Interpreting and visualizing regression models using Stata:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
College Station, Tex.
Stata Press
2012
|
| Edition: | 1. ed. |
| Series: | A Stata Press publication
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Item Description: | Literaturverz. S. 545 - 547 |
| Physical Description: | XXVIII, 558 S. graph. Darst. |
| ISBN: | 9781597181075 1597181072 |
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| 245 | 1 | 0 | |a Interpreting and visualizing regression models using Stata |c Michael N. Mitchell |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a College Station, Tex. |b Stata Press |c 2012 | |
| 300 | |a XXVIII, 558 S. |b graph. Darst. | ||
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| _version_ | 1804148993338376192 |
|---|---|
| adam_text | Contents
List of tables
xv
List of figures
xvii
Preface
xxvii
Acknowledgments
xxix
1
Introduction
1
1.1
Overview of the book
........................... 1
1.2
Getting the most out of this book
.................... 3
1.3
Downloading the example
datasets
and programs
........... 4
1.4
The GSS
dataset
............................. 4
1.4.1
Income
.............................. 5
1.4.2
Age
................................ 6
1.4.3
Education
............................ 10
1.4.4
Gender
.............................. 12
1.5
The pain
datasets
............................. 12
1.6
The optimism
datasets
.......................... 12
1.7
The school
datasets
............................ 13
1.8
The sleep
datasets
............................ 13
1 Continuous predictors
15
2
Continuous predictors: Linear
17
2.1
Chapter overview
............................. 17
2.2
Simple linear regression
......................... 17
2.2.1
Computing predicted means using the margins command
. . 20
2.2.2
Graphing predicted means using the marginsplot command
22
2.3
Multiple regression
............................ 25
vi
Contents
2.3.1 Computing
adjusted means using the margins command
. . 26
2.3.2
Some technical details about adjusted means
......... 28
2.3.3
Graphing adjusted means using the marginsplot command
. 29
2.4
Checking for nonlinearity graphically
.................. 30
2.4.1
Using scatterplots to check for nonlinearity
.......... 31
2.4.2
Checking for nonlinearity using residuals
........... 31
2.4.3
Checking for nonlinearity using locally weighted smoother
. 33
2.4.4
Graphing outcome mean at each level of predictor
...... 34
2.4.5
Summary
............................ 37
2.5
Checking for nonlinearity analytically
................. 37
2.5.1
Adding power terms
...................... 38
2.5.2
Using factor variables
...................... 39
2.6
Summary
................................. 43
3
Continuous predictors: Polynomials
45
3.1
Chapter overview
............................. 45
3.2
Quadratic (squared) terms
........................ 45
3.2.1
Overview
............................. 45
3.2.2
Examples
............................ 49
3.3
Cubic (third power) terms
........................ 55
3.3.1
Overview
............................. 55
3.3.2
Examples
............................ 56
3.4
Fractional polynomial regression
.................... 62
3.4.1
Overview
............................. 62
3.4.2
Example using fractional polynomial regression
....... 66
3.5
Main effects with polynomial terms
................... 75
3.6
Summary
................................. 77
4
Continuous predictors: Piecewise models
79
4.1
Chapter overview
............................. 79
4.2
Introduction to piecewise regression models
.............. 80
4.3
Piecewise with one known knot
..................... 82
Contents
vii
4.3.1
Overview
............................. 82
4.3.2
Examples using the GSS
.................... 83
4.4
Piecewise with two known knots
.................... 91
4.4.1
Overview
............................. 91
4.4.2
Examples using the GSS
.................... 91
4.5
Piecewise with one knot and one jump
................. 96
4.5.1
Overview
............................. 96
4.5.2
Examples using the GSS
.................... 97
4.6
Piecewise with two knots and two jumps
................ 102
4.6.1
Overview
............................. 102
4.6.2
Examples using the GSS
.................... 102
4.7
Piecewise with an unknown knot
.................... 109
4.8
Piecewise model with multiple unknown knots
............. 113
4.9
Piecewise models and the marginsplot command
........... 120
4.10
Automating graphs of piecewise models
................ 123
4.11
Summary
................................. 126
5
Continuous by continuous interactions
127
5.1
Chapter overview
............................. 127
5.2
Linear by linear interactions
....................... 127
5.2.1
Overview
............................. 127
5.2.2
Example using GSS data
.................... 132
5.2.3
Interpreting the interaction in terms of age
.......... 133
5.2.4
Interpreting the interaction in terms of education
...... 135
5.2.5
Interpreting the interaction in terms of age slope
...... 137
5.2.6
Interpreting the interaction in terms of the
educ
slope
. . . 138
5.3
Linear by quadratic interactions
..................... 140
5.3.1
Overview
............................. 140
5.3.2
Example using GSS data
.................... 143
5.4
Summary
................................. 148
viii Contents
6
Continuous by continuous by continuous interactions
149
6.1
Chapter overview
............................. 149
6.2
Overview
................................. 149
6.3
Examples using the GSS data
...................... 154
6.3.1
A model without a three-way interaction
........... 154
6.3.2
A three-way interaction model
................. 158
6.4
Summary
................................. 164
II Categorical predictors
165
7
Categorical predictors
167
7.1
Chapter overview
............................. 167
7.2
Comparing two groups using a t test
.................. 168
7.3
More groups and more predictors
.................... 169
7.4
Overview of contrast operators
..................... 175
7.5
Compare each group against a reference group
............. 176
7.5.1
Selecting a specific contrast
.................. 177
7.5.2
Selecting a different reference group
.............. 178
7.5.3
Selecting a contrast and reference group
........... 179
7.6
Compare each group against the grand mean
............. 179
7.6.1
Selecting a specific contrast
.................. 181
7.7
Compare adjacent means
......................... 182
7.7.1
Reverse adjacent contrasts
................... 185
7.7.2
Selecting a specific contrast
.................. 186
7.8
Comparing the mean of subsequent or previous levels
......... 187
7.8.1
Comparing the mean of previous levels
............ 191
7.8.2
Selecting a specific contrast
.................. 192
7.9
Polynomial contrasts
........................... 193
7.10
Custom contrasts
............................. 195
7.11
Weighted contrasts
............................ 198
7.12
Pairwise comparisons
...........................200
Contents ix
7.13
Interpreting confidence intervals
..................... 202
7.14
Testing categorical variables using regression
............. 205
7.15
Summary
................................. 208
8
Categorical by categorical interactions
209
8.1
Chapter overview
............................. 209
8.2
Two by two models: Example
1..................... 211
8.2.1
Simple effects
.......................... 215
8.2.2
Estimating the size of the interaction
............. 216
8.2.3
More about interaction
..................... 217
8.2.4
Summary
............................ 218
8.3
Two by three models
........................... 218
8.3.1
Example
2............................ 218
8.3.2
Example
3............................ 223
8.3.3
Summary
............................ 228
8.4
Three by three models: Example
4................... 228
8.4.1
Simple effects
.......................... 230
8.4.2
Simple contrasts
......................... 231
8.4.3
Partial interaction
....................... 233
8.4.4
Interaction contrasts
...................... 234
8.4.5
Summary
............................ 236
8.5
Unbalanced designs
............................ 236
8.6
Main effects with interactions: anova versus regress
.......... 241
8.7
Interpreting confidence intervals
..................... 244
8.8
Summary
................................. 246
9
Categorical by categorical by categorical interactions
249
9.1
Chapter overview
............................. 249
9.2
Two by two by two models
....................... 250
9.2.1
Simple interactions by season
................. 252
9.2.2
Simple interactions by depression status
........... 253
9.2.3
Simple effects
.......................... 255
χ
Contents
9.3
Two by two by three models
....................... 255
9.3.1
Simple interactions by depression status
........... 258
9.3.2
Simple partial interaction by depression status
........ 258
9.3.3
Simple contrasts
......................... 260
9.3.4
Partial interactions
....................... 260
9.4
Three by three by three models and beyond
.............. 262
9.4.1
Partial interactions and interaction contrasts
......... 264
9.4.2
Simple interactions
....................... 268
9.4.3
Simple effects and simple comparisons
............ 271
9.5
Summary
................................. 272
III Continuous and categorical predictors
273
10
Linear by categorical interactions
275
10.1
Chapter overview
............................. 275
10.2
Linear and two-level categorical: No interaction
............ 275
10.2.1
Overview
............................. 275
10.2.2
Examples using the GSS
.................... 278
10.3
Linear by two-level categorical interactions
............... 283
10.3.1
Overview
............................. 283
10.3.2
Examples using the GSS
.................... 285
10.4
Linear by three-level categorical interactions
.............. 290
10.4.1
Overview
............................. 290
10.4.2
Examples using the GSS
.................... 293
10.5
Summary
................................. 299
11
Polynomial by categorical interactions
301
11.1
Chapter overview
............................. 301
11.2
Quadratic by categorical interactions
.................. 301
11.2.1
Overview
............................. 302
11.2.2
Quadratic by two-level categorical
............... 305
11.2.3
Quadratic by three-level categorical
.............. 312
Contents xi
11.3
Cubic by categorical interactions
.................... 318
11.4
Summary
................................. 323
12
Piecewise by categorical interactions
325
12.1
Chapter overview
............................. 325
12.2
One knot arid one jump
......................... 328
12.2.1
Comparing slopes across gender
................ 332
12.2.2
Comparing slopes across education
.............. 333
12.2.3
Difference in differences of slopes
............... 333
12.2.4
Comparing changes in intercepts
............... 334
12.2.5
Computing and comparing adjusted means
.......... 334
12.2.6
Graphing adjusted means
................... 337
12.3
Two knots and two jumps
........................ 341
12.3.1
Comparing slopes across gender
................ 346
12.3.2
Comparing slopes across education
.............. 347
12.3.3
Difference in differences of slopes
............... 348
12.3.4
Comparing changes in intercepts by gender
......... 349
12.3.5
Comparing changes in intercepts by education
........ 350
12.3.6
Computing and comparing adjusted means
.......... 351
12.3.7
Graphing adjusted means
................... 354
12.4
Comparing coding schemes
....................... 356
12.4.1
Coding scheme
#1....................... 356
12.4.2
Coding scheme
#2....................... 358
12.4.3
Coding scheme
#3....................... 360
12.4.4
Coding scheme
#4....................... 361
12.4.5
Choosing coding schemes
.................... 363
12.5
Summary
................................. 364
13
Continuous by continuous by categorical interactions
365
13.1
Chapter overview
............................. 365
13.2
Linear by linear by categorical interactions
............... 366
13.2.1
Fitting separate models for males and females
........ 366
xjj Contents
13.2.2
Fitting a combined model for males and females
....... 368
13.2.3
Interpreting the interaction focusing in the age slope
.... 370
13.2.4
Interpreting the interaction focusing on the
educ
slope
. . . 372
13.2.5
Estimating and comparing adjusted means by gender
.... 374
13.3
Linear by quadratic by categorical interactions
............ 376
13.3.1
Fitting separate models for males and females
........ 376
13.3.2
Fitting a common model for males and females
....... 378
13.3.3
Interpreting the interaction
.................. 379
13.3.4
Estimating and comparing adjusted means by gender
.... 380
13.4
Summary
................................. 382
14
Continuous by categorical by categorical interactions
383
14.1
Chapter overview
............................. 383
14.2
Simple effects of gender on the age slope
................ 387
14.3
Simple effects of education on the age slope
.............. 388
14.4
Simple contrasts on education for the age slope
............ 389
14.5
Partial interaction on education for the age slope
........... 389
14.6
Summary
................................. 390
IV Beyond ordinary linear regression
391
15
Multilevel models
393
15.1
Chapter overview
............................. 393
15.2
Example
1:
Continuous by continuous interaction
........... 394
15.3
Example
2:
Continuous by categorical interaction
........... 397
15.4
Example
3:
Categorical by continuous interaction
........... 401
15.5
Example
4:
Categorical by categorical interaction
........... 404
15.6
Summary
................................. 408
16
Time as a continuous predictor
411
16.1
Chapter overview
............................. 411
16.2
Example
1:
Linear effect of time
.................... 412
16.3
Example
2:
Linear effect of time by a categorical predictor
...... 416
Contents xiii
16.4
Example
3:
Piecewise modeling of time
................. 421
16.5
Example
4:
Piecewise effects of time by a categorical predictor
. . . 426
16.5.1
Baseline slopes
......................... 430
16.5.2
Change in slopes: Treatment versus baseline
......... 431
16.5.3
Jump at treatment
....................... 432
16.5.4
Comparisons among groups
.................. 433
16.6
Summary
................................. 434
17
Time as a categorical predictor
437
17.1
Chapter overview
............................. 437
17.2
Example
1:
Time treated as a categorical variable
........... 438
17.3
Example
2:
Time (categorical) by two groups
............. 443
17.4
Example
3:
Time (categorical) by three groups
............ 447
17.5
Comparing models with different residual covariance structures
. . . 452
17.6
Summary
................................. 454
18
Nonlinear models
455
18.1
Chapter overview
............................. 455
18.2
Binary logistic regression
......................... 456
18.2.1
A logistic model with one categorical predictor
....... 456
18.2.2
A logistic model with one continuous predictor
....... 463
18.2.3
A logistic model with covariates
................ 465
18.3
Multinomial logistic regression
..................... 470
18.4
Ordinal logistic regression
........................ 475
18.5
Poisson
regression
............................. 478
18.6
More applications of nonlinear models
................. 481
18.6.1
Categorical by categorical interaction
............. 481
18.6.2
Categorical by continuous interaction
............. 487
18.6.3
Piecewise modeling
....................... 492
18.7
Summary
................................. 498
19
Complex survey data
499
XIV
Contents
V Appendices
505
A The margins command
507
A.I The predict() and expression() options
................. 507
A.
2
The at() option
.............................. 510
A.3 Margins with factor variables
...................... 513
A.4 Margins with factor variables and the at() option
........... 517
A.
5
The dydxQ and related options
..................... 519
В
The marginsplot command
523
С
The contrast command
535
D
The pwcompare command
539
References
545
Author index
549
Subject index
551
Interpreting and Visualizing Regression Models Using
Stata
provides clear and simple
examples illustrating how to interpret and visualize a wide variety of regression models.
Including over
180
figures, the book illustrates linear models with continuous predictors
(modeled linearly, using polynomials, and piecewise), interactions of continuous predictors,
categorical predictors, interactions of categorical predictors, as well as interactions of
continuous and categorical predictors. The book also illustrates how to interpret (and
visualize) results from multilevel models, models where time is a continuous predictor,
models with time as a categorical predictor, nonlinear models (such as logistic or ordinal
logistic regression), as well as models involving complex survey data. The examples illustrate
the use of the
Stata
margins, marginsplot, contrast, and pwcompare
commands. For example, the use of the contrast command is illustrated for models
with interactions of categorical variables, showing how you can precisely understand and
dissect such interactions with surgical precision.
If you ever find yourself wishing for simple and straightforward advice about how to
interpret and visualize regression models using
Stata,
this book is for you.
Michael Mitchell is a senior statistician in disaster preparedness and response. He is the
author of
Л
Visual Guide to
Stata
Graphics as well as Data Management Using
Stata.
Previously, he worked for
12
years as a statistical consultant and manager of the UCLA ATS
Statistical Consulting Group. There, he envisioned the UCLA Statistical Consulting Resources
website and wrote hundreds of web pages about
Stata.
Telephone:
979-696-4600
800-782-8272
бОО-ЅТАТАРС
Fax:
979-696-4601
service@stata-press.com
stata-press.com
ISBN
978-1-59718-107-5
90000 >
9 781597И
181075
|
| any_adam_object | 1 |
| author | Mitchell, Michael N. |
| author_GND | (DE-588)139115366 |
| author_facet | Mitchell, Michael N. |
| author_role | aut |
| author_sort | Mitchell, Michael N. |
| author_variant | m n m mn mnm |
| building | Verbundindex |
| bvnumber | BV039996215 |
| classification_rvk | MR 2100 MR 2200 QH 234 ST 601 |
| classification_tum | DAT 307f |
| ctrlnum | (OCoLC)796190418 (DE-599)BVBBV039996215 |
| discipline | Informatik Soziologie Wirtschaftswissenschaften |
| edition | 1. ed. |
| format | Book |
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| id | DE-604.BV039996215 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:15:52Z |
| institution | BVB |
| isbn | 9781597181075 1597181072 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024853249 |
| oclc_num | 796190418 |
| open_access_boolean | |
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| physical | XXVIII, 558 S. graph. Darst. |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | Stata Press |
| record_format | marc |
| series2 | A Stata Press publication |
| spelling | Mitchell, Michael N. Verfasser (DE-588)139115366 aut Interpreting and visualizing regression models using Stata Michael N. Mitchell 1. ed. College Station, Tex. Stata Press 2012 XXVIII, 558 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier A Stata Press publication Literaturverz. S. 545 - 547 Visualisierung (DE-588)4188417-6 gnd rswk-swf Regressionsanalyse (DE-588)4129903-6 gnd rswk-swf Stata (DE-588)4617285-3 gnd rswk-swf Regressionsmodell (DE-588)4127980-3 gnd rswk-swf Regressionsanalyse (DE-588)4129903-6 s Stata (DE-588)4617285-3 s DE-604 Regressionsmodell (DE-588)4127980-3 s Visualisierung (DE-588)4188417-6 s b DE-604 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024853249&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024853249&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Mitchell, Michael N. Interpreting and visualizing regression models using Stata Visualisierung (DE-588)4188417-6 gnd Regressionsanalyse (DE-588)4129903-6 gnd Stata (DE-588)4617285-3 gnd Regressionsmodell (DE-588)4127980-3 gnd |
| subject_GND | (DE-588)4188417-6 (DE-588)4129903-6 (DE-588)4617285-3 (DE-588)4127980-3 |
| title | Interpreting and visualizing regression models using Stata |
| title_auth | Interpreting and visualizing regression models using Stata |
| title_exact_search | Interpreting and visualizing regression models using Stata |
| title_full | Interpreting and visualizing regression models using Stata Michael N. Mitchell |
| title_fullStr | Interpreting and visualizing regression models using Stata Michael N. Mitchell |
| title_full_unstemmed | Interpreting and visualizing regression models using Stata Michael N. Mitchell |
| title_short | Interpreting and visualizing regression models using Stata |
| title_sort | interpreting and visualizing regression models using stata |
| topic | Visualisierung (DE-588)4188417-6 gnd Regressionsanalyse (DE-588)4129903-6 gnd Stata (DE-588)4617285-3 gnd Regressionsmodell (DE-588)4127980-3 gnd |
| topic_facet | Visualisierung Regressionsanalyse Stata Regressionsmodell |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024853249&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=024853249&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT mitchellmichaeln interpretingandvisualizingregressionmodelsusingstata |