I'm analysing some user activity data for a social networking website. For each user, I have indicators of activity such as:
- number of visited pages
- number of comments
- number of shares
- number of likes
- number of friends
All the variables are simple counts, with no categorical data. Now, I would like to come up with a single "activity index" that captures the overall user activity. Clearly, I could use a simple mean of these variables, but, as is reasonable to expect in this context, many of them are highly dependent (e.g. people who comment a lot tend also to visit a lot of pages, etc.). To do so, I scaled the variables, and then ran a PCA, which found the following components:
Importance of components:
Comp.1 Comp.2 Comp.3 Comp.4 Comp.5
Standard deviation 1.5586900 1.1886741 0.8548985 0.48575879 0.43672236
Proportion of Variance 0.4859029 0.2825892 0.1461703 0.04719232 0.03814528
Cumulative Proportion 0.4859029 0.7684921 0.9146624 0.96185472 1.00000000
It seems clear that there are two important components here, so I can't use only the first one as the index.
How would you approach this problem to obtain a suitable activity index that takes variable dependency into account?
EDIT: Would a linear combination of PCA components weighted on the proportion of variance be wrong?
Thanks for any feedback.