I have read in several answers to questions on this site that the best way to choose the random structure for a mixed effects model is by using theoretical knowledge. On the other hand I have also read the advice in Barr et al (2013) to “keep it maximal”, that is, to fit the maximal random structure by including all fixed effects, including interactions, as random slopes. However, this seems to often lead to models which either won’t converge, or do converge, but with a warning of a “singular fit”. In the accepted answer to [this] (Is a singular fit with no correlations near +/- 1 or variances of zero, a false positive in lme4) question it is stated that singular models should be simplified.

But how is this done when the reported correlations are not near +/-1 and there is no theoretical knowledge to help choose.

An example would be much appreciated.