help rel_clust
-------------------------------------------------------------------------------

Title

    rel_clust -- relative clusterability and weighted variables for cluster
                  analysis

Syntax

    rel_clust varlist [if] [in] [, options]


    options            Description
    -------------------------------------------------------------------------
    Main
      suffix(suffix)   generation of transformed variables of varlist adding
                       suffix to their variable names (default transformation
                       is vr_ratio)
      transf(arg)      type of variable transformation (requires option
                       suffix)
      norc             no output of "relative clusterability" indices
      replace          replace existing variables requested by suffix

    Sub (arguments of transf)
      vr_ratio         variance-to-range ratio weighting (see Steinley &
                       Brusco, 2008, p. 83f.) (default when using option
                       suffix)
      range            range transformation [xij/range(xj)]
      z_score          z-score transformation [xij-(mean(xj))/sd(xj)]
    -------------------------------------------------------------------------

Description

    rel_clust computes indices of relative clusterability of varlist
    according to Steinley and Brusco (2008) and optionally generates
    transformed or weighted variables for use in cluster analysis.

    rel_clust can be used to transform the variables of varlist by
    z-standardization, by standardization by range, or by variance-to-range
    (VR) ratio weighting. The VR ratio weighting procedure was designed
    specifically for cluster analysis: It reflects the degree of
    "clusterability" of the set of variables used. According to Steinley and
    Brusco (2008), VR ratio weighting of variables together with their
    proposed variable selection procedure clearly increases the ability of
    K-means cluster analysis to accurately recover the true cluster
    structure.

Options

        +------+
    ----+ Main +-------------------------------------------------------------

    suffix(suffix) requests the generation of transformed variables. The
        names of the new variables will be the original variable names with
        suffix added. Transformation to variance-to-range ratio weighted
        variables is the default.

    transf(arg) specifies the type of transformation (only necessary if other
        than variance-to-range ratio weighting is requested). Three
        transformations are possible according to arg (see below).

    norc requests not to show the table of "relative clusterability" per
        variable in the results window.

    replace requests that the variables specified by using option suffix will
        replace already existing variables.

        +---------------------+
    ----+ Sub (option transf) +----------------------------------------------

    vr_ratio requests a transformation by variance-to-range ratio weighting
        of the original variables (see Steinley & Brusco, 2008, p. 83f.)
        (default when using option suffix).

    range requests a range transformation [xij/range(xj)] of the original
        variables.

    z_score requests a z-score transformation [xij-(mean(xj))/sd(xj)] of the
        original variables.


Example

    The following commands replicate the results shown in Steinley & Brusco
    (2008) - as to the "relative clusterability" indices see Table 7, p. 102
    (x1 to x4), as to the variance and range of the original and transformed
    variables see Table 6, p. 99:

    . webuse iris
    . tabstat seplen-petwid, s(v r) f(%5.2f)
    . rel_clust seplen-petwid, tr(z) su(_z1)
    . tabstat *z1, s(v r) f(%5.2f)
    . rel_clust seplen-petwid, tr(ra) su(_z2) norc
    . tabstat *z2, s(v r) f(%5.2f)
    . rel_clust seplen-petwid, su(_z3) norc
    . tabstat *z3, s(v r) f(%5.2f)


Saved Results

    rel_clust saves the following in r():

    Scalars
      r(N)        number of valid cases (listwise)

    Macros 
      r(trans)    type of transformation used (if requested by option suffix)
      r(vars)     list of variables used

    Matrices
      r(RC)       matrix of relative clusterability index per variable


References

    Steinley, D. & Brusco, M. J. (2008). A new variable weighting and
        selection procedure for K-means cluster analysis. Multivariate
        Behavioral Research, 43, 77-108.

Also see

    Help: cluster kmeans

Author

    Dirk Enzmann
    Institute of Criminal Sciences, Hamburg
    email: mailto:dirk.enzmann@uni-hamburg.de