How to interpret r2m and r2c in a LMM (R)?

Question

I am quite unsure how to interpret the r2c and r2m results from a linear mixed model that measures the effect of size and beta on debt ratio on some companies.

The model looks like this:

lmmodel <- lmer(Debt_ratio ~ size + Beta_value + (1|company), data = df). 

Using the r.squaredGLMM function I get the following output:

R2m       R2c
0.02457679 0.5501743

As I have understood it, R2m tells you how much of the fixed effects (size and beta) explain the variance in Debt_ratio. However, I am unsure how to interpret the R2c value once the random effects is included (the companies). I've tried to look at other threads / sites, but I am still not sure what it tells me.

Answer 1

The substantial difference between R2m and R2c suggests that the random effects account for a large portion of the variance in debt ratio. This means that the company-specific variations have an impact on the debt ratio. In practical terms, if you’re looking to predict debt ratio, including the random effects of companies in your model adds a significant amount of explanatory power. This is why the R2c is so much higher than the R2m. And the very low R2m suggests that the fixed effects (in your case, size and Beta value) do not have much explanatory power on their own. Hope this helps!