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I know there is a question that asked about a similar warning, but that user's "error" had to do with dummy coding while I think my problem has to be with statistical power and understanding random intercepts. I am attempting to run a binary logistic mixed model regression but I keep running into the "this parameter is redundant" error. This is the model:

  • Presence vs absence (dependent)
  • By ploidy (fixed: 3 variations)
  • Treatment (fixed: 2 variations)
  • Interaction of ploidy by treatment
  • Lineages (random: 10 variations) nested within ploidy
  • One covariate.

Every time I run the model, SPSS leaves the residual effect and random effect tables blank excluding the random intercept. SPSS states that lineage is redundant. I took a look at my covariance parameter summary and I simply think there is not enough power to run a random effect in addition to all the fixed effects. My sample size is $n=99$. I am also a little lost about the random intercept. Is there a possibility that the lineage intercept is almost exactly like the random effect intercept?

Below are a few of my results - please let me know what you all think. I can also easily attach my data if you are interested.

Covariance Parameters Summary

Residual Effect table

Random effect table

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I don't know the particulars of SPSS with respect to mixed models, but I do know that the output seems to convey what is normal in mixed models with poorly fit random effects structures. I believe your suspicion is correct. It seems your random slope here has close to zero variance, which is likely why it is flagged as redundant. Because of that, its possible that your model is singular and not interpretable. This is a common problem with mixed models not converging (Matuschek et al., 2017).

You could instead try to fit it with a random intercepts-only model instead and see if the model converges, giving you sensible output. It would also help to plot your data to see why the model is behaving this way. Often scatterplots will paint a clearer picture. It could also be that your data is simply coded wrong somewhere here, so it wouldn't hurt to look there as well.

As a side note, you mentioned that you have a sample of $n=99$. Given you are fitting three main effects and one two-way interaction, it may be possible that even with a random effects model you will have a hard time observing a statistically significant effect if it indeed exists (see Gelman et al., 2022, which discusses that large sample sizes are needed for interactions).

References

  • Gelman, A., Hill, J., & Vehtari, A. (2022). Regression and other stories. Cambridge University Press.
  • Matuschek, H., Kliegl, R., Vasishth, S., Baayen, H., & Bates, D. (2017). Balancing Type I error and power in linear mixed models. Journal of Memory and Language, 94, 305–315. https://doi.org/10.1016/j.jml.2017.01.001
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  • $\begingroup$ To clarify, are you suggesting that I ran essentially the same model but the minor change would be removing lineage, but keeping the random intercept in? I don't mind giving any option a go to hopefully diagnose the problem. $\endgroup$
    – bribina
    Commented Nov 21, 2023 at 23:00

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