[R-sig-ME] Query about fitting glmmTMB zero-inflated negative binomial model

[William Silver]

Hi there,

I�ve been referred to post my problem on this mailing list, so apologies in advance if I�m not following best practice.

Essentially, I�m attempting to fit two zero-inflated negative binomial models. My two dependent variables are mode of accessing a news website (i.e., through social media, or through search engine) and I have raw counts for each individual (N = 900). Zero-inflated models are most theoretically plausible because some people do not use social media or search engines to access news. The distribution is extremely right skewed with an excess of zeros, and the right tail extends far out. On the advice of my professor, I truncated the models to exclude the 10-20 participants with extremely high counts, so that outliers would not be driving the model. Initially, I was met with NAs in the model summary and followed Ben Bolker�s advice here<https://stackoverflow.com/questions/62239351/why-am-i-getting-nas-in-the-model-summary-output-zero-inflated-glmm-with-glmmtm>. I looked for combinations of categories that were zero, and the categories I�ve found I have either dropped or combined. This fixed the NA issue initially when I ran the model with a different optimiser, following Ben Bolker�s advice here<https://stackoverflow.com/questions/62478569/understanding-and-fixing-false-convergence-errors-in-glmmtmb-lme4>, however this still seems to be a problem depending on which variables I include. I�ve pasted the model output below in which the standard errors look much more normal, however when running analysis of residuals, there are some significant problems.

The problem I�m now met with a number of various warnings about model convergence which I�ve been unable to resolve. The first was �Error in e_complex_check(eigs$values) : detected complex eigenvalues of covariance matrix (max(abs(Im))=3.48036e-15: try se=FALSE?�, which disappears when including se=FALSE in the command. I�m then met with �Warning: In fitTMB(TMBStruc) : Model convergence problem. See vignette('troubleshooting')�. I�ve consulted the vignette<https://cran.r-project.org/web/packages/glmmTMB/vignettes/troubleshooting.html> it directs to, but am fairly new to statistics and find this all fairly advanced. I�ve tried applying the diagnose_vcov function, but am unsure how to interpret the results. Can I trust these models, given these warnings? Are there any recommendations someone might have for addressing the warnings if they are a significant issue?

These errors are only occurring in the ZINB models (and this is the case for both glmmTMB and pscl packages). The ZI poisson models on the same variables run fine, but suffer from overdispersion (with which I hoped to solve by using the ZINB technique because it is better adapted for dealing with this). Ideally, I�d use the ZINB models over the ZIP models as they are better suited, but am wary of using them given these seemingly unresolvable warnings. I�d really appreciate any guidance anyone could give.

Thank you so much in advance,

Best wishes,

William

Output:

zinb.am.se.test = glmmTMB(total_se_refer ~ diet_rob + polinterest + poleffic + age + trstmedia_sm + dummy_L_all + dummy_C_all + female_dum + trstmedia_sm + trstmedia_public, ziformula = ~ diet_rob + polinterest + poleffic + age + trstmedia_sm + dummy_L_all + dummy_C_all + female_dum + trstmedia_sm + trstmedia_public, data=df.trunc.se , family = nbinom1, se = FALSE, control = glmmTMBControl(optimizer = optim, optArgs = list(method="CG")))
Warning message:
In fitTMB(TMBStruc) :
  Model convergence problem; . See vignette('troubleshooting')
> summary(zinb.am.se.test)
Family: nbinom1  ( log )
Formula:          total_se_refer ~ diet_rob + polinterest + poleffic + age + trstmedia_sm +
    dummy_L_all + dummy_C_all + female_dum + trstmedia_sm + trstmedia_public
Zero inflation:
~diet_rob + polinterest + poleffic + age + trstmedia_sm + dummy_L_all +
    dummy_C_all + female_dum + trstmedia_sm + trstmedia_public
Data: df.trunc.se

     AIC      BIC   logLik deviance df.resid
  8316.0   8417.3  -4137.0   8274.0      899


Dispersion parameter for nbinom1 family (): 2.87

Conditional model:
                  Estimate Std. Error z value Pr(>|z|)
(Intercept)       0.096117   0.168652   0.570 0.568738
diet_rob         -0.007591   0.138051  -0.055 0.956151
polinterest       0.211511   0.030390   6.960  3.4e-12 ***
poleffic          0.089956   0.009867   9.117  < 2e-16 ***
age               0.001146   0.001934   0.592 0.553555
trstmedia_sm      0.090851   0.026701   3.402 0.000668 ***
dummy_L_all       0.088489   0.069593   1.272 0.203539
dummy_C_all      -0.035509   0.062070  -0.572 0.567264
female_dum        0.049242   0.053296   0.924 0.355518
trstmedia_public  0.165294   0.027917   5.921  3.2e-09 ***
---
Signif. codes:  0 �***� 0.001 �**� 0.01 �*� 0.05 �.� 0.1 � � 1

Zero-inflation model:
                  Estimate Std. Error z value Pr(>|z|)
(Intercept)      -0.018224   0.425006  -0.043   0.9658
diet_rob          0.005089   0.404882   0.013   0.9900
polinterest      -0.046104   0.087863  -0.525   0.5998
poleffic         -0.062502   0.028639  -2.182   0.0291 *
age              -0.001789   0.005584  -0.320   0.7487
trstmedia_sm     -0.042205   0.085556  -0.493   0.6218
dummy_L_all      -0.005172   0.209608  -0.025   0.9803
dummy_C_all      -0.005723   0.183298  -0.031   0.9751
female_dum       -0.007491   0.165891  -0.045   0.9640
trstmedia_public -0.049461   0.082624  -0.599   0.5494
---
Signif. codes:  0 �***� 0.001 �**� 0.01 �*� 0.05 �.� 0.1 � � 1
Warning messages:
1: In vcov.glmmTMB(object, include_mapped = TRUE) :
  Calculating sdreport. Use se=TRUE in glmmTMB to avoid repetitive calculation of sdreport
2: In vcov.glmmTMB(object) :
  Calculating sdreport. Use se=TRUE in glmmTMB to avoid repetitive calculation of sdreport

> summary(zinb.am.sm.test)
Family: nbinom1  ( log )
Formula:          total_sm_refer ~ diet_rob + polinterest + poleffic + age + trstmedia_sm +
    dummy_L_all + dummy_C_all + female_dum + trstmedia_sm + trstmedia_public
Zero inflation:
~diet_rob + polinterest + poleffic + age + trstmedia_sm + dummy_L_all +
    dummy_C_all + female_dum + trstmedia_sm + trstmedia_public
Data: df.trunc.sm

     AIC      BIC   logLik deviance df.resid
  5259.0   5360.3  -2608.5   5217.0      902


Dispersion parameter for nbinom1 family (): 10.6

Conditional model:
                 Estimate Std. Error z value Pr(>|z|)
(Intercept)       0.10901    0.68090   0.160   0.8728
diet_rob          0.08175    0.65938   0.124   0.9013
polinterest       0.15325    0.11435   1.340   0.1802
poleffic          0.03901    0.13561   0.288   0.7736
age               0.01047    0.01093   0.958   0.3379
trstmedia_sm      0.24108    0.13696   1.760   0.0784 .
dummy_L_all       0.16702    0.89975   0.186   0.8527
dummy_C_all       0.01118    1.46559   0.008   0.9939
female_dum        0.12071    0.65590   0.184   0.8540
trstmedia_public -0.01846    0.32520  -0.057   0.9547
---
Signif. codes:  0 �***� 0.001 �**� 0.01 �*� 0.05 �.� 0.1 � � 1

Zero-inflation model:
                   Estimate Std. Error z value Pr(>|z|)
(Intercept)      -0.0301001  1.3829502  -0.022    0.983
diet_rob         -0.0233937  2.3407518  -0.010    0.992
polinterest      -0.0897813  0.3597496  -0.250    0.803
poleffic         -0.0455312  0.3529030  -0.129    0.897
age              -0.0003903  0.0204699  -0.019    0.985
trstmedia_sm     -0.0884604  0.1374919  -0.643    0.520
dummy_L_all      -0.0205767  2.2994896  -0.009    0.993
dummy_C_all      -0.0167199  3.9414142  -0.004    0.997
female_dum       -0.0339406  1.8302418  -0.018    0.985
trstmedia_public -0.0408538  0.6763691  -0.060    0.952
Warning messages:
1: In vcov.glmmTMB(object, include_mapped = TRUE) :
  Calculating sdreport. Use se=TRUE in glmmTMB to avoid repetitive calculation of sdreport
2: In vcov.glmmTMB(object) :
  Calculating sdreport. Use se=TRUE in glmmTMB to avoid repetitive calculation of sdreport

	[[alternative HTML version deleted]]