# How to go about nested random effects if model yields convergence problems?

I've built a mixed effects logistic regression model using glmer().

I'm trying to measure clause transitivity (2 possibilities: transitive/intransitive)

Each observation is a clause and clauses are nested within households and, in turn, socio-economic status. So those are my random variables, which -I understand- should be nested.

My fixed effects are word order, speaker (adult, child), addressee (target child, other participant) and language.

The formula looks like this:

Transitivity ~ order + speaker + addressee + language + (1|household/ses).

As a result I'm getting convergence problems I can't solve. So I was wondering, on a theoretical level, if I could treat 'household' and 'ses' as two non-nested random effects (as below). Or perhaps I should drop household as a random effect (supposing that ses variability is greater than individual household variability)?

Transitivity ~ order + speaker + addressee + language + (1|household) + (1|ses).

Other important info:

Number of observations: 2207

**Random effects

number of households = 24 (4 of ses1, 8 of ses2, 12 of ses3)

numbers of ses = 3 (ses1: 659 clauses, ses2: 576 clauses, ses3: 972 clauses)

** Fixed effects

levels of word order = 3

levels of speaker = 2

levels of language = 3 (language 1: 1562 clauses, language 2: 256 clauses, language 3: 389 clauses)

Thanks!

• I'm surprised that you're treating ses as a random effect. Can you explain why? I wouldn't think the levels of SES would be exchangeable ... – Ben Bolker Mar 11 at 15:26
• Ses and language are quite superimposed in the study -and in the world-. As some languages are indigenous, people who speak them are frequently low ses. As I want to single out the effect of language alone, and I'm not interested in the effect of ses, in this case I treated ses as a random effect. (3 out of 4 households in ses1 are indigenous, while 1 out of 12 households in ses3 is indigenous). – Leandra Mar 11 at 15:50

From the description, levels of household are nested within levels of ses. However, your model formula (1|household/ses) says the opposite - this says that ses is nested within household. Instead you would want:
(1|ses/household)

However, if ses really is the upper layer of nesting, then with only 3 of them, it makes no sense at all to fit random intercepts. You would be asking the software to estimate a variance for a normally distributed variable from only 3 observations.
ses should be a fixed effect here, provided that it is either a potential confounder (a cause of the outcome and exposures) or a competing exposure (only a cause of the outcome), and not a mediator, in which case the model should be:
Transitivity ~ order + speaker + addressee + language + ses + (1|household)