Latent curve models: a structural equation perspective
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Hoboken, NJ
Wiley-Interscience
2009
|
| Edition: | [Nachdr. der Ausg. 2006] |
| Series: | Wiley series in probability and statistics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| 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 |
| 250 | |a [Nachdr. der Ausg. 2006] | ||
| 264 | 1 | |a Hoboken, NJ |b Wiley-Interscience |c 2009 | |
| 300 | |a XII, 285 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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Record in the Search Index
| _version_ | 1826846411839242240 |
|---|---|
| adam_text |
Contents
Preface
x¡
1
Introduction
1
1.1
Conceptualization and Analysis of Trajectories,
2
1.1.1
Trajectories of Crime Rates,
3
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:
195OS-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
vi
CONTENTS
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
CONTENTS
vij
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
S
Conditional Latent Curve Models
126
5.1
Conditional
Modei
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 Covariates 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
y t
on
λ,
Regressions,
157
viii CONTENTS
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 6A: 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
CONTENTS
¡χ
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 |
| 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- |
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| building | Verbundindex |
| bvnumber | BV037181471 |
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| ctrlnum | (OCoLC)706986284 (DE-599)BVBBV037181471 |
| discipline | Soziologie Psychologie Wirtschaftswissenschaften |
| edition | [Nachdr. der Ausg. 2006] |
| format | Book |
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| id | DE-604.BV037181471 |
| illustrated | Illustrated |
| indexdate | 2025-03-17T13:01:42Z |
| institution | BVB |
| isbn | 047145592X 9780471455929 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-021096074 |
| oclc_num | 706986284 |
| open_access_boolean | |
| owner | DE-188 DE-20 |
| owner_facet | DE-188 DE-20 |
| physical | XII, 285 S. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| 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 [Nachdr. der Ausg. 2006] Hoboken, NJ Wiley-Interscience 2009 XII, 285 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and statistics Hier auch später erschienene, unveränderte Nachdrucke 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 1\p DE-604 Curran, Patrick J. 1965- Verfasser (DE-588)135855721 aut Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021096074&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bollen, Kenneth A. 1951- Curran, Patrick J. 1965- Latent curve models a structural equation perspective 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_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 | 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 | Latent structure analysis Latent variables Psychologie Latente Variable Analyse latenter Strukturen Statistik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021096074&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT bollenkennetha latentcurvemodelsastructuralequationperspective AT curranpatrickj latentcurvemodelsastructuralequationperspective |