(a)
,
, and hence
;
(b),
,
, and hence
;
(c),
,
,
,
, hence
and
;
(d),
,
,
,
, hence
and
.
(1) Bias in the point estimate:
;
(2) Sampling variability of the point estimate:
;
(3) Mean square error:
;
(4) Approximate bias in the standard error estimate:
.
Correct Specification: (a), (b), (c), (d)
Misspecification of a Nonliear Propensity Score Model: (a), (b), (c), (d)
Misspeification of a Non-Additive Propensity Score Model: (a), (b), (c), (d)
Correct Specification: (a), (b), (c), (d)
Misspecification of a Nonliear Outcome Model: (a), (b), (c), (d)
Misspeification of a Non-Additive Outcome Model: (a), (b), (c), (d)
(c*)
,
,
,
,
, hence
and
;
(d*)
,
,
,
,
, hence
and
.