It is best to have the route distance between ports, the size of the shipping alliance market, direct service, the number of ships owned by the shipping alliance and the congestion of ships in the port.
It seems to be that you will end in real Big Data crunching, as none of such data is available just off-the-shelf for free. Most of your variables could be gathered just by collecting AIS data of container vessels (aka the beacon signals of the vessels used for identification and anti-collision purposes), crowd founded by a couple organizations, including MarineTraffic / Kpler, VesselTracker etc. and further distributed by EIKON etc.. By this you can obtain route distances, direct services, port congestion based on the traces of vessels from the past employed by services operated by liner shipping companies. In order to identify ownership of vessels you need access to some ship register, as on average about 50% of vessels are owned by liner shipping companies and the rest by so-called non-operating vessel owners - may the ownership of vessel does not matter but who operates it and puts it on a certain service. Finally, when it comes on alliance membership, this may be the most easy data to gather, but then you have to count vessel by vessel to get the aggregated figures you want to have... By the way, this is the approach most consultancies in the shipping industry make their market analysis today...