$model … The model that is related with the form. It is usually a “Form-Only” model, not an ActiveRecord model backed by a db table.
$attribute … The attribute that will get the selected result. It must be an array, because the checkbox list handles an array.
$items … The checkbox items. It must be an array of '$value => $label' pairs. $label is used to render the checkbox label, and $value will come into the array of $attribute when it is selected.
You have an errors in passed params to the map() function.
At first, swap $notificationtype and $notification. It should looks like: Html::activeCheckboxList($notificationtype, 'dropbox', ArrayHelper::map($notification, 'text','type')).
Use pluralized names for arrays or any other collections. not $notification, but $notifications
The second error is pointing incorrect key in map() function(it is the second parameter). It MUST be a column with type an integer.
E.g, let’s assume, in NotificationType model you have attribute like id(it is your primary key in the related table), so id must be passed as the second parameter, and third parameter may be type or text.
something like this: <?= Html::activeCheckboxList($notificationtype, 'dropbox', ArrayHelper::map($notification, 'id','type')) ?>