Analysis of longitudinal categorical and count data subject to measurement error

Thesis (Ph.D.)--Memorial University of Newfoundland, 2011. Mathematics and Statistics Bibliography: leaves 200-211. In biomedical, social, behavioral, and environmental studies, the data are frequently collected from surveys, registration systems, clinical trials, and other observational or experime...

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Main Author: Ji, Yunqi
Other Authors: Memorial University of Newfoundland. Dept. of Mathematics and Statistics
Format: Thesis
Language:English
Published: 2011
Subjects:
Online Access:http://collections.mun.ca/cdm/ref/collection/theses5/id/21842
id ftmemorialunivdc:oai:collections.mun.ca:theses5/21842
record_format openpolar
institution Open Polar
collection Memorial University of Newfoundland: Digital Archives Initiative (DAI)
op_collection_id ftmemorialunivdc
language English
topic Linear models (Statistics)
Longitudinal method
Error analysis (Mathematics)
spellingShingle Linear models (Statistics)
Longitudinal method
Error analysis (Mathematics)
Ji, Yunqi
Analysis of longitudinal categorical and count data subject to measurement error
topic_facet Linear models (Statistics)
Longitudinal method
Error analysis (Mathematics)
description Thesis (Ph.D.)--Memorial University of Newfoundland, 2011. Mathematics and Statistics Bibliography: leaves 200-211. In biomedical, social, behavioral, and environmental studies, the data are frequently collected from surveys, registration systems, clinical trials, and other observational or experimental studies, which are often contaminated with measurement errors. This may be due to the imperfect instruments and procedures, limited experience and knowledge of examiners and examinees. Ignoring measurement errors in responses results in biased estimates of model parameters. Explicit models are required to describe the misclassifications on categorical responses and count errors on aggregation responses. To obtain more reliable inference, one needs to take the measurement errors into consideration when developing statistical methods to analyze mis-measured data. -- In this thesis, we define a generalized thinning operation, based on which we propose a transition model for categorical longitudinal data. This new transition model can flexibly accommodate a variety of linear and nonlinear transition models. We also discuss a thinning-operation-based transition model and an ordinary linear transition model for dynamic count data. -- Most importantly, we present some new measurement error models for categorical data and count data, which link the true responses with the observed, possibly mis-measured responses by explicit expressions. A meaningful application of the explicit misclassification model is to describe the unbalanced misclassifications in categorical data, which provides an alternative way to jointly model the data suffering from both misclassification and some missing values due to "unsure" answers. Moreover, the count error models which accommodate both the overcounted and undercounted data can be used to describe some interesting count data of disease cases with different situations of the dynamic population sizes of an area. We apply these explicit measurement error models and transition models to analyze the longitudinal discrete data subject to measurement errors. -- Methods based on the generalized estimating equations (GEE), generalized quasi-likelihood (GQL), the second order GQL (GQL2), and maximum likelihood (ML) are developed to obtain unbiased hence consistent estimates of the unknown parameters in longitudinal models for categorical and count responses. The explicit measurement error models lead to simple development of the GEE, GQL and GQL2 approaches. Intensive simulations are conducted to examine the performance of these approaches. These methods tend to provide satisfactory estimates of model parameters, estimated standard errors and confidence intervals. Surprisingly the generalized quasi-likelihood approach performs almost as good as the likelihood approach when the latter is applicable in some first-order transition models. In the linear transition model for dynamic count data, even the GQL approach provide almost as good estimates as the ML approach. These findings provide us an efficient alternative to analyze longitudinal data when complicated dependence structure is taken into account the modeling. The proposed methods are illustrated by an example of children asthma data from Harvard Six Cities Study.
author2 Memorial University of Newfoundland. Dept. of Mathematics and Statistics
format Thesis
author Ji, Yunqi
author_facet Ji, Yunqi
author_sort Ji, Yunqi
title Analysis of longitudinal categorical and count data subject to measurement error
title_short Analysis of longitudinal categorical and count data subject to measurement error
title_full Analysis of longitudinal categorical and count data subject to measurement error
title_fullStr Analysis of longitudinal categorical and count data subject to measurement error
title_full_unstemmed Analysis of longitudinal categorical and count data subject to measurement error
title_sort analysis of longitudinal categorical and count data subject to measurement error
publishDate 2011
url http://collections.mun.ca/cdm/ref/collection/theses5/id/21842
genre Newfoundland studies
University of Newfoundland
genre_facet Newfoundland studies
University of Newfoundland
op_source Paper copy kept in the Centre for Newfoundland Studies, Memorial University Libraries
op_relation Electronic Theses and Dissertations
(22.37 MB) -- http://collections.mun.ca/PDFs/theses/Ji_Yunqi.pdf
http://collections.mun.ca/cdm/ref/collection/theses5/id/21842
op_rights The author retains copyright ownership and moral rights in this thesis. Neither the thesis nor substantial extracts from it may be printed or otherwise reproduced without the author's permission.
_version_ 1766112468002668544
spelling ftmemorialunivdc:oai:collections.mun.ca:theses5/21842 2023-05-15T17:23:28+02:00 Analysis of longitudinal categorical and count data subject to measurement error Ji, Yunqi Memorial University of Newfoundland. Dept. of Mathematics and Statistics 2011 xii, 211 leaves : ill. Image/jpeg; Application/pdf http://collections.mun.ca/cdm/ref/collection/theses5/id/21842 Eng eng Electronic Theses and Dissertations (22.37 MB) -- http://collections.mun.ca/PDFs/theses/Ji_Yunqi.pdf http://collections.mun.ca/cdm/ref/collection/theses5/id/21842 The author retains copyright ownership and moral rights in this thesis. Neither the thesis nor substantial extracts from it may be printed or otherwise reproduced without the author's permission. Paper copy kept in the Centre for Newfoundland Studies, Memorial University Libraries Linear models (Statistics) Longitudinal method Error analysis (Mathematics) Text Electronic thesis or dissertation 2011 ftmemorialunivdc 2015-08-06T19:22:48Z Thesis (Ph.D.)--Memorial University of Newfoundland, 2011. Mathematics and Statistics Bibliography: leaves 200-211. In biomedical, social, behavioral, and environmental studies, the data are frequently collected from surveys, registration systems, clinical trials, and other observational or experimental studies, which are often contaminated with measurement errors. This may be due to the imperfect instruments and procedures, limited experience and knowledge of examiners and examinees. Ignoring measurement errors in responses results in biased estimates of model parameters. Explicit models are required to describe the misclassifications on categorical responses and count errors on aggregation responses. To obtain more reliable inference, one needs to take the measurement errors into consideration when developing statistical methods to analyze mis-measured data. -- In this thesis, we define a generalized thinning operation, based on which we propose a transition model for categorical longitudinal data. This new transition model can flexibly accommodate a variety of linear and nonlinear transition models. We also discuss a thinning-operation-based transition model and an ordinary linear transition model for dynamic count data. -- Most importantly, we present some new measurement error models for categorical data and count data, which link the true responses with the observed, possibly mis-measured responses by explicit expressions. A meaningful application of the explicit misclassification model is to describe the unbalanced misclassifications in categorical data, which provides an alternative way to jointly model the data suffering from both misclassification and some missing values due to "unsure" answers. Moreover, the count error models which accommodate both the overcounted and undercounted data can be used to describe some interesting count data of disease cases with different situations of the dynamic population sizes of an area. We apply these explicit measurement error models and transition models to analyze the longitudinal discrete data subject to measurement errors. -- Methods based on the generalized estimating equations (GEE), generalized quasi-likelihood (GQL), the second order GQL (GQL2), and maximum likelihood (ML) are developed to obtain unbiased hence consistent estimates of the unknown parameters in longitudinal models for categorical and count responses. The explicit measurement error models lead to simple development of the GEE, GQL and GQL2 approaches. Intensive simulations are conducted to examine the performance of these approaches. These methods tend to provide satisfactory estimates of model parameters, estimated standard errors and confidence intervals. Surprisingly the generalized quasi-likelihood approach performs almost as good as the likelihood approach when the latter is applicable in some first-order transition models. In the linear transition model for dynamic count data, even the GQL approach provide almost as good estimates as the ML approach. These findings provide us an efficient alternative to analyze longitudinal data when complicated dependence structure is taken into account the modeling. The proposed methods are illustrated by an example of children asthma data from Harvard Six Cities Study. Thesis Newfoundland studies University of Newfoundland Memorial University of Newfoundland: Digital Archives Initiative (DAI)