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Does anyone know how to do cluster analysis that considers the uncertainty (s.e. or confidence intervals in the data?) I want to do cluster analysis on group estimates state-level and regional estimates), but I do not know how to define or include the error in these data.

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    $\begingroup$ Welcome to the site. Please edit your question to include more details about the analysis you are trying to do, as your question is too broad the way it is posted. See How to Ask for tips on asking a good question. Most statistical packages can perform clustered analysis, but each package has different commands for it. Specifying that you want clustered standard errors may also differ by procedure within the package. Giving us more details about what you're trying to do will help us guide you in the right direction $\endgroup$ Commented Apr 21, 2016 at 3:13
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    $\begingroup$ If you expand your definition of uncertainty to include "degree of membership" or probabilistic approaches to clustering, you would have a wider class of models to consider. For instance, latent class clustering algorithms use maximum likelihood-based, finite mixture models as their engines which can produce assignment rules that are probabilities of an object belonging to a cluster. $\endgroup$
    – user78229
    Commented Apr 21, 2016 at 11:35

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See for example:

Schubert, E., Koos, A., Emrich, T., Züfle, A., Schmid, K. A., & Zimek, A. (2015).
A framework for clustering uncertain data.
Proceedings of the VLDB Endowment, 8(12), 1976-1979.

and the references therein.

There is uncertain k-means in several variants, fuzzy DBSCAN, ... many more

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