Quasi-least squares regression:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton, FL [u.a.]
CRC Press
2014
|
| Series: | Monographs on statistics and applied probability
132 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | XVII, 203 S. graph. Darst. |
| ISBN: | 9781420099935 1420099930 |
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| adam_text | Contents
Preface
xiii
I Introduction
1
1
Introduction
3
1.1
GEE and QLS for Analysis of Correlated Data
3
1.2
Why Traditional Approaches for Independent Measurements Are
Not Appropriate for Analysis of Longitudinal Weight Loss Study
4
1.3
Attractive Features of Both QLS and GEE
5
1.4
When QLS Might Be Considered as an Alternative to GEE
7
1.5
Motivating Studies
8
1.5.1
Longitudinal Study of Obesity in Children Following Renal
Transplant: With Binary and Continuous Measurements
That Are Unequally Spaced in Time
8
1.5.2
Longitudinal Study of Sentence Recognition Scores That
Stabilize over Time in a Hearing Recognition Study
9
1.5.3
Longitudinal Study for Comparison of Two Treatments for
Toenail Infection
11
1.5.4
Multivariate Longitudinal
Dataset
12
1.5.5
Familial
Dataset
13
1.6
Summary
15
1.7
Exercises
15
2
Review of Generalized Linear Models
17
2.1
Background
17
2.2
Generalized Linear Models
18
2.2.1
linear Model
18
2.2.2
Generalized Linear Model
18
2.2.3
Estimation of the Parameters
20
2.2.4
Quasi-LUcelihood
21
2.3
Generalized Estimating Equations
22
2.3.1
Notation for Correlated Data
22
2.3.2
GEE Estimating Equation for
β
22
2.3.3
Working Correlation Structures Available for GEE
23
νϋ
viii Contents
2.3.4
The Concept of the Working versus the True Correlation
Structure
26
2.3.5
Moment Estimates of the Dispersion and the Correlation
Parameters
26
2.3.6
Algorithm for Estimation
28
2.3.7
Asymptotic Distribution of the GEE Estimators and Esti¬
mates of Covariance
29
2.4
Application for Obesity Study Provided in Chapter
1 32
2.5
Exercises
39
Π
Quasi-Least Squares Theory and Applications
41
3
History and Theory of Quasi-Least Squares Regression
43
3.1
Why QLS is a Quasi ^Least Squares Approach
44
3.2
The Least Squares Approach Employed in Stage One of QLS for
Estimation of a
47
3.2.1
Benefits of a Least Squares Approach for Estimation of a
48
3.2.2
QLS Stage One Estimates of a for the AR(1
)
Structure
51
3.2.3
Limiting Value of the Stage One QLS Estimator of
α
53
3.3
Stage Two QLS Estimates of the Correlation Parameter for the
ARO)
Structure
54
3.3.1
Elimination of the Asymptotic Bias in the Stage One QLS
Estimate of a
54
3.4
Algorithm for QLS
57
3.4.1
Asymptotic Distribution of the Regression Parameter for
QLS
59
3.5
Other Approaches Based on GEE
59
3.6
Example
60
3.7
Summary
62
3.8
Exercises
63
4
Mixed Linear Structures and Familial Data
65
4.1
Notation for Data from Nuclear Families
65
4.2
Familial Correlation Structures for Analysis of Data from Nuclear
Families
66
4.3
Other Work on Assessment of Familial Correlations with QLS
69
4.4
Justification of Implementation of QLS for Familial Structures via
Consideration of the Class of Mixed Linear Correlation Structures
70
4.4.1
Definition of Mixed linear Correlation Structures
70
4.4.2
Results for General Correlation Structures (for Stage One of
QLS) and for Linear Correlation Structures (for Stage Two
of QLS)
71
4.4.2.1
Results for Stage One
71
4.4.2.2
Results for Stage Two
72
Contents ix
4.5 Demonstration
of
QLS
for Analysis of Balanced Familial Data
Using
Stata
Software
73
4.6
Demonstration of QLS for Analysis of Unbalanced Familial Data
Using
R
Software
76
4.7
Simulations to Compare Implementation of QLS with Correct
Specification of the Trio Structure versus Correct Specification
with GEE and Incorrect Specification of the Exchangeable Working
Structure with GEE
77
4.8
Summary and Future Research Directions
79
4.9
Exercises
80
5
Correlation Structures for Clustered and Longitudinal Data
83
5.1
Characteristics of Clustered and Longitudinal Data
84
5.2
The Exchangeable Correlation Structure for Clustered Data
85
5.2.1
Solutions to the QLS Stage One and Stage TWo Estimating
Equations for a
85
5.2.2
Demonstration of Implementation of the Exchangeable
Structure for QLS
87
5.3
The Tri-Diagonal Correlation Structure
89
5.3.1
Solutions to the QLS Stage One and Stage Two Estimating
Equations for a
89
5.3.2
Demonstration of Implementation of the Tri-Diagonal
Structure for QLS
90
5.4
The AR(1) Structure for Analysis of (Planned) Equally Spaced
Longitudinal Data
91
5.4.1
Solutions to the QLS Stage One and Stage Two Estimating
Equations for a
91
5.4.2
Demonstration of Implementation of the AR(1) Structure
for QLS
92
5.5
The Markov Structure for Analysis of Unequally Spaced Longitudi¬
nal Data
94
5.5.1
Solutions to the QLS Stage One and Stage Two Estimating
Equations for
α
94
5.5.2
Demonstration of Implementation of the Markov Structure
for QLS
96
5.5.3
Generalized Markov Structure
97
5.6
The Unstructured Matrix for Analysis of Balanced Data
98
5.6.1
Obtaining a Solution to the Stage One Estimating Equation
for the Unstructured Matrix
99
5.6.2
Obtaining a Solution to the Stage Two Estimating Equation
for the Unstructured Matrix
101
5.6.3
Demonstration of Implementation of the Unstructured
Matrix for QLS
102
5.7
Other Structures
106
Contents
5.8 Implementation
of
QLS
for Patterned Correlation Structures
107
5.8.1
Algorithm for Implementation of QLS Using Software
That Allows for Application of a User-Specified Working
Correlation Structure That Is Treated as Fixed and Known
in the GEE Estimating Equation for
β
107
5.8.2
When Software for GEE Is Not Available, or Is Not Utilized
108
5.9
Summary
109
5.10
Exercises
109
5.11
Appendix
110
Analysis of Data with Multiple Sources of Correlation
113
6.1
Characteristics of Data with Multiple Sources of Correlation
113
6.2
Multi-Source Correlated Data That Are Totally Balanced
113
6.2.1
Example of Multivariate Longitudinal Data That Are Totally
Balanced
113
6.2.2
Notation
114
6.2.3
Working Correlation Structure for Balanced Data
115
6.2.4
Prior Implementation of the
Kronecker
Product Structure
117
6.2.5
Implementation of QLS for Analysis
118
6.3
Multi-Source Correlated Data That Are Balanced within Clusters
123
6.3.1
Example
123
6.3.2
Notation
123
6.3.3
Correlation Structure for Data That Are Balanced within
Clusters
124
6.3.4
Algorithm for Implementation of QLS for Multi-Source
Correlated Data That Are
В
alanced within Clusters
124
6.3.5
Implementation of QLS for Analysis
126
6.4
Multi-Source Correlated Data That Are Unbalanced
129
6.4.1
Example
129
6.4.2
Notation
130
6.4.3
Correlation Structure for Data That Are Unbalanced
130
6.4.4
Algorithm for Implementation of QLS for Multi-Source
Correlated Data That Are Unbalanced
131
6.4.5
Implementation of QLS for Analysis
133
6.5
Asymptotic Relative Efficiency Calculations
134
6.6
Summary
136
6.7
Exercises
138
6.8
Appendix: The Limiting Value of the QLS Estimate of the Associa¬
tion Parameter When the True Correlation Structure Is Misspecified
as Exchangeable
139
Correlated Binary Data
141
7.0.1
Notation for Correlated Binary Data
142
7.1
Additional Constraints for Binary Data
142
Contents xi
7.1.1 Negative
Estimated Bivariate Probabilities for the Toenail
Data
143
7.1.2
Prentice Constraints to Ensure Valid Induced Bivariate
Distributions
144
7.1.3
Simplification of the Prentice Constraints for Decaying
Product Correlation Structures
146
7.1.4
Conditions to Ensure the Existence of an Underlying
Multi
variate
Distribution
149
7.2
When Violation Is Likely to Occur
149
7.2.1
When the Model Is Correctly Specified
150
7.2.2
When the Working Structure Is Incorrectly Specified
150
7.2.3
When the Model for the Mean Is Incorrect
154
7.2.4
When the Assumption of Missing Completely at Random Is
Violated
154
7.3
Implications of Violation of Constraints for Binary Data
154
7.4
Comparison among GEE, QLS, and MARK1ML
155
7.4.1
Comparisons with ALR
156
7.5
Prentice-Corrected QLS and GEE
157
7.6
Summary
159
7.7
Exercises
160
8
Assessing Goodness of fit and Choice of Correlation Structure for
QLS and GEE
161
8.1
Simulation Scenarios
166
8.2
Simulation Results
168
8.2.1
True AR(1) Structure
168
8.2.2
True Markov Structure
168
8.2.3
True Decaying Product Structure
169
8.3
Summary and Recommendations
171
8.4
Exercises
172
9
Sample Size and Demonstration
175
9.1
Two-Group Comparisons
177
9.1.1
Two-Group Comparisons
177
9
Л
. 1.1
Tíme-
Averaged Comparison of Group Means
177
9.1.1.2
Time-Averaged Comparison of Proportions
180
9.1.1.3
Comparison of Change over Time for Continuous
Outcomes
181
9
Л
. 1.4
Comparison of Change over Time for Binary
Outcomes
182
9.2
More Complex Situations
182
9.3
Worked Example
183
9.3.1
Sample Size for a Future Study
187
9.4
Discussion and Summary
188
xii Contents
9.5
Exercises
190
Bibliography
191
Index
201
Statistics
Drawing on the authors substantial expertise in modeling longitudinal and
clustered data, Quasi-Least Squares Regression provides a thorough
treatment of quasi-least squares (QLS) regression—a computational ap¬
proach for the estimation of correlation parameters within the framework
of generalized estimating equations (GEEs). The authors present a detailed
evaluation of QLS methodology, demonstrating the advantages of QLS in
comparison with alternative methods. They describe how QLS can be used
to extend the application of the traditional GEE approach to the analysis
of unequally spaced longitudinal data, familial data, and data with mul¬
tiple sources of correlation. In some settings, QLS also allows for improved
analysis with an unstructured correlation matrix.
Special focus is given to goodness-of-fit analysis as well as new strate¬
gies for selecting the appropriate working correlation structure for QLS and
GEE. A chapter on longitudinal binary data tackles recent issues raised in
the statistical literature regarding the appropriateness of semi-parametric
methods, such as GEE and QLS, for the analysis of binary data; this chap¬
ter includes a comparison with the first-order Markov maximum-likelihood
(MARKI
ML) approach for binary data.
Examples throughout the book demonstrate each topic of discussion. In
particular, a fully worked out example leads readers from model building
and interpretation to the planning stages for a future study (including sam¬
ple size calculations). The code provided enables readers to replicate many
of the examples in
Stata·,
often with corresponding R,
SAS9,
or
MATLAB9
code offered in the text or on the book s website.
About the Authors
Justine Shutts, PhD, is an Associate Professor of Biostatistics and Co-
Director of the Pediatrics Section in the Division of Biostatistics and Epide¬
miology at the Perelman School of Medicine,
University
of Pennsylvania.
Joseph M.
Hübe,
PhD, is a Solar System Ambassador with the JetPropul-
sion Laboratory, an Adjunct Professor of Statistics at Arizona State Univer¬
sity, and an Emeritus Professor at tr«
University
of Hawaii.
|
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2/3 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV042103980 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T01:12:48Z |
| institution | BVB |
| isbn | 9781420099935 1420099930 |
| language | English |
| lccn | 013047324 |
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| physical | XVII, 203 S. graph. Darst. |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | CRC Press |
| record_format | marc |
| series | Monographs on statistics and applied probability |
| series2 | Monographs on statistics and applied probability A Chapman & Hall book |
| spelling | Shults, Justine Verfasser (DE-588)1060499657 aut Quasi-least squares regression Justine Shults ; Joseph M. Hilbe Quasi least squares regression Boca Raton, FL [u.a.] CRC Press 2014 XVII, 203 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Monographs on statistics and applied probability 132 A Chapman & Hall book Mathematisches Modell Least squares Regression analysis Mathematical models Regressionsmodell (DE-588)4127980-3 gnd rswk-swf Methode der kleinsten Quadrate (DE-588)4038974-1 gnd rswk-swf Methode der kleinsten Quadrate (DE-588)4038974-1 s Regressionsmodell (DE-588)4127980-3 s DE-604 Hilbe, Joseph M. 1944-2017 Verfasser (DE-588)128751851 aut Monographs on statistics and applied probability 132 (DE-604)BV002494005 132 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027544544&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027544544&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Shults, Justine Hilbe, Joseph M. 1944-2017 Quasi-least squares regression Monographs on statistics and applied probability Mathematisches Modell Least squares Regression analysis Mathematical models Regressionsmodell (DE-588)4127980-3 gnd Methode der kleinsten Quadrate (DE-588)4038974-1 gnd |
| subject_GND | (DE-588)4127980-3 (DE-588)4038974-1 |
| title | Quasi-least squares regression |
| title_alt | Quasi least squares regression |
| title_auth | Quasi-least squares regression |
| title_exact_search | Quasi-least squares regression |
| title_full | Quasi-least squares regression Justine Shults ; Joseph M. Hilbe |
| title_fullStr | Quasi-least squares regression Justine Shults ; Joseph M. Hilbe |
| title_full_unstemmed | Quasi-least squares regression Justine Shults ; Joseph M. Hilbe |
| title_short | Quasi-least squares regression |
| title_sort | quasi least squares regression |
| topic | Mathematisches Modell Least squares Regression analysis Mathematical models Regressionsmodell (DE-588)4127980-3 gnd Methode der kleinsten Quadrate (DE-588)4038974-1 gnd |
| topic_facet | Mathematisches Modell Least squares Regression analysis Mathematical models Regressionsmodell Methode der kleinsten Quadrate |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027544544&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027544544&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002494005 |
| work_keys_str_mv | AT shultsjustine quasileastsquaresregression AT hilbejosephm quasileastsquaresregression |