The authors of the lme4-package give some recommendations how to deal with singular fits, though they mention that there's no gold-standard:

Here's what they suggest when you have singular fits (note that these recommendations are partly going into opposite directions):

- avoid fitting overly complex models, such that the variance-covariance matrices can be estimated precisely enough (Matuschek et al. 2017)

- use some form of model selection to choose a model that balances predictive accuracy and overfitting/type I error (Bates et al. 2015, Matuschek et al. 2017)

- “keep it maximal”, i.e. fit the most complex model consistent with the experimental design, removing only terms required to allow a non-singular fit (Barr et al. 2013)

Bates D, Kliegl R, Vasishth S, Baayen H. Parsimonious Mixed Models. arXiv:1506.04967, June 2015.

Barr DJ, Levy R, Scheepers C, Tily HJ. Random effects structure for confirmatory hypothesis testing: Keep it maximal. Journal of Memory and Language, 68(3):255–278, April 2013.

Matuschek H, Kliegl R, Vasishth S, Baayen H, Bates D. Balancing type I error and power in linear mixed models. Journal of Memory and Language, 94:305–315, 2017.

Nice grab from the manual, I get alot of this when fitting multistage nested random effects. Just use the estimates and move on...

Leonhard Kratzer you are right! I should have included my code. Here it is in a .txt

model1

Leonhard Kratzer Hi, thank you again! Clutch is a categorical variable with two levels: first clutch and second clutch of egg. Yes, nest identifies the units where my individual samples are included.

I will write some background down, hopefully it will help you understand the design.

I work with wild birds to see the effect of living in noisy environments on some oxidative stress parameters. For this, we took a blood sample for each of the nestlings of each nest to do the laboratory stuff. Because of the limited blood sample, some oxidative stress parameters couldn't be measured for every nestling.

I must highlight that some oxidative stress parameters have a smaller N because we couldn't perform all oxidative assays for every nestling.

Could it be possible that 'singular fit' appeared when there are many nests with only one nestling?

Good to see it is not a big problem! Thank you again. I am not an English speaker, so sorry if it is been hard to understand

Leonhard Kratzer Nest is treated as a random variable because birds belonging to the same nest are not independent between themselves. The thing is that I have to used nest as a random variable and I get that singular fit.

Yes, I dropped some non-significant variables from the model and ran them again and I still get that singular fit message.

Leonhard Kratzer Yes! It is exactly that. In ecology, when comparing birds of different nests, nest should be included as a random variable because birds belonging to the same nest are more similar between them, so you want to control that. N = 114 and nests are 46.

Thank you!!

The authors of the lme4-package give some recommendations how to deal with singular fits, though they mention that there's no gold-standard:

Here's what they suggest when you have singular fits (note that these recommendations are partly going into opposite directions):

- avoid fitting overly complex models, such that the variance-covariance matrices can be estimated precisely enough (Matuschek et al. 2017)

- use some form of model selection to choose a model that balances predictive accuracy and overfitting/type I error (Bates et al. 2015, Matuschek et al. 2017)

- “keep it maximal”, i.e. fit the most complex model consistent with the experimental design, removing only terms required to allow a non-singular fit (Barr et al. 2013)

Bates D, Kliegl R, Vasishth S, Baayen H. Parsimonious Mixed Models. arXiv:1506.04967, June 2015.

Barr DJ, Levy R, Scheepers C, Tily HJ. Random effects structure for confirmatory hypothesis testing: Keep it maximal. Journal of Memory and Language, 68(3):255–278, April 2013.

Matuschek H, Kliegl R, Vasishth S, Baayen H, Bates D. Balancing type I error and power in linear mixed models. Journal of Memory and Language, 94:305–315, 2017.

One issue with the recent lmer warnings is that there are times when a small or zero variance is not that surprising, and you'd rather just stay with the model and say 'how big?', with maybe a profile likelihood to give a possible range for your variance. That's particularly true when you're looking at a number of features or materials, some of which may not be homogeneous but most are. At those times, it's kind of annoying when you get a message that essentially forces you to drop a term you'd like to have an interval on. Being told 'singular fit' in those circumstances is like going to a GP for a close-out checkup on a sprained wrist and being told you may need your arm amputated to make sure it doesn't heal badly. You could, but it's not likely to be the best answer and it sure causes a lot of alarm.

The warning just indicates that one or more variances are (very close to) zero, nothing less and nothing more. The only thing changed in this regard is that lme4 now explicitely warns the user, but you're not "more forced" to drop a term than before.