What about a Netflix style pop-up when you click on the stars, suggesting users leave comments, or write a full review? Clicking on full review takes you to a page where you answer in-depth questions (like have you bought this) and leave comments (or questions are suggested for you to answer).
Some people will want to do a quick review, others will want to leave a comment, and still others will want to fully explain how it helped them or what they liked/disliked. This way you take into account various user participation levels with the app the user is reviewing. The final rating could be a weighted average of the three types of reviews, with in-depth and commented reviews being rated higher. Knowing your review will count more and be more important if you put more effort into it is another psychological tool to get people to write about the apps they care about.