  The study of treatment effects is often complicated by noncompliance and
missing data. In the one-sided noncompliance setting where of interest are the
complier and noncomplier average causal effects (CACE and NACE), we address
outcome missingness of the \textit{latent missing at random} type (LMAR, also
known as \textit{latent ignorability}). That is, conditional on covariates and
treatment assigned, the missingness may depend on compliance type. Within the
instrumental variable (IV) approach to noncompliance, methods have been
proposed for handling LMAR outcome that additionally invoke an exclusion
restriction type assumption on missingness, but no solution has been proposed
for when a non-IV approach is used. This paper focuses on effect identification
in the presence of LMAR outcome, with a view to flexibly accommodate different
principal identification approaches. We show that under treatment assignment
ignorability and LMAR only, effect nonidentifiability boils down to a set of
two connected mixture equations involving unidentified stratum-specific
response probabilities and outcome means. This clarifies that (except for a
special case) effect identification generally requires two additional
assumptions: a \textit{specific missingness mechanism} assumption and a
\textit{principal identification} assumption. This provides a template for
identifying effects based on separate choices of these assumptions. We consider
a range of specific missingness assumptions, including those that have appeared
in the literature and some new ones. Incidentally, we find an issue in the
existing assumptions, and propose a modification of the assumptions to avoid
the issue. Results under different assumptions are illustrated using data from
the Baltimore Experience Corps Trial.
