I am running a linear mixed effects model in which three of the regressor are inherently related. For sake of conceptual example: let's say I would like to see how the relative time employees arrive at work each day (early vs. late vs. exactly on time) influences their annual performance rating, over several years. Per year I have five pieces of data about each employee: the employee name, the performance rating, the percentage of days they arrived early, the percentage of days they arrived late, and the percentage of days they arrived exactly at 5pm.
The mixed model, accounting for the random effect of employee over multiple years/observations, would therefore be:
rating ~ PercentageEarly + PercentageLate + PercentageOnTime + (1|Employee)
Of course, these three fixed regressors are inherently related, as they together add up to 100 for each case observed. And indeed, when running this through
lme4 package in
R, the third regressor is dropped due to rank deficiency.
Obviously this would be a non-issue if only dealing with two such regressors. However, with three, how might the relative impact of each be considered, with separate coefficients? Alternatively, if only given a coefficient for the first two regressors (the current scenario), how might I interpret the relative impact of the third?
Apologies if this has been covered elsewhere; I wasn't sure of the exact terminology for describing such inherently related regressors and in turn may have missed a relevant posting.