I have theoretical* solution building off Paulpro's answer above that uses the uniqueness property of Set to filter a list of element names from JQuery:
var radioNames = new Set(Array.from($('input:radio').map(function() { return this.name } )));
var inputGroupCount = radioNames.length;
if( $('input:radio:checked').length < inputGroupCount){
// At least one group isn't checked
}
This uses the map() function to extract the name attributes from the radio groups. This is then converted to an Array, which is used as the constructor argument for Set.
Unfortunately, as of April 2016 there is no support for Set(iterable) and Array.from() in IE; Opera and Safari have limited support.
If you can ensure your users are on Chrome or Firefox, or this is backend code, then go ahead!