Can I use "continuous" random effects in this instance?
I have the following lmer model:
m1 <- lmer(V1 ~ V2 + V3 + V4 + V5 * V6 + (1|V7) + (1|V8) + (1|V9), data = data)
V1 is resultant mean error (continuous between 0 and 1)
V2 is categorical (three categories)
V3 is categorical (binary)
V4 is categorical (three categories)
V5 is categorical (five categories)
V6 is categorical (binary)
V7, V8 and V9 technically represent continuous data (which could sensibly have any value between 0 and 1) but for this study have been forced to represent fixed values in the format of V7 = {0.55, 0.1 … 0.95}, V8 = {0.05, 0.1 … 0.45} and V9 = {0.05, 0.1 … 0.95}
They are included in the lmer as crossed random effects, as V7, V8 and V9 do not have hierarchy, but they are distinct groupings of values.
I would like my model to tell me how the specific variance of V7, V8 and V9 contributes to the structure of my model. I do get a sensible output from the specification above (e.g. I can see that 76% of the variance is explained by something else, and 11% by V8) BUT using continuous random effects is not best practice.
Random effects:
Groups Name Variance Std.Dev.
V9 (Intercept) 0.004028 0.06347
V7 (Intercept) 0.001120 0.03346
V8 (Intercept) 0.004406 0.06638
Residual 0.030254 0.17394
Number of obs: 120000, groups: V9, 10; V7, 5; V8, 5
Overall, I'm seeking help on whether there are better ways to model my data.
(For my study, ignoring the continuous nature of V7 - V9 is reasonable. I don't care that each value of V7 has a biological meaning.)
