What is the test for deference given to an agency's interpretation of its own regulations?

Turning now to the merits of this appeal, we note that " 'an agency's construction of its own regulations is entitled to substantial deference.' " Martin, 111 S.Ct. at 1175 (quoting Lyng v. Payne, 476 U.S. 926, 939 (1986)). Even where "the meaning of [regulatory] language is not free from doubt, the reviewing court should give effect to the agency's interpretation so long as it is reasonable, that is, so long as the interpretation sensibly conforms to the purpose and wording of the regulations[.]" Id. at 1176 (citations and internal quotations omitted).