Multiple regression: testing and interpreting interactions
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Newbury Park [u.a.]
Sage
1998
|
| Ausgabe: | 1. paperback print., reprint. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 211 S. graph. Darst. |
| ISBN: | 0803936052 0761907122 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV023094864 | ||
| 003 | DE-604 | ||
| 005 | 20111006 | ||
| 007 | t | ||
| 008 | 080123s1998 d||| |||| 00||| engod | ||
| 020 | |a 0803936052 |9 0-8039-3605-2 | ||
| 020 | |a 0761907122 |9 0-7619-0712-2 | ||
| 035 | |a (OCoLC)608591759 | ||
| 035 | |a (DE-599)BVBBV023094864 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-19 |a DE-473 |a DE-11 |a DE-945 |a DE-20 | ||
| 084 | |a CM 2500 |0 (DE-625)18944: |2 rvk | ||
| 084 | |a CM 3000 |0 (DE-625)18945: |2 rvk | ||
| 084 | |a MR 2300 |0 (DE-625)123490: |2 rvk | ||
| 084 | |a QH 234 |0 (DE-625)141549: |2 rvk | ||
| 084 | |a SK 840 |0 (DE-625)143261: |2 rvk | ||
| 100 | 1 | |a Aiken, Leona S. |e Verfasser |0 (DE-588)171946707 |4 aut | |
| 245 | 1 | 0 | |a Multiple regression |b testing and interpreting interactions |c Leona S. Aiken ; Stephen G. West |
| 250 | |a 1. paperback print., reprint. | ||
| 264 | 1 | |a Newbury Park [u.a.] |b Sage |c 1998 | |
| 300 | |a XI, 211 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 0 | 7 | |a Regressionsanalyse |0 (DE-588)4129903-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Multiple Regression |0 (DE-588)4170720-5 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4151278-9 |a Einführung |2 gnd-content | |
| 689 | 0 | 0 | |a Multiple Regression |0 (DE-588)4170720-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Regressionsanalyse |0 (DE-588)4129903-6 |D s |
| 689 | 1 | |5 DE-604 | |
| 700 | 1 | |a West, Stephen G. |e Verfasser |4 aut | |
| 856 | 4 | 2 | |m Digitalisierung UB Bamberg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016297682&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-016297682 | ||
Datensatz im Suchindex
| _version_ | 1804137349624365056 |
|---|---|
| adam_text | Contents
Preface
ix
1.
Introduction
1
2.
Interactions
Between Continuous Predictors in Multiple
Regression
9
What Interactions Signify in Regression
9
Data Set for Numerical Examples
10
Probing Significant Interactions in Regression Equations
12
Plotting the Interaction
12
Post Hoc Probing
14
Ordinal Versus
Disordinal
Interactions
22
Optional Section: The Derivation of Standard Errors of Simple Slopes
24
Summary
27
3.
The Effects of Predictor Scaling on Coefficients of
Regression Equations
28
The Problem of Scale
Invariance
28
Linear Regression with no Higher Order Terms
29
Regression Equations with Higher Order Terms
30
Simple Slopes of Simple Regression Equations
31
Ordinal Versus
Disordinal
Interactions
31
Numerical Example
—
Centered Versus Uncentered Data
32
Should the Criterion
Y
Be Centered?
35
Multicollinearity: Essential Versus Nonessential Ill-Conditioning
35
Interpreting the Regression Coefficients
36
The Interaction Term XZ
36
The First Order Terms X and
Z
37
A Geometric Interpretation
39
Standardized Solutions with Multiplicative Terms
40
Appropriate Standardized Solution with Interaction Terms
43
Simple Slope Analysis from the Standardized Solution AA
Relationship Between Raw and
Standardized
Solution
45
Summary
47
4.
Testing and Probing Three-Way Interactions
49
Specifying, Testing, and Interpreting Three-Way Interactions
49
Probing Three-Way Interactions
50
Simple Regression Equation
50
Numerical Example
50
Graphing the Three-Way Interaction
52
Testing Simple Slopes for Significance
54
Standard Errors by Computer
54
Crossing Point of Simple Regression Equations with Three-Predictor
Interaction
58
Simple Slopes and Their Variances in a Series of Regression
Equations
59
Summary
61
Structuring Regression Equations to Reflect Higher Order
Relationships
62
Structuring and Interpreting Regression Equations Involving
Higher Order Relationships
63
Case I: Curvilinear X Relationship
63
A Progression of More Complex Equations with Curvilinear
Relationships
65
Representation of Curvilinearity in ANOVA Versus MR
70
Post Hoc Probing of More Complex Regression Equations
72
Case
1:
Curvilinear X Equation
72
The Progression of More Complex Curvilinear Equations Revisited
78
Coefficients of Simple Slopes by Computer
89
Three Final Issues
92
Curvilinearity Versus Interaction
92
What Terms Should Be Included in the Regression Equation
? 93
Other Methods of Representing Curvilinearity
95
Summary
97
6.
Model and Effect
Testing with Higher Order Terms
100
Some Issues in Testing Lower Order Effects in Models
Containing Higher Order Terms
100
Question
1,
Interpretation of Lower Order Terms When fc3 Is
Significant
102
Question
2.
Should Lower Order Coefficients Be Tested in Reduced
Models When b-s Is Nonsignificant?
103
Exploring Regression Equations Containing Higher Order Terms
with Global Tests
105
Some Global Tests of Models with Higher Order Terms
107
Structuring Regression Equations with Higher Order Terms
110
Sequential Model Revision of Regression Equations Containing
Higher Order Terms: Exploratory Tests 111
Application of Sequential Testing Following a Global Test
112
General Application of Sequential Testing
113
Present Approach Versus That Recommended by Cohen
(1978) 113
Variable Selection Algorithms
114
Summary
114
7.
Interactions Between Categorical and Continuous Variables
116
Coding Categorical Variables
116
Dummy Variable Coding
116
Unweighted Effects Coding
127
Choice of Coding System
129
Centering Revisited
130
Post Hoc Probing of Significant Interactions
130
Testing Simple Slopes Within Groups
131
Computer Procedure
131
Differences Between Regression Lines at a Specific Point
132
Identifying Regions of Significance
134
Summary
137
8.
Reliability and Statistical Power
139
Reliability
140
Biased Regression Coefficients with Measurement Error
140
Corrected Estimates of Regression Coefficients in Equations
Containing Higher Order Terms
145
Statistical Power
156
Statistical Power Analysis
156
The Effects of Measurement Error on Statistical Power
160
Some Corroborative Evidence: Simulation Studies
165
The Median Split Approach: The Cost of Dichotomization
167
Principal Component Regression Is Not a Cure for Power Woes
168
Coming Full Circle
169
Summary
170
9.
Conclusion:
Some Contrasts Between
ANOVA
and MR in
Practice
172
Appendix A: Mathematical Underpinnings
177
Appendix B: Algorithm for Identifying Scale-Independent Terms
183
Appendix C:
SAS
Program for Test of Critical Region(s)
188
References
190
Glossary of Symbols
198
Author Index
204
Subject Index
207
About the Authors
212
|
| adam_txt |
Contents
Preface
ix
1.
Introduction
1
2.
Interactions
Between Continuous Predictors in Multiple
Regression
9
What Interactions Signify in Regression
9
Data Set for Numerical Examples
10
Probing Significant Interactions in Regression Equations
12
Plotting the Interaction
12
Post Hoc Probing
14
Ordinal Versus
Disordinal
Interactions
22
Optional Section: The Derivation of Standard Errors of Simple Slopes
24
Summary
27
3.
The Effects of Predictor Scaling on Coefficients of
Regression Equations
28
The Problem of Scale
Invariance
28
Linear Regression with no Higher Order Terms
29
Regression Equations with Higher Order Terms
30
Simple Slopes of Simple Regression Equations
31
Ordinal Versus
Disordinal
Interactions
31
Numerical Example
—
Centered Versus Uncentered Data
32
Should the Criterion
Y
Be Centered?
35
Multicollinearity: Essential Versus Nonessential Ill-Conditioning
35
Interpreting the Regression Coefficients
36
The Interaction Term XZ
36
The First Order Terms X and
Z
37
A Geometric Interpretation
39
Standardized Solutions with Multiplicative Terms
40
Appropriate Standardized Solution with Interaction Terms
43
Simple Slope Analysis from the Standardized Solution AA
Relationship Between Raw and
'
'Standardized
' '
Solution
45
Summary
47
4.
Testing and Probing Three-Way Interactions
49
Specifying, Testing, and Interpreting Three-Way Interactions
49
Probing Three-Way Interactions
50
Simple Regression Equation
50
Numerical Example
50
Graphing the Three-Way Interaction
52
Testing Simple Slopes for Significance
54
Standard Errors by Computer
54
Crossing Point of Simple Regression Equations with Three-Predictor
Interaction
58
Simple Slopes and Their Variances in a Series of Regression
Equations
59
Summary
61
Structuring Regression Equations to Reflect Higher Order
Relationships
62
Structuring and Interpreting Regression Equations Involving
Higher Order Relationships
63
Case I: Curvilinear X Relationship
63
A Progression of More Complex Equations with Curvilinear
Relationships
65
Representation of Curvilinearity in ANOVA Versus MR
70
Post Hoc Probing of More Complex Regression Equations
72
Case
1:
Curvilinear X Equation
72
The Progression of More Complex Curvilinear Equations Revisited
78
Coefficients of Simple Slopes by Computer
89
Three Final Issues
92
Curvilinearity Versus Interaction
92
What Terms Should Be Included in the Regression Equation
? 93
Other Methods of Representing Curvilinearity
95
Summary
97
6.
Model and Effect
Testing with Higher Order Terms
100
Some Issues in Testing Lower Order Effects in Models
Containing Higher Order Terms
100
Question
1,
Interpretation of Lower Order Terms When fc3 Is
Significant
102
Question
2.
Should Lower Order Coefficients Be Tested in Reduced
Models When b-s Is Nonsignificant?
103
Exploring Regression Equations Containing Higher Order Terms
with Global Tests
105
Some Global Tests of Models with Higher Order Terms
107
Structuring Regression Equations with Higher Order Terms
110
Sequential Model Revision of Regression Equations Containing
Higher Order Terms: Exploratory Tests 111
Application of Sequential Testing Following a Global Test
112
General Application of Sequential Testing
113
Present Approach Versus That Recommended by Cohen
(1978) 113
Variable Selection Algorithms
114
Summary
114
7.
Interactions Between Categorical and Continuous Variables
116
Coding Categorical Variables
116
Dummy Variable Coding
116
Unweighted Effects Coding
127
Choice of Coding System
129
Centering Revisited
130
Post Hoc Probing of Significant Interactions
130
Testing Simple Slopes Within Groups
131
Computer Procedure
131
Differences Between Regression Lines at a Specific Point
132
Identifying Regions of Significance
134
Summary
137
8.
Reliability and Statistical Power
139
Reliability
140
Biased Regression Coefficients with Measurement Error
140
Corrected Estimates of Regression Coefficients in Equations
Containing Higher Order Terms
145
Statistical Power
156
Statistical Power Analysis
156
The Effects of Measurement Error on Statistical Power
160
Some Corroborative Evidence: Simulation Studies
165
The Median Split Approach: The Cost of Dichotomization
167
Principal Component Regression Is Not a Cure for Power Woes
168
Coming Full Circle
169
Summary
170
9.
Conclusion:
Some Contrasts Between
ANOVA
and MR in
Practice
172
Appendix A: Mathematical Underpinnings
177
Appendix B: Algorithm for Identifying Scale-Independent Terms
183
Appendix C:
SAS
Program for Test of Critical Region(s)
188
References
190
Glossary of Symbols
198
Author Index
204
Subject Index
207
About the Authors
212 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Aiken, Leona S. West, Stephen G. |
| author_GND | (DE-588)171946707 |
| author_facet | Aiken, Leona S. West, Stephen G. |
| author_role | aut aut |
| author_sort | Aiken, Leona S. |
| author_variant | l s a ls lsa s g w sg sgw |
| building | Verbundindex |
| bvnumber | BV023094864 |
| classification_rvk | CM 2500 CM 3000 MR 2300 QH 234 SK 840 |
| ctrlnum | (OCoLC)608591759 (DE-599)BVBBV023094864 |
| discipline | Soziologie Psychologie Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Soziologie Psychologie Mathematik Wirtschaftswissenschaften |
| edition | 1. paperback print., reprint. |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01773nam a2200445 c 4500</leader><controlfield tag="001">BV023094864</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20111006 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">080123s1998 d||| |||| 00||| engod</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0803936052</subfield><subfield code="9">0-8039-3605-2</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0761907122</subfield><subfield code="9">0-7619-0712-2</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)608591759</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV023094864</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-19</subfield><subfield code="a">DE-473</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-945</subfield><subfield code="a">DE-20</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">CM 2500</subfield><subfield code="0">(DE-625)18944:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">CM 3000</subfield><subfield code="0">(DE-625)18945:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MR 2300</subfield><subfield code="0">(DE-625)123490:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">QH 234</subfield><subfield code="0">(DE-625)141549:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 840</subfield><subfield code="0">(DE-625)143261:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Aiken, Leona S.</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)171946707</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Multiple regression</subfield><subfield code="b">testing and interpreting interactions</subfield><subfield code="c">Leona S. Aiken ; Stephen G. West</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">1. paperback print., reprint.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Newbury Park [u.a.]</subfield><subfield code="b">Sage</subfield><subfield code="c">1998</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XI, 211 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Regressionsanalyse</subfield><subfield code="0">(DE-588)4129903-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Multiple Regression</subfield><subfield code="0">(DE-588)4170720-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="655" ind1=" " ind2="7"><subfield code="0">(DE-588)4151278-9</subfield><subfield code="a">Einführung</subfield><subfield code="2">gnd-content</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Multiple Regression</subfield><subfield code="0">(DE-588)4170720-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Regressionsanalyse</subfield><subfield code="0">(DE-588)4129903-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">West, Stephen G.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Bamberg</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016297682&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-016297682</subfield></datafield></record></collection> |
| genre | (DE-588)4151278-9 Einführung gnd-content |
| genre_facet | Einführung |
| id | DE-604.BV023094864 |
| illustrated | Illustrated |
| index_date | 2024-07-02T19:42:33Z |
| indexdate | 2024-07-09T21:10:53Z |
| institution | BVB |
| isbn | 0803936052 0761907122 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016297682 |
| oclc_num | 608591759 |
| open_access_boolean | |
| owner | DE-19 DE-BY-UBM DE-473 DE-BY-UBG DE-11 DE-945 DE-20 |
| owner_facet | DE-19 DE-BY-UBM DE-473 DE-BY-UBG DE-11 DE-945 DE-20 |
| physical | XI, 211 S. graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Sage |
| record_format | marc |
| spelling | Aiken, Leona S. Verfasser (DE-588)171946707 aut Multiple regression testing and interpreting interactions Leona S. Aiken ; Stephen G. West 1. paperback print., reprint. Newbury Park [u.a.] Sage 1998 XI, 211 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Regressionsanalyse (DE-588)4129903-6 gnd rswk-swf Multiple Regression (DE-588)4170720-5 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Multiple Regression (DE-588)4170720-5 s DE-604 Regressionsanalyse (DE-588)4129903-6 s West, Stephen G. Verfasser aut Digitalisierung UB Bamberg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016297682&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Aiken, Leona S. West, Stephen G. Multiple regression testing and interpreting interactions Regressionsanalyse (DE-588)4129903-6 gnd Multiple Regression (DE-588)4170720-5 gnd |
| subject_GND | (DE-588)4129903-6 (DE-588)4170720-5 (DE-588)4151278-9 |
| title | Multiple regression testing and interpreting interactions |
| title_auth | Multiple regression testing and interpreting interactions |
| title_exact_search | Multiple regression testing and interpreting interactions |
| title_exact_search_txtP | Multiple regression testing and interpreting interactions |
| title_full | Multiple regression testing and interpreting interactions Leona S. Aiken ; Stephen G. West |
| title_fullStr | Multiple regression testing and interpreting interactions Leona S. Aiken ; Stephen G. West |
| title_full_unstemmed | Multiple regression testing and interpreting interactions Leona S. Aiken ; Stephen G. West |
| title_short | Multiple regression |
| title_sort | multiple regression testing and interpreting interactions |
| title_sub | testing and interpreting interactions |
| topic | Regressionsanalyse (DE-588)4129903-6 gnd Multiple Regression (DE-588)4170720-5 gnd |
| topic_facet | Regressionsanalyse Multiple Regression Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016297682&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT aikenleonas multipleregressiontestingandinterpretinginteractions AT weststepheng multipleregressiontestingandinterpretinginteractions |