On LinkedIn, it's relatively easy to derive relationships between other people.
For example: if I'm looking at a page for someone working at Company X with title Manager of Customer Service, and I see that another person from Company X with title Customer Service Representative has left them a recommendation, it's easy to take the recommendation in the supervisor/employee context.
Further, it's very common in LinkedIn recommendations to explicitly mention relationships. For instance, you might see,
While I was a Customer Service Rep on Bill's team at Company X, I enjoyed working for him because...
In the traditional context, a formal "recommendation" is usually given from a position of authority. However, LinkedIn is a much less formal environment, and it's very common (and useful) for recommendations to come from a wide variety of perspectives - supervisors, subordinates, clients, vendors, and so on. It's also common to request and collect a large number of recommendations, versus formal recommendations, where you'd typically only gather a few.
This provides value by presenting the individual from a variety of perspectives, which speaks more to the big picture than a formal recommendation can. In other words, You're not any more or less qualified to do this than anyone else in this person's network.
All that said, if you do write the recommendation, it's best to:
- Be Brief. LinkedIn recommendations are typically a few sentences, maybe two paragraphs.
- Be specific. Call out the specific behaviors or traits about this person that stood out to you and made an impact on your relationship.
- Be honest. Don't consider your recommendation only in the context of being positive or negative, just be honest about the person.