For a really basic analysis of this question, we might look to a person's identity within a family structure and examine how this affects a person's sense of self. This can be very similar to the example pointed above by litteacher8.
Outside of being a grandparent, we can see important and definitive status issues related to whether or not a person has siblings and, if so, where that person stands in the age order.
For instance, if you have a younger sibling ten years younger than you are, this "structural" family relationship will likely have a deep impact on how you define yourself. Your responsibilities, your values and the lessons you learn will be shaped significantly by the fact that you have a younger person to watch out for and take care of as you grow up.
Considering roles, we might look at the various expectations placed on individuals regarding gender. Females and males experience the world differently, to some degree, as a result of gender roles and gender-oriented identity concepts. This difference in experience can be seen as both a cause and effect of identity formation/self-hood.