How to handle empty string query parameters in angularjs?

Question

I have a query on my $resource like so:

userResource.query(
    {
        lastName: vm.lastName,
        pageSize: vm.pagingData.pageSize,
        pageNumber: vm.pagingData.pageNumber
    },
    function(data) {
        vm.totalItems = data.totalItems;
        vm.totalPages = data.totalPages;
        vm.pageNumber = data.pageNumber;
        vm.users = data.items;
    });

This works great until the vm.lastName is an empty string. When its empty I see the lastName=&pageNumber... etc in the URL. I get this response from my web api 2 controller even though the lastName is an optional parameter.

{"message":"The request is invalid.","modelState":{"lastName.String":["A value is required but was not present in the request."]}}

This seems like a stupid question but I can't figure out how to leave the parameter off the query in angularjs if its blank. Thanks!