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glmmTMB with beta family and 0-inflation

2 messages · Caroline Zanchi, Ben Bolker

Original
Caroline Zanchi
# 
Dear community,

I am having trouble understanding the way 0-inflation is taken into 
account in mixed-effects beta regressions with the glmmTMB package.

I have a dataset which consists in readouts of bacterial cells which 
express or not a certain behaviour according to the state of their 
parent cell and over time. The response variable is expressed as a 
number of cells expressing the behaviour over the total number of cells. 
There are 0s in one parental state, but not the other.

I fitted :

M1 <- glmmTMB(propCFU~ parent_state * TIME + (1|SAMPLE), 
data=prop_daughters, ziformula= ~1, family=beta_family(link = "logit"))

Which gives :

summary(M1)
 ?Family: beta? ( logit )
Formula:????????? propCFUdaught ~ parent_treat * TIME + (1 | SAMPLE)
Zero inflation:???????????????? ~1
Data: prop_daughters

 ????? AIC?????? BIC??? logLik -2*log(L)? df.resid
 ?? -672.9??? -640.7???? 349.4??? -698.9??????? 75

Random effects:

Conditional model:
 ?Groups Name??????? Variance? Std.Dev.
 ?SAMPLE (Intercept) 4.322e-09 6.574e-05
Number of obs: 88, groups:? SAMPLE, 30

Dispersion parameter for beta family ():? 327

Conditional model:
 ????????????????????????????? Estimate Std. Error z value Pr(>|z|)
(Intercept)?????????????????? -7.67870??? 0.73063 -10.510 <2e-16 ***
parent_treatstationary???????? 1.22248??? 0.75556?? 1.618 0.106
TIME20???????????????????????? 0.06966??? 0.80420?? 0.087 0.931
TIME40???????????????????????? 0.70438??? 0.78492?? 0.897 0.370
TIME60???????????????????????? 1.00432??? 0.81196?? 1.237 0.216
TIME80???????????????????????? 0.91809??? 0.81363?? 1.128 0.259
parent_treatstationary:TIME20 -0.16829??? 0.90534? -0.186 0.853
parent_treatstationary:TIME40 -1.34558??? 0.94120? -1.430 0.153
parent_treatstationary:TIME60 -1.43812??? 0.91828? -1.566 0.117
parent_treatstationary:TIME80 -0.50110??? 0.98536? -0.509 0.611
---
Signif. codes:? 0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1

Zero-inflation model:
 ??????????? Estimate Std. Error z value Pr(>|z|)
(Intercept)? -0.8150???? 0.2312? -3.526 0.000422 ***

... and a pretty terrible fit, because of the 0s I suppose :

plot(simulateResiduals(M1))

... which makes me think that the 0s might not be properly taken into 
account.

Is there anything I am doing wrong ? I would take any advice on how to 
improve this.

Thank you ! (for taking the time to read it so close to holiday time...)

Caroline
1 day later
Ben Bolker
# 
Hi Caroline,

  comments below/inline.
On 12/19/25 07:37, Caroline Zanchi wrote:
In principle, if you know the original total number of cells, you 
could use a zero-inflated beta-binomial model instead of a hurdle-beta. 
This may not matter as much if the total number of cells is very large 
(in which case the beta-binomial will approximate a beta pretty well 
anyway).  (You might not even need the zero-inflation, if the 
conditional distribution is such that the proportion of non-CFU 
daughters is well described by the zeros in the beta-binomial distribution).

  You could also try family = "ordbeta".

     >
Your fit is singular. (There's little enough among-sample variance 
that it is estimated as zero -- all the variance can be explained by the 
variability in the conditional distribution.)  You can see the GLMM FAQ 
for more discussion of singular fits.
This corresponds to a very sharp (low-variance) conditional 
distribution. From ?beta_binomial:

V=mu*(1-mu)/(phi+1)
Nothing here looks especially strange.>
We can't see the simulated residuals plot (the mailing list doesn't 
accept attachments), so we don't know what's wrong.

   Nothing looks obviously wrong with your model. You might also try 
performance::check_model() for a different set of diagnostics.