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@PHDTHESIS{Kornely:822585,
author = {Kornely, Mia Johanna Katharina},
othercontributors = {Kateri, Maria and Moustaki, Irini},
title = {{M}ultidimensional modeling and inference of dichotomous
item response data},
school = {RWTH Aachen University},
type = {Dissertation},
address = {Aachen},
publisher = {RWTH Aachen University},
reportid = {RWTH-2021-06836},
pages = {1 Online-Ressource : Illustrationen},
year = {2021},
note = {Veröffentlicht auf dem Publikationsserver der RWTH Aachen
University; Dissertation, RWTH Aachen University, 2021},
abstract = {To analyze the fairness of an educational system of a
country and to help with development of pedagogical
concepts, questionnaire and test based surveys are important
tools. An essential challenge in conducting such surveys is
the measurement of not directly observable traits such as
the ability of students in different subjects. These traits
are modeled by latent variables. This thesis restricts on
dichotomous items where the possible responses to each item
can be categorized in a set of two options (e.g., "correct"
and "incorrect") and on continuous latent variables. In item
response theory (IRT) the probability of a correct response
to an item depending on the latent variable is modeled.
Multidimensional models suppose that there are several
latent variables which are collected in a latent vector.
Chapter 1 provides an overview of IRT models and methods for
estimating model parameters and latent vectors. A particular
emphasis lies on generalized linear latent variable models
(GLLVM) and models that have a closed form expression of the
marginal distribution of the response vector. Chapter 2
introduces an extension of GLLVM with respect to link
functions and distributions of the latent vector that depend
on parameters for their respective shapes. It is pointed out
how this is connected to several models in the literature
which are unified in this class. The consistency and
asymptotic efficiency of the marginal maximum likelihood
estimator (MMLE) for the model parameters is proved. This
also implies that these asymptotic properties hold for many
classic models, thus contributing to the estimation theory
for IRT models in general. The asymptotic chi-square
distribution of Wald, score and likelihood-ratio
test-statistics is derived using the asymptotic efficiency
of the MMLE. Model fitting, estimation of latent traits,
nested model tests and model selection are studied in
simulation studies. In Chapter 3 the asymptotic theory of
estimating latent vectors is discussed. The estimation of
latent vectors can be interpreted as (empirical) Bayesian
point estimation with previous estimation of the
(multidimensional) IRT model parameters. A primary target of
this chapter is the investigation of variants of a
Bernstein-von Mises theorem of latent vectors, i.e. the
asymptotic posterior normality (APN) of latent vectors. This
chapter provides a comprehensive analysis of questions
related to Bernstein-von Mises theorems and the asymptotics
of latent vector estimation for binary IRT. Current results
regarding the asymptotics of the posterior of a single
latent variable in the IRT literature are extended with
respect to the multivariate case but also to the type of the
convergence, the considered estimators and their asymptotic
efficiency. In Chapter 4 a linear approximation of the
expected a-posteriori estimator (aEAP) for latent vectors is
obtained using the component statistics and the APN theory
of Chapter 3. Properties of the aEAP are examined using a
simulation study. A new EM-algorithm for MMLE of high
dimensional logit models is derived using the APN theory
once more and combining it with the aEAP. This EM-algorithm
is easy to implement for any dimension of the latent vector
by simplifying steps of similar adaptive algorithms for high
dimensional settings. Chapter 5 focuses on parameter
estimation for large high-dimensional IRT settings in which
classic methods are unfeasible. Based on a pseudo likelihood
procedure for a class of generalized IRT models that cannot
always be interpreted as latent variable models, a method is
obtained whose resulting fitted models are guaranteed to be
equivalent to latent variable models. The implemented
procedure is fast but the parameter estimates are biased.
Bias and efficiency of the estimator are studied via
simulations.},
cin = {116510 / 110000},
ddc = {510},
cid = {$I:(DE-82)116510_20140620$ / $I:(DE-82)110000_20140620$},
typ = {PUB:(DE-HGF)11},
doi = {10.18154/RWTH-2021-06836},
url = {https://publications.rwth-aachen.de/record/822585},
}
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