Distances of Points to Class Centroids

Function finds Euclidean or squared Mahalanobis distances of points to class centroids in betadisper or ordination results.

Usage

# Default S3 method
centredist(x, group, distance = c("euclidean",
    "mahalanobis"), display = "sites", w, ...)
# S3 method for class 'betadisper'
centredist(x, ...)
# S3 method for class 'cca'
centredist(x, group, distance = c("euclidean", "mahalanobis"),
    display = c("sites", "species"), rank = 2, ...)
# S3 method for class 'rda'
centredist(x, group, distance = c("euclidean", "mahalanobis"),
    display = "sites", rank = 2, ...)
# S3 method for class 'dbrda'
centredist(x, group, distance = c("euclidean","mahalanobis"),
    display = "sites", rank = 2, ...)
# S3 method for class 'wcmdscale'
centredist(x, group, distance= c("euclidean","mahalanobis"),
    display = "sites", rank = 2, ...)

Arguments

x: An ordination result object, or a matrix for the default method or a betadisper result object.
group: Factor to define classes for which centroids are found.
distance: Use either simple Euclidean distance or squared Mahalanobis distances that take into account the shape of covariance ellipses.
display: Kind of scores.
w: Weights. If x has weights (such as cca result), these will be used.
rank: Number of axes used in ordination methods.
...: Other arguments to functions (ignored).

Details

Function finds either simple Euclidean distances of all points to their centroid as given by argument group or squared Mahalanobis distances of points to the centroid. In addition to the distances, it returns information of the original group and the nearest group for each point.

Currently the distances are scaled so that the sum of squared Euclidean distance will give the residual (unexplained) eigenvalue in constrained ordination with given group. The distances may not correspond to the distances in ordination plots with specific scaling and setting argument scaling gives an error. Due to restriction of this scaling, Euclidean distances for species scores are only allowed in ca and cca. These restrictions may be relaxed in the future versions of the method.

Squared Mahalanobis distances (mahalanobis) are scaled by the within group covariance matrix, and they are consistent with ordiellipse.

Mahalanobis distances can only be calculated for group that are larger than rank. For rank = 2, minimum permissible group has three points. However, even this can fail in degenerate cases, such as three points on a line. Euclidean distances can be calculated for any rank. With rank = "full" distance-based methods wcmdscale, pco, dbrda and betadisper will handle negative eigenvalues and associated eigenvectors, but with numeric rank they will only use real eigenvectors with positive eigenvalues.

There are specific methods for some ordination models, but many will be handled by the default method (including metaMDS and monoMDS).

The specific method for betadisper ignores most arguments and calculates the distances as specified in model fitting. The betadisper result with argument type = "centroid" is equal to wcmdscale, pco or dbrda with the same group and rank = "full".

Value

Function returns a list with components

centre: Centre to which a point was originally allocated.
nearest: Nearest centre to a point.
distances: Distance matrix where each observation point is a row, and column gives the distance of the point to that centre.

Author

Jari Oksanen

Note

centerdist is a synonym of centredist.

Examples

  data(dune, dune.env)
  d <- vegdist(dune) # Bray-Curtis
  mod <- with(dune.env, betadisper(d, Management))
  centredist(mod)
#> 
#> distances:  bray 
#> 
#>    centre nearest         BF        HF        NM        SF
#> 1      SF      BF 0.49644568 0.5418457 0.8517511 0.5644371
#> 2      BF      BF 0.25251672 0.3780172 0.7075570 0.4114648
#> 3      SF      SF 0.41470128 0.3855665 0.6204737 0.1110907
#> 4      SF      SF 0.42624976 0.4393619 0.6358864 0.2266270
#> 5      HF      HF 0.37738597 0.2087227 0.6498706 0.5146204
#> 6      HF      HF 0.34039792 0.2456723 0.6126336 0.5642756
#> 7      HF      HF 0.29310989 0.1150411 0.6612193 0.4818030
#> 8      HF      SF 0.50164812 0.4375138 0.4274640 0.2449894
#> 9      HF      SF 0.53148596 0.3887899 0.5918427 0.2614780
#> 10     BF      BF 0.03881034 0.2868014 0.6154078 0.5175787
#> 11     BF      BF 0.36741961 0.4427340 0.5443921 0.5525589
#> 12     SF      SF 0.67759762 0.5249557 0.5627151 0.3810054
#> 13     SF      SF 0.67165475 0.5651190 0.5987912 0.3495776
#> 14     NM      NM 0.75201600 0.7713289 0.4241926 0.6703521
#> 15     NM      NM 0.81690124 0.7245346 0.3013518 0.6254642
#> 16     SF      NM 0.86797919 0.7654150 0.4951610 0.5510415
#> 17     NM      NM 0.66496238 0.6792701 0.6563399 0.8377509
#> 18     NM      BF 0.44376561 0.5052147 0.5074504 0.6320749
#> 19     NM      NM 0.67278867 0.6880656 0.5126987 0.7579196
#> 20     NM      NM 0.86808311 0.7719325 0.3037948 0.6683067
  ## equal to metric scaling when using centroids instead of medians
  modc <- with(dune.env, betadisper(d, Management, type = "centroid"))
  ord <- pco(d)
  all.equal(centredist(modc), centredist(ord, dune.env$Management, rank="full"),
     check.attributes = FALSE)
#> [1] TRUE