I have a dataset where rows are individuals and I want to measure the magnitude of the change in the distribution of their spending from year to year.
So for Person A:
T1 his values are: 30% A 30% B and 40% C
T2 his values are: 90% A 5% B and 5% C
I want to create a measure that will indicate the magnitude of the change that takes into account the change in proportion for each category.
EDIT Added more details below:
I have data for around 80K observations and 15 time points for each observation. Essentially I want to identify meaningful deviations in their spending behavior. So, to start, I figured I would need calculate the change from t1 to t2. Later, I except I will have to look at longer periods, but for right now I wanted to keep it as simple as possible
I'm using this measure as a way to gauge an individuals priorities in terms of how they allocate their money. So if someone who has allocated just 10% of their spending on Category A in T1 but then it becomes 90% in T2. This is more meaningful to me then a person to goes from 70% to 90% during the same time period. I know I could look at simple percent change for each category, but I wasn't sure if there was a more robust way to identify how large the change in behavior is across all of the categories