The method of likelihood imputation is devised under the framework of
latent structure models where the observation is a statistic of the co
mplete data which can only be specified on a latent basis. The imputed
data set is chosen to differ least from the observed one in their inf
ormation contents - a concept with general implications for the analys
is of incomplete-data. In contrast to the standard conditional-mean si
ngle imputation, our procedure depends on an entire likelihood region
instead of any single point in it, and yields consistent parameter est
imators nevertheless. We explain its implementations and illustrate wi
th data from panel surveys and linear regression with censorship. We a
lso discuss its potentials in sensitivity analysis.