You will find in this directory, a log file for each Shinken daemon :
and an other more global :
Note : there is a daily rotation of log files (for X days by default but you can edit this in configuration ?).
Those files are also in this directory and they are suffixed with a date like this : arbiterd.log.2015-09-02
To launch Shinken in debug mode :
service shinken -d [debug level] restart
or
service shinken-[daemon name] -d [debug level] restart