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We have fitted a linear mixed model to the data of a split-plot design with 2 factors (between: condition.t - 3 levels; within: SM.blockDiff - 2 levels). As there were in total 6 measurements per person (person ID: VP), we also wanted to include a time polynomial time factor (blockID.c).

The model was fitted in R using the mixed method from the package afex which is essentially a wrapper around lmerTest/lmer. This fit worked without problems or warnings.

model <- mixed(quest ~ factor(blockID.c)  * condition.t * SM.blockDiff + (poly(blockID.c, 4)|VP), data=df)

We now wanted to perform a post-hoc power-analysis on the interaction term of condition.t * SM.blockDiff using the powerSim method from the package simr. This was done with the following call:

power <- powerSim(model$full_model, test = fcompare(~ condition.t+SM.blockDiff, "kr"), nsim=200)

During progression of the simulation multiple warnings about singular fits appeared and the print of this power calculation also lists that:

> power
Power for model comparison, (95% confidence interval):
      54.50% (47.33, 61.54)

Test: Kenward-Roger (package pbkrtest)
      Comparison to ~condition.t + SM.blockDiff + [re]

Based on 200 simulations, (165 warnings, 0 errors)
alpha = 0.05, nrow = 288

Time elapsed: 0 h 12 m 29 s

nb: result might be an observed power calculation

When calling the warnings from the result, these are full of messages like this:

> head(power$warnings)
    stage index                                                                         message
1 Testing     1                   Model failed to converge with 1 negative eigenvalue: -1.9e-01
2 Testing     2 Model failed to converge with max|grad| = 0.00668068 (tol = 0.002, component 1)
3 Fitting     3  Model failed to converge with max|grad| = 0.0053056 (tol = 0.002, component 1)
4 Testing     3                   Model failed to converge with 1 negative eigenvalue: -1.3e-01
5 Testing     4                   Model failed to converge with 1 negative eigenvalue: -9.7e-04
6 Fitting     5                   Model failed to converge with 1 negative eigenvalue: -4.9e-02

I know about "regular" singular fits in LMMs and how to interpret or avoid them, however I'm unsure what to make of them in this case.

Do I need to worry about them or can I just ignore them and trust the results? This official vignette also seems to have singular fits however does not mention them. Also the singular fits there don't seem to show up on the printed summary.

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Do I need to worry about them or can I just ignore them and trust the results?

Yes, you need to worry about them. Those don't look like singular fit warnings - more like convergence warnings. That is the models have not converged, unlike a singular fit where the model converges, usually to boundary on the parameter space such as a zero variance or +1 or -1 correlation.

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  • $\begingroup$ Sorry for the late reply. I actually asked the package author about the problem and got confirmation that those warnings are rather serious: github.com/pitakakariki/simr/issues/169#issuecomment-654482182 $\endgroup$
    – Dom42
    Commented Aug 26, 2020 at 11:15
  • $\begingroup$ Thanks for the link. That's pretty much what I thought ! $\endgroup$
    – Robert Long
    Commented Aug 26, 2020 at 11:43

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