Multilevel model using glmer: Singularity issue

Question

I'm using R to run a logistic multilevel model with random intercepts. I'm using the frequentist approach (glmer). I'm not able to use Bayesian methods due to the research centre's policy.

When I run my code it says that my model is singular. I'm not sure why or how to fix the issue. Any advice would be appreciated!

More information about the multilevel model I used:

I'm using a multilevel modelling method used in intersectionality research called multilevel analysis of individual heterogeneity and discriminatory accuracy (MAIHDA). The method uses individual level data as level 2 (the intersection group) and nests individuals within their intersections.

My outcome is binary and I have three categorical variables as fixed effects (gender, martial status, and disability). The random effect (level 2) is called intersect1 which includes each unique combination of the categorical variables (gender x marital x disability).

This is the code: MAIHDA_full <- glmer(IPV_pos ~ factor(sexgender) + factor(marital) + factor(disability) + (1|intersect1), data=Data, family=binomial, control=glmerControl(optimizer=”bobyqa”,optCtrl=list(maxfun=2e5)))

Just curious. Why does your research center ban Bayesian methods? — hyena, Jan 12 '22 at 03:22
The following post may help https://stats.stackexchange.com/questions/378939/dealing-with-singular-fit-in-mixed-models — hyena, Jan 12 '22 at 03:25
Goodness me I cannot imagine working somewhere that bans Bayesian analysis! — user438383, Jan 12 '22 at 11:28
@hyena It's because the Bayesian package calls other packages from the internet, and we don't have access to the internet in the research centre for privacy reasons. — bella1998, Jan 12 '22 at 16:33

score 2 · Accepted Answer · answered Jan 12 '22 at 11:26

The usual reason for a singular fit with mixed effects models is that either the random structure is overfitted - typically because of the inclusion of random slopes, or in the case such as this where we only have random intercepts, then the variation in the intercepts is so small that the model cannot detect it.

Looking at your model formula I suspect the issue is:

The random effect (level 2) is called intersect1 which includes each unique combination of the categorical variables (gender x marital x disability).

If I have understood this correctly, the model is equivalent to:

IPV_pos ~ sexgender + marital + disability + (1 | sexgender:marital:disability)

It is likely that any variation in sexgender:marital:disability is captured by the fixed effects, leading to near-zero variation in the random intercepts.

I suspect you will find almost identical results if you don't use any random effect.

Thank you so much for your help! That makes sense. – bella1998 Jan 12 '22 at 16:32 — bella1998, Jan 12 '22 at 16:32

Multilevel model using glmer: Singularity issue

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