I am working with a colleague who wants to include a term in our linear mixed effect model that is also an individual component of a scale that we constructed and have in our model (both as predictors). For example, it's something like this:
d1 <- data.frame(A=rnorm(100),
B=rnorm(100),
C=rnorm(100),
G=sample(LETTERS[1:4], replace=TRUE, 100))
d1["D"] <- rnorm(100) + d1$C
fm <- lmer(A ~ B + C + D + (1 | G), data=d1)
This does not feel right, but I don't know exactly why and I can't convince my colleague of that, particularly because the inclusion of both the scale and the component of the scale yields a much more interesting model than either of them alone... Making it even more difficult to convince my colleague, I calculated the variance inflation factor of models containing both the constructed scale and the component, and the values were all less than 2.3 (although the correlation between the terms is relatively high).
Am I correct that building a model in such a fashion is inadvisable? If yes, could someone explain why it's inadvisable so I can convince my colleague that we should not do it?
(I should also note that the actual constructed scale has 18 components and the model has 8 predictors in total).
