Need to switch between lookup field types, and radio button not working with lookup field

Need to switch between lookup field types, and radio button not working with lookup field

The options for a lookup field display type are 

Dropdown
Radio Button
Multi Select
Checkbox

Once the field is created, how do I change between types. 

Also, when I select a radio button in a lookup field, it is displayed as a dropdown and not a radio button.  How can this be fixed?

Thanks