false convergence (8) with binary covariate (0, 1) but NOT if covariate is (no, yes)?

a) Why is that so?

b) How can I fix the false convergence problem if my covariate has also a binary format?

Dear list,

The false convergence warning message (8) seems to be a common problem in
lmer. I've searched the archives to find a solution and found out that one
approach would be standardizing my covariate to mean-center the data.

However, what if the covariate itself (in this case SameMate) has a binary
value (0,1)?

After testing for the effect of the breeding success on site-fidelity (and
finally understanding the summary output), I would like to account for the
effect of breeding success (successfull=1, unsuccessfull=0) on mate-fidelity
(mate-fidelity=1, no mate-fidelity=0).

I.e. does the model including BreedSuc1 fits better than without it:

fm<-lmer(SameMate~BreedSuc1+(1|Bird),family="binomial")
fm1<-lmer(SameMate~1+(1|Bird),family="binomial")

Both models get the warning message:

In mer_finalize(ans) : false convergence (8)

anova(fm,fm1)
Data:
Models:
fm1: SameMate ~ 1 + (1 | Bird)
fm:   SameMate ~ BreedSuc1 + (1 | Bird)
      Df    AIC      BIC        logLik   Chisq  Chi Df   Pr(>Chisq)
fm1  2    48.659  52.946  -22.330
fm    3    50.342  56.771  -22.171 0.3174      1     0.5732

Now the weird thing:

I simply changed the coding of my covariate from "0,1" to "no, yes". Now,
only model fm1 gets the false convergence message:

fm<-lmer(SameMate~BreedSuc1+(1|Bird),family="binomial")
fm1<-lmer(SameMate~1+(1|Bird),family="binomial")

Warning message:
In mer_finalize(ans) : false convergence (8)

Data:
Models:
fm1: SameMate ~ 1 + (1 | Bird)
fm:   SameMate ~ BreedSuc1 + (1 | Bird)
        Df    AIC     BIC        logLik       Chisq Chi Df
Pr(>Chisq)
fm1   2     47.490 51.468   -21.745
fm     3     54.096 60.063    -24.048     0             1          1

a) Why is that so?
b) How can I fix the false convergence problem if my covariate has also a
binary format?

I would highly appreciate suggestions and ideas.

Cheers,

Julia

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