First you need to categorize activities into mutual exclusive groups and sub groups. then you can count members of activities in each group or sub groups. Then you need to compute proportion of income generated from different activities in group or sub group. Final use inverse simpson index for calculating diversity index.
Your selection of accurate diversification index can be decided by your definition for the term diversification, and the reasons for households to diversify. Diversification can be defined in different ways. Usually, diversification focuses on the number of income sources and the balance among them. Different methods have been used to quantify the magnitude of diversification. These include: (i) Herfindal Index, (ii) Simpson Index, (iii) Ogive Index, and (iv) Composite Entropy Index.
To choose the appropriate index, first, the researcher has to identify the reasons for households to diversify their livelihood/income sources.
Since livelihood is more than income… Here, you have to be careful on using the terminologies – livelihood and income.