Ergm stuck when adding gw*degree or gwesp

[MikeGacho]

I'm interested in modeling degree distribution, reciprocity and triad closure for a directed network.
A model with only edges + mutual runs very fast and smooth. However, a model with gwodegree, gwidegree or gwesp runs for some iterations, with long runtime, and then gets stuck for hours. I've tried setting different values for the decay parameters of gw*degree and gwesp (e.g., 0.25-1) as well as different values of MCMC.burnin and MCMC.samplesize but no success so far. Same when I use gw*degree or gwesp with fixed=FALSE.
Does anyone have any suggestion? I would greatly appreciate any help/comment.

For example:

mod0<-ergm(bnetwork ~ edges + gwodegree(0.1, fixed=TRUE), 
             control = control.ergm(MCMC.burnin = 10000, 
                             MCMC.samplesize = 20000, 
                             MCMLE.maxit = 300, 
                             parallel = 4, parallel.type = "PSOCK"), 
                             verbose =TRUE)

Evaluating network in model.
Initializing unconstrained Metropolis-Hastings proposal: ‘ergm:MH_TNT’.
Initializing model...
Model initialized.
Using initial method 'MPLE'.
Fitting initial model.
Starting maximum pseudolikelihood estimation (MPLE):
Obtaining the responsible dyads.
Evaluating the predictor and response matrix.
Maximizing the pseudolikelihood.
Finished MPLE.
Starting Monte Carlo maximum likelihood estimation (MCMLE):
Density guard set to 850060 from an initial count of 42322 edges.

Iteration 1 of at most 300 with parameter:
           edges gwodeg.fixed.0.1 
        -1.13693        -31.42723 
Starting unconstrained MCMC...
Back from unconstrained MCMC.
New interval = 32768.
Average estimating function values:
           edges gwodeg.fixed.0.1 
     140.4840652       -0.6055715 
Starting MCMLE Optimization...
Optimizing with step length 1.0000.
Using lognormal metric (see control.ergm function).
Using log-normal approx (no optim)
The log-likelihood improved by 1.4257.
Estimating equations are not within tolerance region.

Iteration 2 of at most 300 with parameter:
           edges gwodeg.fixed.0.1 
       -1.143216       -28.176799 
Starting unconstrained MCMC...
Back from unconstrained MCMC.
New interval = 32768.
Average estimating function values:
           edges gwodeg.fixed.0.1 
     -60.2275037       -0.6055715 
Starting MCMLE Optimization...
Optimizing with step length 1.0000.
Using lognormal metric (see control.ergm function).
Using log-normal approx (no optim)
The log-likelihood improved by 0.8010.
Distance from origin on tolerance region scale: 16.01944 (previously 27.87493).
Estimating equations are not within tolerance region.

Iteration 3 of at most 300 with parameter:
           edges gwodeg.fixed.0.1 
       -1.143067       -25.546154 
Starting unconstrained MCMC...
Back from unconstrained MCMC.
New interval = 32768.
Average estimating function values:
           edges gwodeg.fixed.0.1 
     -57.2878403       -0.6055715 
Starting MCMLE Optimization...
Optimizing with step length 1.0000.
Using lognormal metric (see control.ergm function).
Using log-normal approx (no optim)
The log-likelihood improved by 0.8012.
Distance from origin on tolerance region scale: 16.02249 (previously 16.03569).
Estimating equations are not within tolerance region.

Iteration 4 of at most 300 with parameter:
           edges gwodeg.fixed.0.1 
       -1.142888       -22.917084 
Starting unconstrained MCMC...
Back from unconstrained MCMC.
New interval = 32768.
Average estimating function values:
           edges gwodeg.fixed.0.1 
     -49.0833333       -0.6055715 
Starting MCMLE Optimization...
Optimizing with step length 1.0000.
Using lognormal metric (see control.ergm function).
Using log-normal approx (no optim)
The log-likelihood improved by 0.8018.
Distance from origin on tolerance region scale: 16.03546 (previously 16.01231).
Estimating equations are not within tolerance region.

Iteration 5 of at most 300 with parameter:
           edges gwodeg.fixed.0.1 
       -1.143159       -20.247049 
Starting unconstrained MCMC...
Back from unconstrained MCMC.
New interval = 65536.
Average estimating function values:
           edges gwodeg.fixed.0.1 
     -57.7638172       -0.6055715 
Starting MCMLE Optimization...
Optimizing with step length 1.0000.
Using lognormal metric (see control.ergm function).
Using log-normal approx (no optim)
The log-likelihood improved by 0.8007.
Distance from origin on tolerance region scale: 16.01289 (previously 16.02825).
Estimating equations are not within tolerance region.

Iteration 6 of at most 300 with parameter:
           edges gwodeg.fixed.0.1 
       -1.143112       -17.607124 
Starting unconstrained MCMC...
Back from unconstrained MCMC.
New interval = 32768.
Average estimating function values:
           edges gwodeg.fixed.0.1 
     -58.5333684       -0.6055715 
Starting MCMLE Optimization...
Optimizing with step length 1.0000.
Using lognormal metric (see control.ergm function).
Using log-normal approx (no optim)
The log-likelihood improved by 0.8008.
Distance from origin on tolerance region scale: 16.01536 (previously 16.01409).
Estimating equations are not within tolerance region.
Estimating equations did not move closer to tolerance region more than 1 time(s) in 4 steps; increasing sample size.

Iteration 7 of at most 300 with parameter:
           edges gwodeg.fixed.0.1 
       -1.143017       -14.971574 
Starting unconstrained MCMC...
Back from unconstrained MCMC.
New interval = 65536.
Average estimating function values:
           edges gwodeg.fixed.0.1 
     -22.5075869       -0.2621712 
Starting MCMLE Optimization...
Optimizing with step length 1.0000.
Using lognormal metric (see control.ergm function).
Using log-normal approx (no optim)
The log-likelihood improved by 0.1143.
Distance from origin on tolerance region scale: 2.285886 (previously 12.19024).
Estimating equations are not within tolerance region.

Iteration 8 of at most 300 with parameter:
           edges gwodeg.fixed.0.1 
        -1.14308        -14.09424 
Starting unconstrained MCMC...
Back from unconstrained MCMC.
Warning: Model statistics ‘gwodeg.fixed.0.1’ are linear combinations of some set of preceding statistics at the current stage of the estimation. This may indicate that the model is nonidentifiable.
New interval = 131072.
Average estimating function values:
           edges gwodeg.fixed.0.1 
      18.2147631        0.2233067 
Starting MCMLE Optimization...
Optimizing with step length 1.0000.
Using lognormal metric (see control.ergm function).
Using log-normal approx (no optim)
The log-likelihood improved by 1267766818518458280578121728.0000.
Distance from origin on tolerance region scale: 7.27351e+30 (previously 1.002561e+31).
Estimating equations are not within tolerance region.

Iteration 9 of at most 300 with parameter:
           edges gwodeg.fixed.0.1 
    1.691517e+08    -1.135449e+28 
Starting unconstrained MCMC...

These are some network characteristics

> print(bnetwork)
 Network attributes:
  vertices = 419 
  directed = TRUE 
  hyper = FALSE 
  loops = FALSE 
  multiple = FALSE 
  bipartite = FALSE 
  total edges= 42323 
    missing edges= 0 
    non-missing edges= 42323 

 Vertex attribute names: 
    vertex.names 

 Edge attribute names not shown `

` summary(bnetwork  ~  mutual + triangles)
  mutual triangle 
    7269  2199422`

`> range(degree(net, mode=c("out")))
[1]   1 213
> range(degree(net, mode=c("in")))
[1]   0 199
> mean(degree(net, mode=c("out")))
[1] 101.0095
> mean(degree(net, mode=c("in")))
[1] 101.0095