120 CONDITIONAL INFERENTIAL MODELS
form specified in (6.3a). Actually, this first expression is of the more general “non-
separable” form c(X,U) = 0 described in Remark 6.1. So, although (6.15) provides a
suitable decomposition of the baseline association, the requirements of Theorem 6.2
are not met, so the resulting conditional IM may not be valid.
To elaborate on this last point, observe that the distribution for θ obtained via
the distribution of (U
1
,U
2
), given X
1
/U
1
+ X
2
/U
2
= 2, is exactly a type of fiducial
distribution. As we mentioned in Chapter 2, conditioning on the full data, (X
1
,X
2
)
in this case, for fixed θ , makes the distribution of (U
1
,U
2
) degenerate. Therefore,
the “continue to regard” operation, which treats (U
1
,U
2
) as independent chi-squares, ...