Label names within Manipulate with ControlType->RadioButton

Question

I modified an example from the documentation to have a RadioButton control over a specific list of values:

Manipulate[Plot[Sin[a x + b], {x, 0, 6}], {{a, 2, "Multiplier"}, {1, 2}}, {{b, 
   3, "Phase Parameter"}, {3, 4, 5}}, ControlType -> RadioButton]

However, in place of 1, 2, 3, etc. I'd like textual labels (but still need to pass those specific, discrete numeric values to the object inside the Manipulate).

In the spirit of the Multiplier textual label, I tried

Manipulate[Plot[Sin[a x + b], {x, 0, 6}], 
  {{a, 2, "Multiplier"}, {{1, "cat"}, {2, "dog"}}}, 
  {{b, 3, "Phase Parameter"}, {3, 4, 5}}, ControlType -> RadioButton]

to no avail:

How do I get the appearance (and behavior) here that I am after?

Answer 1

You can use RadioButtonBar which allows labeling of the values:

Manipulate[Plot[Sin[a x + b], {x, 0, 6}], 
 {{a, 1, "Multiplier"}, {1 -> "cat",  2 -> "dog"}}, 
 {{b, 3, "Phase Parameter"}, {3, 4, 5}},  ControlType -> RadioButtonBar]

or

 Manipulate[Plot[Sin[a x + b] /. {"cat" -> 1, "dog" -> 2}, {x, 0, 6}], 
  {{a,  "cat", "Multiplier"}, {"cat", "dog"}}, 
   {{b, 3, "Phase Parameter"}, {3, 4, 5}}, ControlType -> RadioButton]