Yii CDbCriteria and Model->findAll, how to add custom column?

I have a calendar app in Yii where I store events per user. I'd like to dynamically build a title for each event.

This code is in my controller:

$criteria = new CDbCriteria;
$criteria->select = array('all_day','end','id','start');
$criteria->condition = 'user_id ='.$user->id;
$events = Calendar::model()->findAll($criteria);
foreach($events as $event) {
  $event->title = 'test title';
}
echo CJSON::encode($events);

In my Calendar model, I've added a new property called $title:

public $title;

But then when I go to echo the JSON, title doesn't show up...

[{"all_day":false,"end":"-948712553","id":"2","start":"-146154706"}]

What do I need to do to add title to the JSON result set?