Dissimilarity Indices and Distance Measures
This function provides a set of alternative dissimilarity indices and distance metrics for classification and ordination, including weighting by species (columns) and shortest-path adjustment for dissimilarity indices.
dsvdis(x,index,weight=rep(1,ncol(x)),step=0.0,
diag=FALSE, upper=FALSE)x |
a matrix of observations, samples as rows and variables as columns |
index |
a specific dissimilarity or distance index (see details below) |
weight |
a vector of weights for species (columns) |
step |
a threshold dissimilarity to initiate shortest-path adjustment (0.0 is a flag for no adjustment) |
diag |
a switch to control returning the diagonal (default=FALSE) |
upper |
a switch to control returning the upper (TRUE) or lower (FALSE) triangle |
The function calculates dissimilarity or distance between rows of a matrix of observations according to a specific index. Three indices convert the data to presence/absence automatically. In contingency table notation, they are:
| steinhaus | 1 - a / (a + b + c) |
| sorensen | 1 - 2a / (2a + b +c) |
| ochiai | 1 - a / √{(a+b) * (a+c)} |
Others are quantitative. For variable i in samples x and y:
| ruzicka | 1 - ∑ min(x_i,y_i) / ∑ max(x_i,y_i) |
| bray/curtis | 1 - ∑[2 * min(x_i,y_i)] / ∑ x_i + y_i |
| roberts | 1 - [(x_i+y_i) * min(x_i,y_i) / max(x_i,y_i)] / (x_i + y_i) |
| chisq | (exp - obs) / √{exp} |
The weight argument allows the assignment of weights to individual species in the calculation of plot-to-plot similarity. The weights can be assigned by life-form, indicator value, or for other investigator specific reasons. For the presence/absence indices the weights should be integers; for the quantitative indices the weights should be in the interval [0,1]. The default (rep(1,ncol(x)) is to set all species = 1.
The threshold dissimilarity ‘step’ sets all values greater than or equal to "step" to 9999.9 and then solves for the shortest path distance connecting plots to other non-9999.9 values in the matrix. Step = 0.0 (the default) is a flag for "no shortest-path correction".
Returns an object of class "dist", equivalent to that from dist.
Ecologists have spent a great deal of time and effort examining the properties of different dissimilarity indices and distances for ecological data. Many of these indices should have more general application however. Dissimilarity indices are bounded [0,1], so that samples with no attributes in common cannot be more dissimilar than 1.0, regardless of their separation along hypothetical or real gradients. The shortest-path adjustment provides a partial solution. Pairs of samples more dissimilar than a specified threshold are set to 9999.9, and the algorithm solves for their actual dissimilarity from the transitive closure of the triangle inequality. Essentially, the dissimilarity is replaced by the shortest connected path between points less than the threshold apart. In this way it is possible to obtain dissimilarities much greater than 1.0.
The chi-square distance is not usually employed directly in cluster analysis or
ordination, but is provided so that you can calculate correspondence analysis
as a principal coordinates analysis (using cmdscale) from a simple
distance matrix.
dist, vegdist
data(bryceveg) # returns a data.frame called "bryceveg" dis.ochiai <- dsvdis(bryceveg,index="ochiai") dis.bc <- dsvdis(bryceveg,index="bray/curtis")
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