Static helper function to set a property on another object
I would argue that setTimestampRadioButton can be improved in three ways.


Side effects. By mutating the passed dataModelObject, the function immediately makes any function that uses setTimestampRadioButton harder to understand as it magically sets a property name that the calling function did not specify. 
Typing. Mutating the argument the function forces you to create a Partial&lt;IDataModel&gt; (or cast an object which is not an IDataModel to IDataModel). This is not ideal. 
Alternative property names. Currently only IDataModel uses the format from a RadioButton, what happens when ITimeModel needs the timestamp format stored in a format property? We are now back to the original problem.


I would instead recommend creating a method to get the expected format. 

public static getTimestampFormat(radioControl: RadioButton): IFormat {
    if (radioControl.value() === 1) {
      return { format: "foo" };
    } else if(radioControl.value() === 2) {
      return { format: "bar" };
    }
    return { format: 
}


This simplifies your generateDataModel method even more. 

public generateDataModel(): IDataModel {
  return {
    name: this._name.value(),
    type: this._type.value(),
    timestamp: Helpers.getTimestampFormat(this._radioControl)
  };
}


Instead of a static helper method, you might also consider adding the method as an instance method of the RadioButton class, or creating a child of the RadioButton class with a TimestampRadioButton class. 

A couple other general things: 


Avoid casting like the plague. It is almost as bad as using the any type as it hides potential problems in a very similar way. 
I can't think of any instance in which adding Object or data to a variable name makes it more descriptive. dataModelObject doesn't really tell you any more than model.