[statnet_help] Convergence assessment in small networks/with limited data

martina morris morrism at uw.edu
Fri Oct 2 10:22:08 PDT 2020

Hi David,

There are two dx issues here: convergence and statistical inference. The
MCMC plots give some insight into both.

Statistical inference:

The principles here are similar to traditional statistical inference -- if
you have a small number of observations (esp. for subgroups), the sampling
distributions of your statistics may not approximate a symmetric or normal
distribution. This is exacerbated by the lower bound at 0.

The MCMC distribution plots (on the right side of the MCMC dx plot layout)
are essentially showing the sampling distribution of the stats under the
model. Asymmetries here suggest the statistical inference may be
compromised. For small nets, you'll often see sawtooth shaped MCMC dx
plots. That is also a function of discrete, integer valued stats that
only vary over a small range. Not inherently a problem for statistical


Convergence is best assessed using the MCMC traceplots on the left hand
side of the plot layout. There, you're looking for a "fuzzy caterpillar".
What you don't want to see is a plot that trends up or down, or one that
has strong serial correlation in the estimates (some modest correlation is
not a problem).


On Fri, 2 Oct 2020, David Kretschmer wrote:

> Dear all,


> I estimate models on relatively small networks (about 20-30 nodes), including dyadic covariates with limited information,

> e.g. with only one or two actual tie observations for the dyadic covariate in some of the networks.


> I wonder about convergence analysis in this setup, in particular when considering density plots.


> The values for the network statistics related to the dyadic covariate produced during ERGM estimation have to be zero or

> positive; they cannot be negative. Because the number of tie observations in the empirical network is so low (only one or

> two instances), the deviations from these observations shown in the convergence analysis very frequently cannot  produce

> symmetrical density plots: Because the number predicted in the ERGM estimation is constrained to be zero or higher, the

> deviations are also constrained in one direction. This is also what I observe when looking at density plots for these

> networks.


> What I would like to know is what this implies *substantively* for the analysis of these networks: Should criteria for

> convergence be relaxed in such settings, i.e., is it also fine for the density plots to be asymmetric? Or does this

> simply mean that results from these networks should not be interpreted at all?


> Any help would be greatly appreciated.


> Best,

> David



> --

> David Kretschmer

> Universität Mannheim

> Mannheimer Zentrum für Europäische Sozialforschung (MZES)

> A5, 6

> 68159 Mannheim

> Tel.: +49-621-181-2024




Professor Emerita of Sociology and Statistics
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University of Washington
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morrism at u.washington.edu

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