[statnet_help] Convergence for parameters estimated with very little information

David Kretschmer dkretsch at mail.uni-mannheim.de
Thu Aug 13 02:21:04 PDT 2020

Dear all,

I fit ERGMs on (a lot of) rather small networks, and for some of the parameters, estimation is based on very little information, i.e., values for corresponding networks statistics are very low, frequently in the range of 2-5 observations (of a specific type of tie). Now I wonder whether/how these estimates can still be used for subsequent analyses.

In particular, I wonder about convergence assessment for these parameters. One thing I frequently observe when analysing convergence for these networks is that the density plots for the marginal distributions of the affected parameters are not symmetrical. Frequently, the maximum/minimum density is at either low or high values, rather than at medium values (i.e., close to zero). The means, however, frequently are close to zero, and in a follow-up GOF analysis, the means are virtually indistinguishable from zero.

At the same time, when using density plots for the follow-up GOF analysis, the plots are sometimes symmetrical around the observed network statistic (or much more so than the density plots from the original convergence assessment). In other cases, however, the density is not symmetrical (though the mean always is very close to the observed network statistic), and sometimes even less symmetrical than the density from the original MCMC.

Now I wonder about what to make of these observations. It seems clear to me that these issues follow from the little information estimation is based on, but unclear whether these observations are problematic, meaning that these networks should be discarded for subsequent analyses, or whether they can still be used.

Any help would be greatly appreciated.


David Kretschmer
Universität Mannheim
Mannheimer Zentrum für Europäische Sozialforschung (MZES)
A5, 6
68159 Mannheim
Tel.: +49-621-181-2024

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