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st: Package "clstop_lbt" available on SSC

From   Dirk Enzmann <>
Subject   st: Package "clstop_lbt" available on SSC
Date   Sun, 03 Feb 2013 18:16:54 +0100

Thanks to Kit Baum, the new package "clstop_lbt" is available on SSC.

"clstop_lbt" adds the rule "lbt" to the post-estimation command -cluster stop- to determine the number of kmeans clusters using Steinley & Brusco's (2011) lower bound technique (LBT). It is used via -cluster stop, rule(lbt)-.

"clstop_lbt" creates the normalized index LBT that measures the closeness of the observed value of the within-cluster sums of squares (SSE) to the the minimum value of SSE in terms of total sums of squares (SST) according to LBT = (SSE - SSE_min)/SST. The method to determine the lower bound of SSE (i.e. SSE_min) is given in Steinley & Brusco (2011, p. 289). If the number of variables is equal or less than the number of clusters k, LBT is equal to the ratio SSE/SST (in this case, the LBT cannot be used).

"clstop_lbt" can also be used to determine whether there is more than one cluster. In this case the ratio SSE(2)/SST of a two cluster solution should be less than the lower bound ratio (LBR) obtainable when there is only one cluster - assuming a (multivariate) normal distribution, the LBR(normal) is 1-2/pi = .3634, assuming a univariate distribution the LBR(univariate) is .25.

A simulation study by Steinley & Brusco (2011) shows that the LBT index outperforms the accuracy and precision of the CH (Calinski/Harabasz) index. However, the LBT requires that the number of variables exceed the number of clusters. In cases of equal or less variables than the number of clusters Steinley & Brusco recommend to use the CH index (which is the default when using -cluster stop-).


Steinley, D. & Brusco, M. J. (2011). Choosing the number of clusters in K-means clustering. Psychological Methods, 16, 285-297. [ ]


Dr. Dirk Enzmann
Institute of Criminal Sciences
Dept. of Criminology
Rothenbaumchaussee 33
D-20148 Hamburg

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