Background: It is becoming increasingly common for individuals and organizations to use social media platforms such as Facebook. These are being used for a wide variety of purposes including disseminating, discussing and seeking health related information. U. S. Federal health agencies are leveraging these platforms to 'engage' social media users to read, spread, promote and encourage health related discussions. However, different agencies and their communications get varying levels of engagement. In this study we use statistical models to identify factors that associate with engagement. Methods: We analyze over 45,000 Facebook posts from 72 Facebook accounts belonging to 24 health agencies. Account usage, user activity, sentiment and content of these posts are studied. We use the hurdle regression model to identify factors associated with the level of engagement and Cox proportional hazards model to identify factors associated with duration of engagement. Results: In our analysis we find that agencies and accounts vary widely in their usage of social media and activity they generate. Statistical analysis shows, for instance, that Facebook posts with more visual cues such as photos or videos or those which express positive sentiment generate more engagement. We further find that posts on certain topics such as occupation or organizations negatively affect the duration of engagement. Conclusions: We present the first comprehensive analyses of engagement with U. S. Federal health agencies on Facebook. In addition, we briefly compare and contrast findings from this study to our earlier study with similar focus but on Twitter to show the robustness of our methods.