik}\right) - 1}$$These new values,$z_{ik}$, are treated as observations of an interval scaled variable.

As far as the weight $\delta_{ijk}$ is concerned:

• $\delta_{ijk}=0$if$x_{ik} = \code{NA}$or$x_{jk} = \code{NA}$;
• $\delta_{ijk}=0$if the variable is asymmetric binary and$x_{ik}=x_{jk}=0$or$x_{ik} = x_{jk} = \code{FALSE}$;
• $\delta_{ijk}=1$in all the other cases.

In practice, NAs and couple of cases with $x_{ik}=x_{jk}=\code{FALSE}$ do not contribute to distance computation.

References

Gower, J. C. (1971), A general coefficient of similarity and some of its properties. Biometrics, 27, 623--637.

Kaufman, L. and Rousseeuw, P.J. (1990), Finding Groups in Data: An Introduction to Cluster Analysis. Wiley, New York.

See Also

daisy, dist

Examples

x1 <- as.logical(rbinom(10,1,0.5)) 
x2 <- sample(letters, 10, replace=TRUE)
x3 <- rnorm(10)
x4 <- ordered(cut(x3, -4:4, include.lowest=TRUE))
xx <- data.frame(x1, x2, x3, x4, stringsAsFactors = FALSE)

# matrix of distances among observations in xx
gower.dist(xx)

# matrix of distances among first obs. in xx
# and the remaining ones
gower.dist(data.x=xx[1:3,], data.y=xx[4:10,])