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Appendix A. Reparameterization of the model.

In this appendix it is demonstrated that the 2Y estimable quantities and (y = 1, 2, 3, …,Y) stand in one to one correspondence with an alternative set of 2Y quantities, namely, , , , (y = 2, 3, …, Y), and (y = 3, 4, …, Y). We refer to the former set as the “basic set” and to the latter as the “alternative set.” Either set can be calculated from the other; the second set is therefore an estimable reparameterization of the first set.

Suppressing dependence on strata in our notation, we have

	(A.1)
and
.	(A.2)

From (A.1) and (A.2) it follows that

and

.

Consequently,

, y = 2, 3, …Y,	(A.3)
and
, y = 3, 4, …Y -1.	(A.4)

Thus the alternative set of values can be calculated from the basic set.

Rearranging (A.3) we obtain

,
i.e.,
;	(A.5)

similarly rearranging (A.4) we obtain

,
i.e.,
.	(A.6)

From (A.5) and (A.6) it follows that the basic set of parameters can be recursively calculated from the alternative set.