Measuring the Effect of Public Relations on Scientific Journals Impact Factor?

I’m looking at the correlation between communications outreach and a scientific journal’s impact factor/citations. I intern for a communications department at a University’s engineering school and we are trying to motivate more of our scientists to share their publications with us for media and press release. The biggest issue we have with convincing scientists to become interested in this is the lack of quantitative data that shows the benefit of us publicizing their journals. I’ve done some prior research and the most I could find was others acknowledging the lack of research done in this area and proposing that social scientists should look into this. Do you have any suggestions for further reading into this topic, either previous studies done, or potentially how to best go about this research on my own? Potentially what factors would be the most useful to compare between journal articles that we have/have not done press releases for, or if this would even be a useful measure?