Multilevel and longitudinal modeling using Stata: Volume 1 Continuous responses
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
College Station, Tex.
Stata Press
2012
|
| Edition: | Third edition |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xxx, 497 Seiten Diagramme |
| ISBN: | 9781597181037 159718103X |
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| 245 | 1 | 0 | |a Multilevel and longitudinal modeling using Stata |n Volume 1 |p Continuous responses |c Sophia Rabe-Hesketh ; Anders Skrondal |
| 250 | |a Third edition | ||
| 264 | 1 | |a College Station, Tex. |b Stata Press |c 2012 | |
| 300 | |a xxx, 497 Seiten |b Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 700 | 1 | |a Skrondal, Anders |d 1961- |e Verfasser |0 (DE-588)14306097X |4 aut | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-024892313 | ||
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|---|---|
| adam_text | Contents
List of Tables
xvii
List of Figures
xix
Preface
xxv
Multilevel and longitudinal models: When and why?
1
I Preliminaries
9
1
Review of linear regression
11
1.1
Introduction
............................... 11
1.2
Is there gender discrimination in faculty salaries?
.......... 11
1.3
Independent-samples
t
test
....................... 12
1.4
One-way analysis of variance
......................
IT
1.5
Simple linear regression
......................... 19
1.6
Dummy variables
............................ 27
1.7
Multiple linear regression
........................ 30
1.8
Interactions
............................... 36
1.9
Dummy variables for more than two groups
............. 42
1.10
Other types of interactions
....................... 48
1.10.1
Interaction between dummy variables
............ 48
1.10.2
Interaction between continuous covariates
.......... 50
1.11
Nonlinear effects
............................. 52
1.12
Residual diagnostics
........................... 54
1.13
V Causal and noncausal interpretations of regression coefficients
. .
5tí
1.13.1
Regression as conditional expectation
............ 56
1.13.2
Regression as structural model
................ 57
vji{
Contents
1.14
Summary and further reading
..................... 59
1.15
Exercises
................................. 60
II Two-level models
71
2
Variance-components models
73
2.1
Introduction
............................... 73
2.2
How reliable are peak-expiratory-flow measurements?
........ 74
2.3
Inspecting within-subject dependence
................. 75
2.4
The variance-components model
.................... 77
2.4.1
Model specification
...................... 77
2.4.2
Path diagram
......................... 78
2.4.3
Between-subject heterogeneity
................ 79
2.4.4
Within-subject dependence
.................. 80
Intraclass correlation
..................... 80
Intraclass correlation versus Pearson correlation
...... 81
2.5
Estimation using
Stata
......................... 82
2.5.1
Data preparation: Reshaping to long form
......... 83
2.5.2
Using xtreg
........................... 84
2.5.3
Using xtmixed
......................... 85
2.6
Hypothesis tests and confidence intervals
............... 87
2.6.1
Hypothesis test and confidence interval for the popula¬
tion mean
............................ 87
2.6.2
Hypothesis test and confidence interval for the between-
cluster variance
........................ 88
Likelihood-ratio tost
...................... 88
♦♦♦
Score test
.......................... 8!)
f
test
..............................
m
Confidence intervals
...................... 92
2.7
Model as data-generating mechanism
................. 93
2.8
Fixed versus random effects
...................... 95
2.9
Crossed versus nested effects
...................... 97
Contents ix
2.10 Parameter
estimation..........................
99
2.10.1 Model
assumptions ......................
99
Mean structure and covariance structure
.......... 100
Distributional assumptions
.................. 101
2.10.2
Different estimation methods
................. 101
2.10.3
Inference for
β
......................... 103
Estimate and standard error: Balanced case
........ 103
Estimate: Unbalanced case
.................. 105
2.11
Assigning values to the random intercepts
.............. 106
2.11.1
Maximum likelihood estimation
.............. 106
Implementation via OLS regression
............. 107
Implementation via the mean total residual
......... 108
2.11.2
Empirical
Bayes
prediction
.................. 109
2.11.3
Empirical
Bayes
standard errors
............... 113
Comparative standard errors
................. 113
Diagnostic standard errors
.................. 114
2.12
Summary and further reading
..................... 115
2.13
Exercises
................................. 116
3
Random-intercept models with covariates
123
3.1
Introduction
............................... 123
3.2
Does smoking during pregnancy affect birthweight?
......... 123
3.2.1
Data
structure
and descriptive statistics
........... 125
3.3
The linear random-intercept model with covariates
......... 127
3.3.1
Model specification
...................... 127
3.3.2
Model assumptions
...................... 128
3.3.3
Mean
structure
......................... 130
3.3.4
Residual variance and hitraclass correlation
......... 130
3.3.5
Graphical illustration of random-intercept model
...... 131
3.4
Estimation using
Stata
......................... 131
3.4.1
Using xtreg
........................... 132
Contents
3.4.2
Using xtmixed
......................... 133
3.5
Coefficients of determination or variance explained
......... 134
3.6
Hypothesis tests and confidence intervals
............... 138
3.6.1
Hypothesis tests for regression coefficients
.......... 138
Hypothesis tests for individual regression coefficients
... 138
Joint hypothesis tests for several regression coefficients
. . 130
3.6.2
Predicted means and confidence intervals
.......... 140
3.6.3
Hypothesis test for random-intercept variance
....... 142
3.7
Between and within effects of level-1 covariates
............ 142
3.7.1
Between-mother effects
.................... 143
3.7.2
Within-mother effects
..................... 145
3.7.3
Relations among estimators
.................. 147
3.7.4
Level-2 endogeneity and cluster-level confounding
..... 149
3.7.5
Allowing for different within and between effects
...... 152
3.7.6
Hausman endogeneity test
.................. 157
3.8
Fixed versus random, effects revisited
................. 158
3.9
Assigning values to random effects: Eesidual diagnostics
...... 160
3.10
More on statistical inference
...................... 164
3.10.1 *$♦
Overview of estimation methods
............. 164
3.10.2
Consequences of using standard regression modeling for
clustered data
......................... 167
3.10.3
V Power and sample-size determination
........... 168
3.11
Summary and further reading
..................... 171
3.12
Exercise«
................................. 172
Random-coefficient models
181
4.1
Introduction
............................... 181
4.2
How effective are different schools?
.................. 181
4.3
Separate linear regressions for each school
.............. 182
4.4
Specification and interpretation of a random-coefficient model
. . . 188
4.4.1
Specification of a random-coefficient model
......... 188
Contents xi
4.4.2 Interpretation
of the random-effects variances and co-
variances
............................ 191
4.5
Estimation using xtmixed
........................ 194
4.5.1
Random-intercept model
................... 194
4.5.2
Random-coefficient model
................... 196
4.6
Testing the slope variance
....................... 197
4.7
Interpretation of estimates
....................... 198
4.8
Assigning values to the random intercepts and slopes
........ 200
4.8.1
Maximum likelihood estimation
.............. 200
4.8.2
Empirical
Bayes
prediction
.................. 201
4.8.3
Model visualization
...................... 203
4.8.4
Residual diagnostics
...................... 204
4.8.5
Inferences for individual schools
............... 207
4.9
Two-stage model formulation
...................... 210
4.10
Some warnings about random-coefficient models
........... 213
4.10.1
Meaningful specification
.................... 213
4.10.2
Many random coefficients
................... 213
4.10.3
Convergence problems
..................... 214
4.10.4
Lack of identification
..................... 214
4.11
Summary and further reading
..................... 215
4.12
Exercises
................................. 216
III Models for longitudinal and panel data
225
Introduction to models for longitudinal and panel data (part III)
227
5
Subject-specific effects and dynamic models
247
5.1
Introduction
............................... 247
5.2
Conventional random-intercept model
................. 248
5.3
Random-intercept models accommodating endogenous covariatcs
. . 250
5.3.1
Consistent estimation of effects of endogenous
time-varying covariates
.................... 250
·· Contents
хи
5.3.2
Consistent estimation
of effects of endogenous
time-varying and endogenous time-constant covariates
. . . 253
5.4
Fixed-intercept model
.......................... 257
5.4.1
Using xtreg or regress with a differencing operator
..... 259
5.4.2 ♦♦♦
Using anova
.........................
2G2
5.5
Random-coefficient model
....................... 265
5.6
Fixed-coefficient model
......................... 267
5.7
Lagged-response or dynamic models
.................. 269
5.7.1
Conventional lagged-response model
............. 269
5.7.2 ♦♦♦
Lagged-response model with subject-specific intercepts
. 273
5.8
Missing data and dropout
....................... 278
5.8.1
V Maximum likelihood estimation under MAR:
A simulation
.......................... 279
5.9
Summary and further reading
..................... 282
5.10
Exercises
................................. 283
6
Marginal models
293
6.1
Introduction
............................... 293
6.2
Mean structure
............................. 293
6.3
Covariance structures
.......................... 294
6.3.1
Unstructured covariance matrix
............... 298
6.3.2
Random-intercept or compound
symmetric/exchangeable structure
.............. 303
6.3.3
Random-coefficient structure
................. 305
6.3.4
Autoregressiw and exponential structures
.......... 308
6.3.5
Moving-average residual structure
.............. 311
6.3.6
Banded and Toeplitz structures
............... 313
6.4
Hybrid and complex marginal models
................. 316
6.4.1
Random effects and correlated level-
1
residuals
....... 316
6.4.2
Heteroskedastic level-1 residuals over occasions
....... 317
6.4.3
Heteroskedastic level-
1
residuals over groups
........ 318
6.4.4
Different covariance matrices over groups
.......... 321
Contents xiii
6.5
Comparing the fit of marginal models
................. 322
6.6
Generalized estimating equations (GEE)
............... 325
6.7
Marginal modeling with few units and many occasions
....... 327
6.7.1
Is a highly organized labor market beneficial for eco¬
nomic growth?
......................... 328
6.7.2
Marginal modeling for long panels
.............. 329
6.7.3
Fitting marginal models for long panels in
Stata
...... 329
6.8
Summary and further reading
..................... 332
6.9
Exercises
................................. 333
7
Growth-curve models
343
7.1
Introduction
............................... 343
7.2
How do children grow?
......................... 343
7.2.1
Observed growth trajectories
................. 344
7.3
Models for nonlinear growth
...................... 345
7.3.1
Polynomial models
....................... 345
Fitting the models
....................... 346
Predicting the mean trajectory
................ 349
Predicting trajectories for individual children
........ 351
7.3.2
Piecewise linear models
.................... 353
Fitting the models
....................... 354
Predicting the mean trajectory
................ 357
7.4
Two-stage model formulation
...................... 358
7.5
Heteroskedasticity
............................ 360
7.5.1
Heteroskedasticity at level
1 ................. 360
7.5.2
HeteroHkedasticity at level
2................. 362
7.6
How does reading improve from kindergarten through third grade?
364
7.7
Growth-curve model as a structural equation model
......... 364
7.7.1
Estimation using
sem
.....................
36G
7.7.2
Estimation using xtmixed
................... 371
7.8
Summary and further reading
..................... 375
xjv
Contents
7.9
Exercises
................................. 376
IV
Models
with nested and crossed random effects
383
8
Higher-level models with nested random effects
385
8.1
Introduction
............................... 385
8.2
Do peak-expiratory-flow measurements vary between methods
within subjects?
............................. 386
8.3
Inspecting sources of variability
.................... 388
8.4
Three-level variance-components models
............... 389
8.5
Different types of intraclass correlation
................ 392
8.6
Estimation using xtmixed
........................ 393
8.7
Empirical
Bayes
prediction
....................... 394
8.8
Testing variance components
...................... 395
8.9
Crossed versus nested random effects revisited
............ 397
8.10
Does nutrition affect cognitive development of Kenyan children?
. . 399
8.11
Describing and plotting three-level data
................ 400
8.11.1
Data structure and missing data
............... 400
8.11.2
Level-1 variables
........................ 401
8.11.3
LeveI-2 variables
........................ 402
8.11.4
Level-3 variables
........................ 403
8.11.5
Plotting growth trajectories
................. 404
8.12
Three-level random-intercept model
.................. 405
8.12.1
Model specification: Reduced form
.............. 405
8.12.2
Model specification: Three-stage formulation
........ 405
8.12.3
Estimation
using xtmixed
................... 406
8.13
Three-level random-coefficient models
................. 409
8.13.1
Random coefficient at the child level
............. 409
8.13.2
Random coefficient at the child and school levels
...... 411
8.14
Residual diagnostics and predictions
.................. 413
8.15
Summary and further reading
..................... 418
8.16
Exercises
................................. 419
Contents xv
9
Crossed random effects
433
9.1
Introduction
............................... 433
9.2
How does investment depend on expected profit and capital stock?
434
9.3
A two-way error-components model
.................. 435
9.3.1
Model specification
...................... 435
9.3.2
Residual variances, covariances, and intraclass correlations
436
Longitudinal correlations
................... 436
Cross-sectional correlations
.................. 436
9.3.3
Estimation using xtmixed
................... 437
9.3.4
Prediction
........................... 441
9.4
How much do primary and secondary schools affect attainment at
age
16?.................................. 443
9.5
Data structure
.............................. 444
9.6
Additive crossed random-effects model
................ 446
9.6.1
Specification
.......................... 446
9.6.2
Estimation using xtmixed
................... 447
9.7
Crossed random-effects model with random interaction
....... 448
9.7.1
Model specification
...................... 448
9.7.2
Intraclass correlations
..................... 448
9.7.3
Estimation using xtmixed
................... 449
9.7.4
Testing variance components
................. 451
9.7.5
Some diagnostics
........................ 453
9.8
^ A trick requiring fewer random effects
............... 456
9.9
Summary and further reading
..................... 459
9.10
Exercises
................................. 460
A Useful
Stata
commands
471
References
473
Author index
485
Subject index
491
|
| any_adam_object | 1 |
| author | Rabe-Hesketh, Sophia Skrondal, Anders 1961- |
| author_GND | (DE-588)13573116X (DE-588)14306097X |
| author_facet | Rabe-Hesketh, Sophia Skrondal, Anders 1961- |
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| bvnumber | BV040035505 |
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| id | DE-604.BV040035505 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T00:16:37Z |
| institution | BVB |
| isbn | 9781597181037 159718103X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024892313 |
| oclc_num | 796196815 |
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| physical | xxx, 497 Seiten Diagramme |
| publishDate | 2012 |
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| publisher | Stata Press |
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| spelling | Rabe-Hesketh, Sophia Verfasser (DE-588)13573116X aut Multilevel and longitudinal modeling using Stata Volume 1 Continuous responses Sophia Rabe-Hesketh ; Anders Skrondal Third edition College Station, Tex. Stata Press 2012 xxx, 497 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Skrondal, Anders 1961- Verfasser (DE-588)14306097X aut (DE-604)BV040035494 1 Digitalisierung UB Bamberg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024892313&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rabe-Hesketh, Sophia Skrondal, Anders 1961- Multilevel and longitudinal modeling using Stata |
| title | Multilevel and longitudinal modeling using Stata |
| title_auth | Multilevel and longitudinal modeling using Stata |
| title_exact_search | Multilevel and longitudinal modeling using Stata |
| title_full | Multilevel and longitudinal modeling using Stata Volume 1 Continuous responses Sophia Rabe-Hesketh ; Anders Skrondal |
| title_fullStr | Multilevel and longitudinal modeling using Stata Volume 1 Continuous responses Sophia Rabe-Hesketh ; Anders Skrondal |
| title_full_unstemmed | Multilevel and longitudinal modeling using Stata Volume 1 Continuous responses Sophia Rabe-Hesketh ; Anders Skrondal |
| title_short | Multilevel and longitudinal modeling using Stata |
| title_sort | multilevel and longitudinal modeling using stata continuous responses |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024892313&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV040035494 |
| work_keys_str_mv | AT rabeheskethsophia multilevelandlongitudinalmodelingusingstatavolume1 AT skrondalanders multilevelandlongitudinalmodelingusingstatavolume1 |