
Overview
An illustrated graduatelevel introduction to causal inference using mediation and moderation analysis, based on partial correlation, regression, and path analysis procedures.
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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 probabilitybased 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 probabilitybased 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 onetailed and twotailed 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 FreedmanSchatzkin 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