Reporting Linear Mixed Effects Models (LMM)

Question

I'm trying to report the difference between the inclusion and exclusion of a site type (i.e. restored habitat/natural habitat). I have done linear mixed effects models and have done an anova showing that for species richness there is a sig. difference between the inclusion of site type, whereas for abundance there is no sig difference.

I'm reporting the anovas with chi-squared, df, and p-value. But how do I actually report the model so you know which of the site types was better. Is it acceptable to just report the mean and CI? Or is there a more normal practice for reporting the models?

I'm trying to follow a similar style to this paper : Gray, C. L. et al. Local biodiversity is higher inside than outside terrestrial protected areas worldwide. Nat. Commun. 7:12306 doi: 10.1038/ncomms12306 (2016).

However, with my data set I am unable to calculate differences for each site to then average them out with CI.

(Note I have to use p values because I have very little data so I can't use AIC and the ajusted AIC package in R (cAIC4 for lme4 models) doesn't work with 0 variance explained by random effects which sometimes mine has because of the hierarchical structure of the model)

Answer 1

Aside from what you've described, I would say that it is standard practice to report

1) The coefficient values. I find plotting these to be better than listing them in tables, but either is fine. Reporting these values lets the reader know which site type is better.

2) The variance terms. This is so you can infer how much of the variance is explained by the random effects. You can use marginal and conditional R^2 (Nakagawa & Schielzeth 2013) for this comparison as well.

3) Finally, if you have a small number of sites, it's helpful to report the site-level intercepts (and slopes, if relevant). This could again be in a plot or table - but ideally both.

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Aside from these general recommendations, I'd like to respond to a couple of your final statements:

a) However, with my data set I am unable to calculate differences for each site to then average them out with CI.

This is hard to understand and doesn't entirely make sense as written.

b) Note I have to use p values because I have very little data so I can't use AIC and the ajusted AIC package in R (cAIC4 for lme4 models) doesn't work with 0 variance explained by random effects which sometimes mine has because of the hierarchical structure of the model

This sounds like your model is improperly specified. I would check this carefully before proceeding.

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Nakagawa, S. & Schielzeth, H. (2013) A general and simple method for obtaining R2 from generalized linear mixed effects models. Methods in Ecology and Evolution, 4, 133–142.