| Summary: | 博士 === 東海大學 === 統計學系 === 97 === Randomized response is an interview technique designed to eliminate
response bias when sensitive questions are asked. In this
dissertation, we present a logistic regression model on randomized
response data when the covariates on some subjects are missing at
random. First, based on validation data set, we propose Horvitz and
Thompson (1952)-type weighted estimators. In particular, we
investigate the Horvitz and Thompson (1952)-type weighted estimators
by using different estimates of the selection probabilities. We
present large sample theory for the proposed estimators and show
that they are more efficient than the estimator using the true
selection probabilities. Simulation results support theoretical
analysis. Under the assumption that the observed covariate and
surrogated variable are categorical, using the empirical average
estimator for the selection probabilities, we shall show that both
augmented inverse probability weighted estimator (AIPW) and mean
score estimator reduce to weighted estimators. Although these
estimating equations are different, they lead numerically to exactly
the same root.
Second, based on validation and non-validation data set, two
semiparametric approaches are developed for analyzing randomized
response data with missing covariates in logistic regression model.
One of the two estimates is an extension of the validation
likelihood estimator of Breslow and Cain (1988). The other is a
joint conditional likelihood estimator based on both validation and
non-validation data set. We present large sample theory for the
proposed estimators. Simulation results show that the joint
conditional likelihood estimator is more efficient than the
validation likelihood estimator, weighted estimator, complete-case
estimator and partial likelihood estimator. We also illustrate these
methods using data from a cable TV study.
|
|---|
