Facebook provides extensive analytics to page administrators. With your Insights Page, you can track over time the following metrics: total fans, unsubscribers and resubscribers, new and removed fans, top countries, age and gender demographics, page views, media (photo, audio, and video) consumption, interactions (total number of comments, wall posts, and likes), post quality, click-through and engagement rates, discussion posts, and reviews.
YouTube also offers comprehensive statistics about your channel as well as each of the videos you upload. With YouTube Insight, you can measure views, unique viewers, relative popularity for all your videos, top videos by percentage of total views, age and gender demographics, and community engagements (total number of ratings, comments, and favorites). All these metrics can be filtered by geographical area (countries and regions). YouTube also provides two other specific metrics for every video: discovery (a breakdown of the source of views) and hot spots (ups and downs of viewership compared to other videos of the same length).
The only metric Twitter makes available to every account holder is the number of followers, followings, and tweets published since the beginning. Several third-party applications like TweetDeck will help you keep track of mentions (retweets and @ replies). You can also use the Twitter search engine, but you will need to do it on a regular basis. In both cases, it’s important to keep track of your results. If you want to compare your institutional account with that of your peer institutions, try using Twitter Grader, which gives a “grade” when you submit the name of an account.
LinkedIn Groups only provides a few metrics, including the number of members, new members, new discussions, and news postings for the last seven days. You will have to keep track of these metrics beyond that point, as no historical data is available.