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Figure . . Centroids of the SOM. he size of each pie segment corresponds to a cluster centroid ater
rescaling each variable separately. he parties have large segments in clusters where they performed
above average
where y is a (possibly multivariate) dependent variable with a conditional density h,
x isavectorofindependentvariables, π k isthepriorprobability ofcomponent k,and
θ k is the component-specific parameter vector for the density function f .
If f is a normal density with component-specific mean μ k
β
k x and variance σ k
=
β
k , σ k
(covariance matrix Σ k for multivariate y ), we have θ k
and Eq. . de-
scribes a mixture of standard linear regression models, also called latent class regres-
sion. A special case is x
=(
)
, which gives a mixture of Gaussians without a regression
part, and this is also called model-based clustering. If f is a member of the expo-
nential family, we get a mixture of generalized linear models (Wedel and DeSarbo,
).
FortheGermanelection data,weusefive-dimensional Gaussians asmixturecom-
ponents such that the parameters θ k are the mean μ k and covariance matrix Σ k of
each component. Using the Bayesian information criterion (BIC) to select the num-
ber of components K (Fraley and Ratery, ) results in K
=
segmentswith
prior probabilities π k
. , . , . , . , .
.helargestcomponent(num-
ber three) has a mean vector μ of
SPD
CDU/CSU
GRUENE
FDP
LINKE
.
.
.
.
.
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