StatMatch (version 1.2.0)

gower.dist: Computes the Gower's Distance


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


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


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
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
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
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.


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


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.


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


Run this code
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

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

Run the code above in your browser using DataLab