I'm assuming you are running recent version of ubuntu or a distribution based on upstart. You can check /var/log/daemon.log for errors.
The standard su takes the syntax su [options] [username]. Checkout man 1 su. You might want to try :
su -c "myCommand" anotheruser >> "myLogfile.log"
Also, a couple of things would happen (mostly not desirable)
myLogfile.log would be owned by root.
myLogfile.log would be created on / (root directory) if you don't use an absolute path like /tmp/myLogfile.log (because upstart runs with pwd set to /).
If you want the file to be owned by anotheruser you might switch the command to.
su -c "myCommand >> /tmp/myLogfile.log" anotheruser
This might cause problems if you have leftover myLogfile.log owned by root from earlier runs or if have not changed myLogfile.log to something like /tmp/myLogfile.log (normally, regular users can't create files on root dir /).
cron, i.e. acrontab@rebootentry, I suppose. (Output will be sent via mail.)sudo -u someuser bash