Latent curve models: a structural equation perspective
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Hoboken, NJ
Wiley-Interscience
c2006
|
| Series: | Wiley series in probability and statistics
|
| Subjects: | |
| Online Access: | Publisher description Table of contents only Contributor biographical information Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke Includes bibliographical references (p. 263-273) and indexes |
| Physical Description: | XII, 285 S. graph. Darst. |
| ISBN: | 047145592X 9780471455929 |
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MARC
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| 100 | 1 | |a Bollen, Kenneth A. |d 1951- |e Verfasser |0 (DE-588)17020717X |4 aut | |
| 245 | 1 | 0 | |a Latent curve models |b a structural equation perspective |c Kenneth A. Bollen ; Patrick J. Curran |
| 264 | 1 | |a Hoboken, NJ |b Wiley-Interscience |c c2006 | |
| 300 | |a XII, 285 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Wiley series in probability and statistics | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 500 | |a Includes bibliographical references (p. 263-273) and indexes | ||
| 650 | 4 | |a Analyse de structure latente | |
| 650 | 4 | |a Variables latentes | |
| 650 | 4 | |a Latent structure analysis | |
| 650 | 4 | |a Latent variables | |
| 650 | 0 | 7 | |a Psychologie |0 (DE-588)4047704-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Latente Variable |0 (DE-588)4166860-1 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Curran, Patrick J. |d 1965- |e Verfasser |0 (DE-588)135855721 |4 aut | |
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| 856 | 4 | |u http://www.loc.gov/catdir/enhancements/fy0653/2005047028-b.html |3 Contributor biographical information | |
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Record in the Search Index
| _version_ | 1826846411131453440 |
|---|---|
| adam_text |
Contents
Preface
xi
1
Introduction
1
1.1
Conceptualization
and Analysis of Trajectories,
2
1.1.1
Trajectories of
Crime Rates,
З
1.1.2
Data Requirements,
7
1.1.3
Summary,
7
1.2
Three Initial Questions About Trajectories,
8
1.2.1
Question
1:
What Is the Trajectory for the Entire
Group?,
8
1.2.2
Question
2:
Do We Need Distinct Trajectories for Each
Case?,
8
1.2.3
Question
3:
If Distinct Trajectories Are Needed, Can We
Identify Variables to Predict These Individual
Trajectories?,
9
1.2.4
Summary,
9
1.3
Brief History of Latent Curve Models,
9
1.3.1
Early Developments: The Nineteenth Century,
10
1.3.2
Fitting Group Trajectories:
1900-1937, 11
1.3.3
Fitting Individual and Group Trajectories:
1938-1950s, 12
1.3.4
Trajectory Modeling with Latent Variables:
1950s-1984, 12
1.3.5
Current Latent Curve Modeling: 1984-present,
13
1.3.6
Summary,
14
1.4
Organization of the Remainder of the Book,
14
2
Unconditional Latent Curve Model
16
2.1
Repeated Measures,
16
2.2
General Model and Assumptions,
19
2.3
Identification,
21
2.4
Case-By-Case Approach,
25
2.4.1
Assessing Model Fit,
29
2.4.2
Limitations of Case-by-Case Approach,
33
2.5
Structural Equation Model Approach,
34
2.5.1
Matrix Expression of the Latent Curve Model,
36
2.5.2
Maximum Likelihood Estimation,
39
2.5.3
Empirical Example,
42
2.5.4
Assessing Model Fit,
44
2.5.5
Components of Fit,
48
2.6
Alternative Approaches to the
SEM,
54
2.7
Conclusions,
55
Appendix 2A: Test Statistics, Nonnormality, and Statistical Power,
55
3
Missing Data and Alternative Metrics of Time
58
3.1
Missing Data,
58
3.1.1
Types of Missing Data,
58
3.1.2
Treatment of Missing Data,
62
3.1.3
Empirical Example,
68
3.1.4
Summary,
72
3.2
Missing Data and Alternative Metrics of Time,
73
3.2.1
Numerical Measure of Time,
73
3.2.2
When Wave of Assessment and Alternative Metrics of
Time Are Equivalent,
74
3.2.3
When Wave of Assessment and Alternative Metrics of
Time Are Different,
77
3.2.4
Reorganizing Data as a Function of Alternative Metrics
of Time,
79
3.2.5
Individually Varying Values of Time,
81
3.2.6
Summary,
82
3.2.7
Empirical Example: Reading Achievement,
83
3.3
Conclusions,
87
4
Nonlinear Trajectories and the Coding of Time
88
4.1
Modeling Nonlinear Functions of Time,
89
4.1.1
Polynomial Trajectories: Quadratic Trajectory Model,
89
4.1.2
Polynomial Trajectories: Cubic Trajectory Models,
97
4.1.3
Summary,
98
4.2
Nonlinear Curve Fitting: Estimated Factor Loadings,
98
4.2.1
Selecting the Metric of Change,
102
4.3
Piecewise Linear Trajectory Models,
103
4.3.1
Identification,
106
4.3.2
Interpretation,
106
4.4
Alternative Parametric Functions,
106
4.4.1
Exponential Trajectory,
107
4.4.2
Parametric Functions with Cycles,
109
4.4.3
Nonlinear Transformations of the Metric
of Time,
112
4.4.4
Nonlinear Transformations of the Repeated Measures,
112
4.5
Linear Transformations of the Metric of Time,
113
4.5.1
Logic of Recoding the Metric of Time,
114
4.5.2
General Framework for Transforming Time,
115
4.5.3
Summary,
120
4.6
Conclusions,
120
Appendix 4A: Identification of Quadratic and Piecewise Latent Curve
Models,
121
4A.1 Quadratic LCM,
121
4A.2 Piecewise LCM,
124
5
Conditional Latent Curve Models
126
5.1
Conditional Model and Assumptions,
126
5.2
Identification,
128
5.3
Structural Equation Modeling Approach,
132
5.3.1
Implied Moment Matrices,
133
5.3.2
Estimation,
136
5.3.3
Model Fit,
137
5.4
Interpretation of Conditional Model Estimates,
139
5.4.1
Direct Effects of Exogenous Co
variâtes on
Latent Curve
Factors,
139
5.4.2
Indirect Effects of Covariates on Repeated Measures,
141
5.4.3
Further Exploring Conditional Effects,
147
5.4.4
Higher-Order Interactions,
150
5.5
Empirical Example,
155
5.5.1
yt on
λ(
Regressions,
157
5.5.2
Regions of Significance and Confidence Bands,
158
5.5.3
Summary,
160
5.6
Conclusions,
160
6
The Analysis of Groups
162
6.1
Dummy Variable Approach,
163
6.1.1
Various Level
2
Models,
165
6.1.2
Identification, Estimation, and Model Fit,
165
6.1.3
Empirical Example,
166
6.1.4
Summary,
169
6.2
Multiple-Group Analysis,
170
6.2.1
Unconditional Latent Curve Model for Multiple Groups,
170
6.2.2
Conditional Latent Curve Model for Multiple Groups,
172
6.3
Unknown Group Membership,
180
6.3.1
Empirical Example,
182
6.4
Conclusions,
184
Appendix
6
A: Case-by-Case Approach to Analysis of Various
Groups,
184
6A.1 Dummy Variable Method,
185
6A.2 Multiple-Group Analysis,
185
6A.3 Unknown Group Membership,
186
6A.4 Appendix Summary,
187
7
Multivariate Latent Curve Models
188
7.1
Time-Invariant Covariates,
188
7.1.1
Empirical Example: Conditional Model of Reading and
Math Achievement,
191
7.2
Time-Varying Covariates,
192
7.2.1
Interpretation of Effects,
194
7.3
Simultaneous Inclusion of Time-Invariant and Time-Varying
Covariates,
195
7.3.1
Interpretation of Conditional TVC Latent Curve Model,
197
7.3.2
Empirical Example: Conditional TVC Model of Reading
and Math Achievement,
197
7.4
Multivariate Latent Curve Models,
198
7.4.1
Multivariate Latent Curve Model with TICs,
201
7.4.2
Multivariate
Latent
Curve Model with TICs and Factor
Regressions,
204
7.4.3
Empirical Example: Multivariate Conditional Latent
Curve Model of Reading and Math Achievement,
204
7.4.4
Summary,
207
7.5
Autoregressive
Latent Trajectory Model,
207
7.5.1
Autoregressive
(Simplex) Model,
208
7.5.2
Unconditional Bivariate ALT Model,
210
7.5.3
Conditional Bivariate ALT Model,
214
7.5.4
Empirical Example: Income Data from the National
Longitudinal Survey of Youth,
215
7.5.5
Summary,
217
7.6
General Equation for All Models,
218
7.6.1
Examples of General Notation,
220
7.7
Implied Moment Matrices,
225
7.8
Conclusions,
228
8
Extensions of Latent Curve Models
229
8.1
Dichotomous and Ordinal Repeated Measures,
229
8.1.1
Assumptions Violated,
230
8.1.2
Corrective Procedures,
232
8.1.3
Empirical Example,
240
8.1.4
Conditional Model,
243
8.1.5
Summary,
244
8.2
Repeated Latent Variables with Multiple Indicators,
245
8.2.1
Single Repeated Measure versus Multiple Indicators,
246
8.2.2
Multiple-Indicator Model,
247
8.2.3
Invariance:
Continuous Multiple Indicators,
254
8.2.4
Dichotomous and Ordinal Multiple Indicators,
257
8.2.5
Conditional Models,
258
8.2.6
Summary,
259
8.3
Latent Covariates,
259
8.4
Conclusions,
262
References
263
Author Index
275
Subject Index
279 |
| adam_txt |
Contents
Preface
xi
1
Introduction
1
1.1
Conceptualization
and Analysis of Trajectories,
2
1.1.1
Trajectories of
Crime Rates,
З
1.1.2
Data Requirements,
7
1.1.3
Summary,
7
1.2
Three Initial Questions About Trajectories,
8
1.2.1
Question
1:
What Is the Trajectory for the Entire
Group?,
8
1.2.2
Question
2:
Do We Need Distinct Trajectories for Each
Case?,
8
1.2.3
Question
3:
If Distinct Trajectories Are Needed, Can We
Identify Variables to Predict These Individual
Trajectories?,
9
1.2.4
Summary,
9
1.3
Brief History of Latent Curve Models,
9
1.3.1
Early Developments: The Nineteenth Century,
10
1.3.2
Fitting Group Trajectories:
1900-1937, 11
1.3.3
Fitting Individual and Group Trajectories:
1938-1950s, 12
1.3.4
Trajectory Modeling with Latent Variables:
1950s-1984, 12
1.3.5
Current Latent Curve Modeling: 1984-present,
13
1.3.6
Summary,
14
1.4
Organization of the Remainder of the Book,
14
2
Unconditional Latent Curve Model
16
2.1
Repeated Measures,
16
2.2
General Model and Assumptions,
19
2.3
Identification,
21
2.4
Case-By-Case Approach,
25
2.4.1
Assessing Model Fit,
29
2.4.2
Limitations of Case-by-Case Approach,
33
2.5
Structural Equation Model Approach,
34
2.5.1
Matrix Expression of the Latent Curve Model,
36
2.5.2
Maximum Likelihood Estimation,
39
2.5.3
Empirical Example,
42
2.5.4
Assessing Model Fit,
44
2.5.5
Components of Fit,
48
2.6
Alternative Approaches to the
SEM,
54
2.7
Conclusions,
55
Appendix 2A: Test Statistics, Nonnormality, and Statistical Power,
55
3
Missing Data and Alternative Metrics of Time
58
3.1
Missing Data,
58
3.1.1
Types of Missing Data,
58
3.1.2
Treatment of Missing Data,
62
3.1.3
Empirical Example,
68
3.1.4
Summary,
72
3.2
Missing Data and Alternative Metrics of Time,
73
3.2.1
Numerical Measure of Time,
73
3.2.2
When Wave of Assessment and Alternative Metrics of
Time Are Equivalent,
74
3.2.3
When Wave of Assessment and Alternative Metrics of
Time Are Different,
77
3.2.4
Reorganizing Data as a Function of Alternative Metrics
of Time,
79
3.2.5
Individually Varying Values of Time,
81
3.2.6
Summary,
82
3.2.7
Empirical Example: Reading Achievement,
83
3.3
Conclusions,
87
4
Nonlinear Trajectories and the Coding of Time
88
4.1
Modeling Nonlinear Functions of Time,
89
4.1.1
Polynomial Trajectories: Quadratic Trajectory Model,
89
4.1.2
Polynomial Trajectories: Cubic Trajectory Models,
97
4.1.3
Summary,
98
4.2
Nonlinear Curve Fitting: Estimated Factor Loadings,
98
4.2.1
Selecting the Metric of Change,
102
4.3
Piecewise Linear Trajectory Models,
103
4.3.1
Identification,
106
4.3.2
Interpretation,
106
4.4
Alternative Parametric Functions,
106
4.4.1
Exponential Trajectory,
107
4.4.2
Parametric Functions with Cycles,
109
4.4.3
Nonlinear Transformations of the Metric
of Time,
112
4.4.4
Nonlinear Transformations of the Repeated Measures,
112
4.5
Linear Transformations of the Metric of Time,
113
4.5.1
Logic of Recoding the Metric of Time,
114
4.5.2
General Framework for Transforming Time,
115
4.5.3
Summary,
120
4.6
Conclusions,
120
Appendix 4A: Identification of Quadratic and Piecewise Latent Curve
Models,
121
4A.1 Quadratic LCM,
121
4A.2 Piecewise LCM,
124
5
Conditional Latent Curve Models
126
5.1
Conditional Model and Assumptions,
126
5.2
Identification,
128
5.3
Structural Equation Modeling Approach,
132
5.3.1
Implied Moment Matrices,
133
5.3.2
Estimation,
136
5.3.3
Model Fit,
137
5.4
Interpretation of Conditional Model Estimates,
139
5.4.1
Direct Effects of Exogenous Co
variâtes on
Latent Curve
Factors,
139
5.4.2
Indirect Effects of Covariates on Repeated Measures,
141
5.4.3
Further Exploring Conditional Effects,
147
5.4.4
Higher-Order Interactions,
150
5.5
Empirical Example,
155
5.5.1
yt on
λ(
Regressions,
157
5.5.2
Regions of Significance and Confidence Bands,
158
5.5.3
Summary,
160
5.6
Conclusions,
160
6
The Analysis of Groups
162
6.1
Dummy Variable Approach,
163
6.1.1
Various Level
2
Models,
165
6.1.2
Identification, Estimation, and Model Fit,
165
6.1.3
Empirical Example,
166
6.1.4
Summary,
169
6.2
Multiple-Group Analysis,
170
6.2.1
Unconditional Latent Curve Model for Multiple Groups,
170
6.2.2
Conditional Latent Curve Model for Multiple Groups,
172
6.3
Unknown Group Membership,
180
6.3.1
Empirical Example,
182
6.4
Conclusions,
184
Appendix
6
A: Case-by-Case Approach to Analysis of Various
Groups,
184
6A.1 Dummy Variable Method,
185
6A.2 Multiple-Group Analysis,
185
6A.3 Unknown Group Membership,
186
6A.4 Appendix Summary,
187
7
Multivariate Latent Curve Models
188
7.1
Time-Invariant Covariates,
188
7.1.1
Empirical Example: Conditional Model of Reading and
Math Achievement,
191
7.2
Time-Varying Covariates,
192
7.2.1
Interpretation of Effects,
194
7.3
Simultaneous Inclusion of Time-Invariant and Time-Varying
Covariates,
195
7.3.1
Interpretation of Conditional TVC Latent Curve Model,
197
7.3.2
Empirical Example: Conditional TVC Model of Reading
and Math Achievement,
197
7.4
Multivariate Latent Curve Models,
198
7.4.1
Multivariate Latent Curve Model with TICs,
201
7.4.2
Multivariate
Latent
Curve Model with TICs and Factor
Regressions,
204
7.4.3
Empirical Example: Multivariate Conditional Latent
Curve Model of Reading and Math Achievement,
204
7.4.4
Summary,
207
7.5
Autoregressive
Latent Trajectory Model,
207
7.5.1
Autoregressive
(Simplex) Model,
208
7.5.2
Unconditional Bivariate ALT Model,
210
7.5.3
Conditional Bivariate ALT Model,
214
7.5.4
Empirical Example: Income Data from the National
Longitudinal Survey of Youth,
215
7.5.5
Summary,
217
7.6
General Equation for All Models,
218
7.6.1
Examples of General Notation,
220
7.7
Implied Moment Matrices,
225
7.8
Conclusions,
228
8
Extensions of Latent Curve Models
229
8.1
Dichotomous and Ordinal Repeated Measures,
229
8.1.1
Assumptions Violated,
230
8.1.2
Corrective Procedures,
232
8.1.3
Empirical Example,
240
8.1.4
Conditional Model,
243
8.1.5
Summary,
244
8.2
Repeated Latent Variables with Multiple Indicators,
245
8.2.1
Single Repeated Measure versus Multiple Indicators,
246
8.2.2
Multiple-Indicator Model,
247
8.2.3
Invariance:
Continuous Multiple Indicators,
254
8.2.4
Dichotomous and Ordinal Multiple Indicators,
257
8.2.5
Conditional Models,
258
8.2.6
Summary,
259
8.3
Latent Covariates,
259
8.4
Conclusions,
262
References
263
Author Index
275
Subject Index
279 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Bollen, Kenneth A. 1951- Curran, Patrick J. 1965- |
| author_GND | (DE-588)17020717X (DE-588)135855721 |
| author_facet | Bollen, Kenneth A. 1951- Curran, Patrick J. 1965- |
| author_role | aut aut |
| author_sort | Bollen, Kenneth A. 1951- |
| author_variant | k a b ka kab p j c pj pjc |
| building | Verbundindex |
| bvnumber | BV022861889 |
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| callnumber-search | QA278.6 |
| callnumber-sort | QA 3278.6 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | CM 4000 MR 2100 QH 253 QH 254 |
| classification_tum | SOZ 720f |
| ctrlnum | (OCoLC)58986172 (DE-599)BVBBV022861889 |
| dewey-full | 519.5/35 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5/35 |
| dewey-search | 519.5/35 |
| dewey-sort | 3519.5 235 |
| dewey-tens | 510 - Mathematics |
| discipline | Soziologie Psychologie Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Soziologie Psychologie Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV022861889 |
| illustrated | Illustrated |
| index_date | 2024-07-02T18:43:54Z |
| indexdate | 2025-03-17T13:01:42Z |
| institution | BVB |
| isbn | 047145592X 9780471455929 |
| language | English |
| lccn | 2005047028 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016067112 |
| oclc_num | 58986172 |
| open_access_boolean | |
| owner | DE-739 DE-29 DE-11 DE-703 DE-355 DE-BY-UBR DE-91 DE-BY-TUM DE-945 DE-N32 DE-19 DE-BY-UBM |
| owner_facet | DE-739 DE-29 DE-11 DE-703 DE-355 DE-BY-UBR DE-91 DE-BY-TUM DE-945 DE-N32 DE-19 DE-BY-UBM |
| physical | XII, 285 S. graph. Darst. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Wiley-Interscience |
| record_format | marc |
| series2 | Wiley series in probability and statistics |
| spelling | Bollen, Kenneth A. 1951- Verfasser (DE-588)17020717X aut Latent curve models a structural equation perspective Kenneth A. Bollen ; Patrick J. Curran Hoboken, NJ Wiley-Interscience c2006 XII, 285 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and statistics Hier auch später erschienene, unveränderte Nachdrucke Includes bibliographical references (p. 263-273) and indexes Analyse de structure latente Variables latentes Latent structure analysis Latent variables Psychologie (DE-588)4047704-6 gnd rswk-swf Latente Variable (DE-588)4166860-1 gnd rswk-swf Analyse latenter Strukturen (DE-588)4142341-0 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Psychologie (DE-588)4047704-6 s Statistik (DE-588)4056995-0 s DE-604 Analyse latenter Strukturen (DE-588)4142341-0 s Latente Variable (DE-588)4166860-1 s b DE-604 Curran, Patrick J. 1965- Verfasser (DE-588)135855721 aut http://www.loc.gov/catdir/enhancements/fy0624/2005047028-d.html Publisher description http://www.loc.gov/catdir/enhancements/fy0624/2005047028-t.html Table of contents only http://www.loc.gov/catdir/enhancements/fy0653/2005047028-b.html Contributor biographical information Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016067112&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bollen, Kenneth A. 1951- Curran, Patrick J. 1965- Latent curve models a structural equation perspective Analyse de structure latente Variables latentes Latent structure analysis Latent variables Psychologie (DE-588)4047704-6 gnd Latente Variable (DE-588)4166860-1 gnd Analyse latenter Strukturen (DE-588)4142341-0 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4047704-6 (DE-588)4166860-1 (DE-588)4142341-0 (DE-588)4056995-0 |
| title | Latent curve models a structural equation perspective |
| title_auth | Latent curve models a structural equation perspective |
| title_exact_search | Latent curve models a structural equation perspective |
| title_exact_search_txtP | Latent curve models a structural equation perspective |
| title_full | Latent curve models a structural equation perspective Kenneth A. Bollen ; Patrick J. Curran |
| title_fullStr | Latent curve models a structural equation perspective Kenneth A. Bollen ; Patrick J. Curran |
| title_full_unstemmed | Latent curve models a structural equation perspective Kenneth A. Bollen ; Patrick J. Curran |
| title_short | Latent curve models |
| title_sort | latent curve models a structural equation perspective |
| title_sub | a structural equation perspective |
| topic | Analyse de structure latente Variables latentes Latent structure analysis Latent variables Psychologie (DE-588)4047704-6 gnd Latente Variable (DE-588)4166860-1 gnd Analyse latenter Strukturen (DE-588)4142341-0 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Analyse de structure latente Variables latentes Latent structure analysis Latent variables Psychologie Latente Variable Analyse latenter Strukturen Statistik |
| url | http://www.loc.gov/catdir/enhancements/fy0624/2005047028-d.html http://www.loc.gov/catdir/enhancements/fy0624/2005047028-t.html http://www.loc.gov/catdir/enhancements/fy0653/2005047028-b.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016067112&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT bollenkennetha latentcurvemodelsastructuralequationperspective AT curranpatrickj latentcurvemodelsastructuralequationperspective |