Packaging SQL Server Express 2012 install won't install due to user rights Is there a way force the above permission window to elevate the user permissions?
It may be that you do not have enough rights granted for your installation.  See: 

SQL Server installation fails if the Setup account does not have certain user rights

Partial comments under Cause: 


  This behavior is by design. In addition to adding the user account
  that is running the Setup as a local administrator, the Setup user
  account requires the following default user rights for the Setup to be
  completed successfully


 -  Local Policy Object Display Name    User Right     
 -  Backup files and directories        SeBackupPrivilege  
 -  Debug Programs                      SeDebugPrivilege  
 -  Manage auditing and security log    SeSecurityPrivilege


Also review the comments at:

InstallShield Limited Edition
 The Install Shield link also suggests ClickOnce Security and Deployment.
 Install SQL Server 2012 from the Installation Wizard (Setup)

If you do not have enough privileges then you probably need to either (1) pursue the extra privileges or (2) have someone with those privileges handle the install.