How do we track attribution on products that our app has helped a merchant sell?

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We have an app that is an interactive personalized recommender and we are working on an attribution report for our merchants to show them the conversion uplift we bring them. We can track events from customers interacting with our widget but we need to figure out how we can attribute a customer completing a purchase from a product we showed them?  We have seen this sort of reporting in many apps and we are wondering how you all did it?