It seems like your 3rd party extension
CiviCRM caused this installation issue, this is what it return that error message.
<b>Fatal error</b>: Uncaught Exception: API error: Mandatory key(s) missing from params array: name_b_a in /home/blueribbon/public_html/administrator/components/com_civicrm/civicrm/CRM/Core/ManagedEntities.php:456
Stack trace:
#0 /home/blueribbon/public_html/administrator/components/com_civicrm/civicrm/CRM/Core/ManagedEntities.php(234): CRM_Core_ManagedEntities->onApiError('RelationshipTyp...', 'create', Array, Array)
#1 /home/blueribbon/public_html/administrator/components/com_civicrm/civicrm/CRM/Core/ManagedEntities.php(179): CRM_Core_ManagedEntities->insertNewEntity(Array)
#2 /home/blueribbon/public_html/administrator/components/com_civicrm/civicrm/CRM/Core/ManagedEntities.php(141): CRM_Core_ManagedEntities->reconcileEnabledModule(Object(CRM_Core_Module), Array)
#3 /home/blueribbon/public_html/administrator/components/com_civicrm/civicrm/CRM/Core/ManagedEntities.php(122): CRM_Core_ManagedEntities->reconcileEnabledModules()
#4 /home/blueribbon/public_html/administrator/components/com_civicrm/civicrm/CRM/Core/Invoke.php(395): C in <b>/home/blueribbon/public_html/administrator/components/com_civicrm/civicrm/CRM/Core/ManagedEntities.php</b> on line <b>456</b><br />
Once i temporary disabled these CiviCRM extension/plugins from your site backend, then that installation work fine now.
By the way, i already help you re-enabled back those CiviCRM extension/plugins on your site, can you give it a check is it all work fine now?