The above posts answer the question about how to construct an ILR basis and get your ILR balances. To add to this, the choice of which basis can ease the interpretation of your results.
You may be interested in a partition the following partition:
(1) (sleeping,sedentary|physical_activity) (2) (sleeping|sedentary).
Since you have three parts in your composition, you will obtain two ILR balances to analyze. By setting up the partition as above, you can obtain balances corresponding to "active or not" (1) and "which form of inactivity" (2).
If you analyze each ILR balance separately, for instance performing regression against time-of-day or time-of-year to see if there are any changes, you can interpret the results in terms of changes in "active or not" and changes in "which form of inactivity".
If, on the other hand, you will perform techniques like PCA which obtain a new basis in ILR space, your results will not depend on your choice of partition. This is because your data exist in CLR-space, the D-1 plane orthogonal to the one-vector, and the ILR balances are different choices of unit-norm axes to describe the data's position on the CLR plane.
Hope this helps!
