Analytics work in soccer has tended to focus on the performance of teams and players, but it is inevitable that attention would turn to match referees.  Assessment of referee performance — especially concerning  specific referees — is extremely important not only to the leagues and the teams, but also (let's admit this) to gambling interests.  For a variety of reasons, from sensitivity to competitive advantage, access to these results is highly restricted.

This article on the BBC Sport website surveys the manner in which English Premier League referees are themselves judged, from conventional means with match assessors to more analytical approaches with assistance from sports data collection companies like Prozone and Opta.  There are some supporters who have compiled data on referee performances in their team's matches; one example is the Untold Arsenal site (agree with their conclusions or not, the articles are worth reading).

Referee analytics is an area of work that will continue to attract attention, but it's very possible that there will be substantial differences in results obtained by fans and insiders because of lack of access to finely-detailed data.