Ogundimu, Emmanuel O. (2013) On sample selection models and skew distributions. PhD thesis, University of Warwick.

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Abstract

This thesis is concerned with methods for dealing with missing data in nonrandom
samples and recurrent events data.
The first part of this thesis is motivated by scores arising from questionnaires
which often follow asymmetric distributions, on a fixed range. This can be due to
scores clustering at one end of the scale or selective reporting. Sometimes, the scores
are further subjected to sample selection resulting in partial observability. Thus,
methods based on complete cases for skew data are inadequate for the analysis of
such data and a general sample selection model is required. Heckman proposed
a full maximum likelihood estimation method under the normality assumption for
sample selection problems, and parametric and non-parametric extensions have been
proposed.
A general selection distribution for a vector Y 2 Rp has a PDF fY given by
fY(y) = fY?(y)
P(S? 2 CjY? = y)
P(S? 2 C)
;
where S? 2 Rq and Y? 2 Rp are two random vectors, and C is a measurable subset of
Rq. We use this generalization to develop a sample selection model with underlying
skew-normal distribution. A link is established between the continuous component
of our model log-likelihood function and an extended version of a generalized skewnormal
distribution. This link is used to derive the expected value of the model,
which extends Heckman's two-step method. The general selection distribution is
also used to establish the closed skew-normal distribution as the continuous component
of the usual multilevel sample selection models. Finite sample performances of
the maximum likelihood estimator of the models are studied via Monte Carlo simulation.
The model parameters are more precisely estimated under the new models,
even in the presence of moderate to extreme skewness, than the Heckman selection
models. Application to data from a study of neck injuries where the responses are
substantially skew successfully discriminates between selection and inherent skewness,
and the multilevel model is used to analyze jointly unit and item non-response.
We also discuss computational and identification issues, and provide an extension
of the model using copula-based sample selection models with truncated marginals. The second part of this thesis is motivated by studies that seek to analyze
processes that generate events repeatedly over time. We consider the number of
events per subject within a specified study period as the primary outcome of interest.
One considerable challenge in the analysis of this type of data is the large proportion
of patients that might discontinue before the end of the study, leading to partially
observed data. Sophisticated sensitivity analyses tools are therefore necessary for
the analysis of such data.
We propose the use of two frequentist based imputation methods for dealing
with missing data in recurrent event data framework. The recurrent events are
modeled as over-dispersed Poisson data, with constant rate function. Different assumptions
about future behavior of dropouts depending on reasons for dropout and
treatment received are made and evaluated in a simulation study. We illustrate our
approach with a clinical trial in patients who suffer from bladder cancer.

Item Type:	Thesis (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Distribution (Probability theory), Sampling (Statistics) -- Mathematical models
Official Date:	February 2013
Dates:	Date Event February 2013 Submitted
Institution:	University of Warwick
Theses Department:	Department of Statistics
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Hutton, Jane (Statistician)
Sponsors:	Engineering and Physical Sciences Research Council (EPSRC)
Extent:	xvi, 107 leaves.
Language:	eng

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