Interpreting standard and nonstandard log-linear models:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Münster ; München [u.a.]
Waxmann
2006
|
| Series: | Internationale Hochschulschriften
455 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 164 S. graph. Darst. |
| ISBN: | 3830916116 |
Staff View
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
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| 100 | 1 | |a Mair, Patrick |e Verfasser |0 (DE-588)131503707 |4 aut | |
| 245 | 1 | 0 | |a Interpreting standard and nonstandard log-linear models |c Patrick Mair |
| 264 | 1 | |a Münster ; München [u.a.] |b Waxmann |c 2006 | |
| 300 | |a 164 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Internationale Hochschulschriften |v 455 | |
| 650 | 4 | |a Log-linear models | |
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Record in the Search Index
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| adam_text | Contents
1
Introduction
..............................................................................................9
2
Analysis of Contingency Tables
............................................................11
2.1
Two-way Tables
.....................................................................................11
2.1.1
Survey Methods in Two-way Tables
.....................................................12
2.1.2
Hypotheses and Testing in Two-way Tables
.........................................15
2.2
Odds Ratios
............................................................................................17
3
Hierarchical Log-Linear Models
..............................................................23
3.1
The Derivation of the Log-Linear Model
................................................23
3.2
Interpretation of Single Parameters in Log-Linear Models
.....................25
3.2.1
Saturated Model and Restrictions
..........................................................25
3.2.2
Interpretation of the Parameters
.............................................................27
3.2.3
Estimation of the Parameters
..................................................................30
3.3
Interpreting Hierarchical Log-Linear Models
........................................30
3.3.1
Hierarchy principle
.................................................................................30
3.3.2
Interpretation of Reduced Models
..........................................................33
3.4
Testing and Model Selection
..................................................................37
3.4.1
Testing for Goodness of Fit
....................................................................37
3.4.2
Model Selection Criteria
........................................................................39
3.4.3
Testing Single Parameters
......................................................................41
3.5
Concluding Example and Further Tasks
................................................42
3.5.1
Example for Model Testing
....................................................................42
3.5.2
Further Tasks in Log-Linear Modeling
..................................................46
4
Generalized Linear Models
....................................................................49
4.1
Introduction and Definitions
..................................................................49
4.2
General Linear Models
...........................................................................51
4.2.1
Definition of the General Linear Model
.................................................51
4.2.2
The Multiple Regression Model
.............................................................52
4.2.3
The Analysis of Variance
.......................................................................53
5
Log-Linear Models in the Context of GLM
...........................................55
5.1
Coding Strategies for Design Matrices
..................................................55
5.1.1
Dummy Coding
......................................................................................56
5.1.2
Unweighted Effect Coding
.....................................................................58
5.1.3
Weighted Effect Coding
.........................................................................59
5.1.4
Orthogonal Coding
.................................................................................59
5.1.5
Nonsense Coding
....................................................................................61
5.1.6
A Computation Procedure for Design Matrices
.....................................61
5.2
Issues of Orthogonality in Design Matrices
...........................................62
5.2.1
Multicollinearity in Regression Models
.................................................62
5.2.2
Orthogonal vs.
Nonorthogonal
Design Vectors
.....................................63
5.2.3
The Phenomenon of Block Orthogonality
.............................................65
5.2.4
Further Aspects of Correlation between Design Vectors
.......................67
5.3
GLM Implementation of Log-Linear Models
........................................69
5.3.1
The Basic GLM Structure of the Log-Linear Representation
................69
5.3.2
Design Matrix Strategies for Log-Linear Modeling
..............................70
5.4
Justification of a New Approach for Parameter Contribution
-
Part
1.. 73
6
Nonstandard
Log-Linear Models
...........................................................75
6.1
Limitations of Nonhierarchical Log-Linear Models
..............................75
6.1.1
Definition of Nonhierarchical Models
...................................................75
6.1.2
Discussions about the Legitimation of Nonhierarchical Models
...........76
6.2
Nonstandard
Models as GLM
................................................................78
6.2.1
Some Introductory Definitions
...............................................................78
6.2.2
The Usefulness of
Nonstandard
Models
................................................80
6.3
Theoretical Funding vs.
Data-Driven
Approach for Parameter
Interpretation
..........................................................................................83
6.4
Justification of a New Approach for Parameter Contribution
-
Part
2.. 84
7
Stepwise Approaches for Model Selection
............................................85
7.1
Ordinary Stepwise Regression
...............................................................85
7.1.1
Criteria for Model Selection Based on Sum of Squares
DecompositionSo
7.1.2
Stepwise Regression, Forward and Backward Elimination
...................87
7.2
Stepwise Procedures for Log-Linear Model Selection
..........................88
7.2.1
Stepwise Selection for a Given Model Hierarchy
..................................89
7.2.2
Screening Effects Procedure
..................................................................90
7.2.3
Goodman s Stepwise Procedure
.............................................................91
7.2.4
Model Selection According to Edwards
&
Havránek
............................92
7.3
Justification of a New Approach for Parameter Contribution
-
Part
3.. 93
8
A Procedure for Analyzing Standard and
Nonstandard
Models
............95
8.1
Entering of the Model Effects
................................................................96
8.1.1
Correlation between Design Vectors and Dependent Variables
in Ordinary Regression
...........................................................................96
8.1.2
Coefficients of Partial Correlation and Determination
in Ordinary Regression
...........................................................................98
8.1.3
Implications of Correlation Analysis in Log-Linear Models
.................99
8.1.4
Implications of Partial Correlations in Log-Linear Models
.................102
8.2
Adopting Goodman s Forward Selection
.............................................104
8.3
Relative Importance of Single Parameters
...........................................105
8.3.1
Relative Importance by Averaging
Orderings
.....................................105
8.3.2
An Approach Based on Information Theory
........................................106
8.3.3
The Dominance Analysis
.....................................................................107
8.4
Some Pseudo-R2 Measures
...................................................................110
8.4.1
The Standard Approach for Pseudo-R2 in Log-Linear Models
............110
8.4.2
Further Proposals of Pseudo-R2 Measures
...........................................111
8.5
Concluding Example
............................................................................112
9
Testing Non-Nested Models
.................................................................115
9.1
General Remarks for Model Testing
....................................................115
9.2
A Likelihood Ratio Test for Non-Nested Models
................................116
9.2.1
General Definitions and Assumptions
..................................................116
9.2.2
Implications for Non-Nested and Overlapping Models
.......................119
9.3
Comparing Two AIC s
.........................................................................121
9.3.1
Introductory Topics
..............................................................................121
9.3.2
The Use of AIC in Log-Linear Models
................................................122
9.3.3
A Test whether Two AIC s Differ Significantly
..................................123
10
Algorithmic Implementation
................................................................127
10.1
General Annotation
..............................................................................127
10.2
Components of the New Procedure
......................................................127
10.2.1
Input and Output
...................................................................................127
10.2.2
Determining the Routine
......................................................................129
11
Examples
..............................................................................................133
11.1
Standard Log-Linear Model
.................................................................133
11.2
Nonstandard
Model with Special Coding Vector
................................139
11.3
Example for Linhart s Test Procedure
.................................................142
11.4
The Weak Wedge
.................................................................................145
12
Summary
...............................................................................................149
13
Discussion
.............................................................................................151
References
.........................................................................................................155
|
| adam_txt |
Contents
1
Introduction
.9
2
Analysis of Contingency Tables
.11
2.1
Two-way Tables
.11
2.1.1
Survey Methods in Two-way Tables
.12
2.1.2
Hypotheses and Testing in Two-way Tables
.15
2.2
Odds Ratios
.17
3
Hierarchical Log-Linear Models
.23
3.1
The Derivation of the Log-Linear Model
.23
3.2
Interpretation of Single Parameters in Log-Linear Models
.25
3.2.1
Saturated Model and Restrictions
.25
3.2.2
Interpretation of the Parameters
.27
3.2.3
Estimation of the Parameters
.30
3.3
Interpreting Hierarchical Log-Linear Models
.30
3.3.1
Hierarchy principle
.30
3.3.2
Interpretation of Reduced Models
.33
3.4
Testing and Model Selection
.37
3.4.1
Testing for Goodness of Fit
.37
3.4.2
Model Selection Criteria
.39
3.4.3
Testing Single Parameters
.41
3.5
Concluding Example and Further Tasks
.42
3.5.1
Example for Model Testing
.42
3.5.2
Further Tasks in Log-Linear Modeling
.46
4
Generalized Linear Models
.49
4.1
Introduction and Definitions
.49
4.2
General Linear Models
.51
4.2.1
Definition of the General Linear Model
.51
4.2.2
The Multiple Regression Model
.52
4.2.3
The Analysis of Variance
.53
5
Log-Linear Models in the Context of GLM
.55
5.1
Coding Strategies for Design Matrices
.55
5.1.1
Dummy Coding
.56
5.1.2
Unweighted Effect Coding
.58
5.1.3
Weighted Effect Coding
.59
5.1.4
Orthogonal Coding
.59
5.1.5
Nonsense Coding
.61
5.1.6
A Computation Procedure for Design Matrices
.61
5.2
Issues of Orthogonality in Design Matrices
.62
5.2.1
Multicollinearity in Regression Models
.62
5.2.2
Orthogonal vs.
Nonorthogonal
Design Vectors
.63
5.2.3
The Phenomenon of Block Orthogonality
.65
5.2.4
Further Aspects of Correlation between Design Vectors
.67
5.3
GLM Implementation of Log-Linear Models
.69
5.3.1
The Basic GLM Structure of the Log-Linear Representation
.69
5.3.2
Design Matrix Strategies for Log-Linear Modeling
.70
5.4
Justification of a New Approach for Parameter Contribution
-
Part
1. 73
6
Nonstandard
Log-Linear Models
.75
6.1
Limitations of Nonhierarchical Log-Linear Models
.75
6.1.1
Definition of Nonhierarchical Models
.75
6.1.2
Discussions about the Legitimation of Nonhierarchical Models
.76
6.2
Nonstandard
Models as GLM
.78
6.2.1
Some Introductory Definitions
.78
6.2.2
The Usefulness of
Nonstandard
Models
.80
6.3
Theoretical Funding vs.
Data-Driven
Approach for Parameter
Interpretation
.83
6.4
Justification of a New Approach for Parameter Contribution
-
Part
2. 84
7
Stepwise Approaches for Model Selection
.85
7.1
Ordinary Stepwise Regression
.85
7.1.1
Criteria for Model Selection Based on Sum of Squares
DecompositionSo
7.1.2
Stepwise Regression, Forward and Backward Elimination
.87
7.2
Stepwise Procedures for Log-Linear Model Selection
.88
7.2.1
Stepwise Selection for a Given Model Hierarchy
.89
7.2.2
Screening Effects Procedure
.90
7.2.3
Goodman's Stepwise Procedure
.91
7.2.4
Model Selection According to Edwards
&
Havránek
.92
7.3
Justification of a New Approach for Parameter Contribution
-
Part
3. 93
8
A Procedure for Analyzing Standard and
Nonstandard
Models
.95
8.1
Entering of the Model Effects
.96
8.1.1
Correlation between Design Vectors and Dependent Variables
in Ordinary Regression
.96
8.1.2
Coefficients of Partial Correlation and Determination
in Ordinary Regression
.98
8.1.3
Implications of Correlation Analysis in Log-Linear Models
.99
8.1.4
Implications of Partial Correlations in Log-Linear Models
.102
8.2
Adopting Goodman's Forward Selection
.104
8.3
Relative Importance of Single Parameters
.105
8.3.1
Relative Importance by Averaging
Orderings
.105
8.3.2
An Approach Based on Information Theory
.106
8.3.3
The Dominance Analysis
.107
8.4
Some Pseudo-R2 Measures
.110
8.4.1
The Standard Approach for Pseudo-R2 in Log-Linear Models
.110
8.4.2
Further Proposals of Pseudo-R2 Measures
.111
8.5
Concluding Example
.112
9
Testing Non-Nested Models
.115
9.1
General Remarks for Model Testing
.115
9.2
A Likelihood Ratio Test for Non-Nested Models
.116
9.2.1
General Definitions and Assumptions
.116
9.2.2
Implications for Non-Nested and Overlapping Models
.119
9.3
Comparing Two AIC's
.121
9.3.1
Introductory Topics
.121
9.3.2
The Use of AIC in Log-Linear Models
.122
9.3.3
A Test whether Two AIC's Differ Significantly
.123
10
Algorithmic Implementation
.127
10.1
General Annotation
.127
10.2
Components of the New Procedure
.127
10.2.1
Input and Output
.127
10.2.2
Determining the Routine
.129
11
Examples
.133
11.1
Standard Log-Linear Model
.133
11.2
Nonstandard
Model with Special Coding Vector
.139
11.3
Example for Linhart's Test Procedure
.142
11.4
The Weak Wedge
.145
12
Summary
.149
13
Discussion
.151
References
.155 |
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| genre | (DE-588)4113937-9 Hochschulschrift gnd-content |
| genre_facet | Hochschulschrift |
| id | DE-604.BV021551177 |
| illustrated | Illustrated |
| index_date | 2024-07-02T14:31:44Z |
| indexdate | 2024-07-09T20:38:25Z |
| institution | BVB |
| isbn | 3830916116 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014767242 |
| oclc_num | 69983430 |
| open_access_boolean | |
| owner | DE-19 DE-BY-UBM DE-12 DE-355 DE-BY-UBR DE-634 |
| owner_facet | DE-19 DE-BY-UBM DE-12 DE-355 DE-BY-UBR DE-634 |
| physical | 164 S. graph. Darst. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Waxmann |
| record_format | marc |
| series | Internationale Hochschulschriften |
| series2 | Internationale Hochschulschriften |
| spelling | Mair, Patrick Verfasser (DE-588)131503707 aut Interpreting standard and nonstandard log-linear models Patrick Mair Münster ; München [u.a.] Waxmann 2006 164 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Internationale Hochschulschriften 455 Log-linear models Log-lineares Modell (DE-588)4036197-4 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Log-lineares Modell (DE-588)4036197-4 s DE-604 Internationale Hochschulschriften 455 (DE-604)BV035417764 455 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014767242&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mair, Patrick Interpreting standard and nonstandard log-linear models Internationale Hochschulschriften Log-linear models Log-lineares Modell (DE-588)4036197-4 gnd |
| subject_GND | (DE-588)4036197-4 (DE-588)4113937-9 |
| title | Interpreting standard and nonstandard log-linear models |
| title_auth | Interpreting standard and nonstandard log-linear models |
| title_exact_search | Interpreting standard and nonstandard log-linear models |
| title_exact_search_txtP | Interpreting standard and nonstandard log-linear models |
| title_full | Interpreting standard and nonstandard log-linear models Patrick Mair |
| title_fullStr | Interpreting standard and nonstandard log-linear models Patrick Mair |
| title_full_unstemmed | Interpreting standard and nonstandard log-linear models Patrick Mair |
| title_short | Interpreting standard and nonstandard log-linear models |
| title_sort | interpreting standard and nonstandard log linear models |
| topic | Log-linear models Log-lineares Modell (DE-588)4036197-4 gnd |
| topic_facet | Log-linear models Log-lineares Modell Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014767242&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV035417764 |
| work_keys_str_mv | AT mairpatrick interpretingstandardandnonstandardloglinearmodels |