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Reference:
Garson, G. D. (2017). Mediation & Moderation: Partial Correlation and Regression Approaches. Asheboro, NC: Statistical Associates Publishers.
 

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ISBN: 978-1-62638-047-9


@c 2017 by G. David Garson and Statistical Associates Publishers. worldwide rights reserved in all languages and on all media. Permission is not granted to copy, distribute, or post e-books or passwords.
 


Overview

An illustrated graduate-level introduction to causal inference using mediation and moderation analysis, based on partial correlation, regression, and path analysis procedures.

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Below is the unformatted table of contents.

MEDIATION & MODERATION: PARTIAL CORRELATION AND REGRESSION APPROACHES

TABLE OF CONTENTS

Introduction	9
Overview	9
Warning with regard to endogeneity	10
Data used in examples	11
Definitions	14
Mediation	14
Moderation	15
Mediation with partial correlation	15
Overview	15
The partial correlation approach is for mediation, not moderation	16
Order of correlation	17
Control variables	17
Mediation in partial correlation	18
Spurious moderation	19
Partial mediation	19
Summary: Types of effects	19
No effect	20
Explanation and partial explanation	20
Spurious correlation	20
Partial explanation	20
Suppression	21
Example: Partial and semipartial correlation	24
SPSS	24
SAS	25
Stata	26
Summary	26
Assumptions of partial correlation	26
Simple models	26
Recursivity	27
Linearity	27
Additivity	27
Data independence	27
Data level	27
Model specification	27
Low multicollinearity	27
Semipartial (part) correlation	28
Overview	28
How it works	29
Why partial r is always larger than semipartial r?	29
Control effects with partial correlation and regression	30
Example data	30
Four types of "controlling"	31
Overview	31
Partial correlation method	31
SPSS	31
SAS	33
Stata	35
Residual method	37
Overview	37
SPSS	38
SAS	39
Stata	41
Rate method	42
Overview	42
SPSS	43
SAS	44
Stata	45
Regression method	46
Overview	46
SPSS	48
SAS	49
Stata	49
Meanings of different coefficients compared	50
Coefficients compared	50
Use of control coefficients	52
Simple mediation with multiple regression	53
Overview	53
Partial correlation mediation model	54
SPSS	55
SAS	56
Stata	57
Mediation with Baron & Kenny's "Causal Steps" and with Hayes's PROCESS	58
SPSS	60
SAS	69
Stata	73
Zhao, Lynch, & Chen mediation model	78
Collins probability-based sequential mediation model	81
Mediation with a categorical independent variable	87
Simple mediation: Summary	88
Overview	88
Partial correlation method	88
Regression method	88
Baron & Kenny method	89
Zhang, Lynch & Chen method	89
Collins probability-based method	90
Simple moderation analysis	90
Overview	90
Warnings about assumptions of regression method moderation analysis	91
The simple moderation model	92
Regression & PROCESS moderation methods compared	94
SPSS	94
SAS	101
Stata	108
Baron & Kenny moderation model	110
SPSS	111
SAS	117
Stata	122
Median split method	126
Overview	126
SPSS	130
SAS	136
Stata	140
MacArthur mediation/moderation model	144
Conditional effects models	148
Overview	148
Simple mediation (Hayes's Model 4)	150
Simple moderation (Hayes's Model 1)	150
Moderated mediation (Hayes's Models 7, 8, 14, and 74)	151
Mediated moderation	153
Moderated mediation: A worked example	155
Example data	155
The model	155
SPSS	157
The regression/path analysis method	157
The PROCESS method	169
SAS	178
Stata	180
The regression/path analysis method	181
The PROCESS method equivalent	181
Multiple mediation models	185
Overview	185
SPSS	186
The partial correlation method	186
The regression (path analysis) method	188
The PROCESS method	192
SAS	199
Overview	199
The partial correlation method	199
The regression method	199
The PROCESS method	200
Stata	200
Overview	200
The partial correlation method	200
The regression method	201
The PROCESS method	201
Using the khb command to partition total effects	201
Using the sureg and nlcom commands to partition total effects	202
Multiple moderation models	206
Overview	206
Warning about statistical power for multiple moderation	208
Example data	209
SPSS	210
The regression/path analysis method	210
The PROCESS method	213
SAS	216
Overview	216
The regression/path analysis method	216
Regression/path analysis output	217
Hierarchical regression output	218
The "stats" file	219
Summary	220
The PROCESS method	220
Stata	221
Overview	221
The regression/path analysis method	221
Regression/path analysis output	221
Hierarchical regression output	222
Summary	223
Moderation with categorical variables	224
Overview	224
The F test and likelihood ratio tests for moderation	225
Graphical method	226
Moderation with a categorical moderator	226
SPSS	227
SAS	236
Stata	243
Graphing moderation (interaction) effects	245
Overview	245
Stata	245
The example	245
Postestimation with the margins command	246
Graphing interactions with the marginsplot command	248
SPSS	249
The example	249
Graphing conditional effects	251
SAS	254
The example	254
Graphing conditional effects	256
FAQs: Partial correlation methods	259
SPSS gives me a choice of one-tailed and two-tailed tests. Which do I want?	259
If partial correlation assumptions are met and measures are reliable and valid, does upholding a model through partial correlation analysis mean that the model is true?	259
Is there any rule which can express the relation of the partial correlation to the original bivariate correlation (ex., is it always lower)?	259
How is partial correlation computed?	259
Why do I have not enough cases to compute partial correlation?	260
Can I use partial correlation for analysis of larger models?	260
Is there a form of partial association for nominal and ordinal variables, analogous to partial r for interval variables?	260
From statistical output for regression, how may we obtain the significance of a partial correlation coefficient like rYX1.X2X3?	262
What do partialled residual scatterplots look like and do?	262
SPSS	262
SAS	262
Stata	266
FAQs: Regression methods	266
Why path models rather than simple regression?	266
May I analyze mediation and moderation separately?	266
What is PROCESS software for mediation and moderation?	267
How do I test the assumptions of OLS regression?	269
What if I have dichotomous mediator variables?	273
What if I have dichotomous moderator variables?	274
What if I have longitudinal data?	274
Explain the controversy about endogeneity in causal research	276
What is specious or spurious mediation?	280
What is the instrumental variable approach to omitted variables in mediation analysis?	281
What is the relation of lagged variables to the endogeneity problem?	282
What is nonlinear moderation?	282
Do the assumptions of OLS regression apply to mediation and moderation analysis?	283
When the moderator is categorical, does it matter what type of coding is used?	284
What is the frequentist vs. Bayesian controversy over significance coefficients?	284
Should variables be centered prior to mediation/moderation analysis?	285
Should data be standardized prior to mediation/moderation analysis?	287
How are regression coefficients interpreted when interactions are in the model?	288
How are compound indirect paths tested in the Sobel or other tests?	289
How do you compute the Sobel, Aroian, and Goodman tests?	291
What is the Freedman-Schatzkin test of mediation?	293
Is it important to test compound indirect paths for moderation?	293
In  Stata, what does bootstrapped sgmediation output look like?	295
Acknowledgments	297
Bibliography	298
Pagecount: 306