Multiple Regression and beyond. An Introduction to Multiple Regression and Structural Equation Modeling [3rd ed.]

Description

Contents......Page 3 Preface......Page 5 --- Multiple Regression......Page 11 Simple Bivariate Regression......Page 12 Example: Homework and Math Achievement......Page 13 REGRESSION IN PERSPECTIVE Relation of Regression to Other Statistical Methods......Page 24 Explaining Variance......Page 26 Advantages of Multiple Regression......Page 27 Causality......Page 28 Correlation and Covariance......Page 29 WORKING WITH EXTANT DATA SETS......Page 30 SUMMARY......Page 32 Notes......Page 33 Multiple Regression......Page 35 The Regression......Page 36 R......Page 40 Interpretations......Page 42 Figural Representation......Page 43 QUESTIONS Controlling for . . .......Page 44 versus ß......Page 45 Comparison Across Samples......Page 47 AND......Page 50 EXERCISES......Page 51 Notes......Page 52 +......Page 53 PREDICTED SCORES AND RESIDUALS......Page 56 REGRESSION LINE......Page 59 LEAST SQUARES......Page 61 ASSUMPTIONS OF REGRESSION AND REGRESSION DIAGNOSTICS......Page 63 EXERCISES......Page 64 Note......Page 65 THREE PREDICTOR VARIABLES......Page 66 Regression Results......Page 69 Interpretation......Page 70 RULES OF THUMB: MAGNITUDE OF EFFECTS......Page 71 TESTING THE DIFFERENCE BETWEEN TWO REGRESSION COEFFICIENTS......Page 72 FOUR INDEPENDENT VARIABLES......Page 73 Trouble in Paradise......Page 74 COMMON CAUSES AND INDIRECT EFFECTS......Page 77 ?......Page 79 PREDICTION AND EXPLANATION......Page 81 SUMMARY......Page 82 EXERCISES......Page 83 Notes......Page 84 3 Types of Multiple Regression......Page 86 SIMULTANEOUS MULTIPLE REGRESSION The Analysis......Page 88 What to Interpret......Page 89 The Analysis......Page 90 Comparison to Simultaneous Regression......Page 92 as a Measure of Effect......Page 96 Other Uses of Sequential Regression......Page 98 Interpretation......Page 102 Summary: Sequential Regression......Page 103 STEPWISE MULTIPLE REGRESSION......Page 104 The Analysis......Page 105 Danger: Stepwise Regression Is Inappropriate for Explanation......Page 106 A Predictive Approach......Page 107 Cross-Validation......Page 108 Additional Dangers......Page 109 Summary: Stepwise Regression......Page 110 THE PURPOSE OF THE RESEARCH......Page 111 Prediction......Page 113 SUMMARY......Page 114 EXERCISES......Page 115 Notes......Page 116 Analysis of Categorical Variables......Page 117 DUMMY VARIABLES Simple Categorical Variables......Page 118 False Memory and Sexual Abuse......Page 119 OTHER METHODS OF CODING CATEGORICAL VARIABLES......Page 125 Effect Coding......Page 126 Criterion Scaling......Page 127 Family Structure and Substance Use......Page 129 ADDITIONAL METHODS AND ISSUES......Page 134 SUMMARY......Page 135 EXERCISES......Page 136 Notes......Page 137 Regression with Categorical & Continuous Variables......Page 138 SEX, ACHIEVEMENT, AND SELF-ESTEEM......Page 139 INTERACTIONS, AKA MODERATION......Page 141 Centering and Cross Products: Achievement and Sex......Page 142 The MR Analysis......Page 143 Interpretation......Page 144 Does Achievement Affect Self-Esteem? It Depends......Page 146 Understanding an Interaction......Page 147 Extensions and Other Examples......Page 149 SPECIFIC TYPES OF INTERACTIONS BETWEEN CATEGORICAL AND CONTINUOUS VARIABLES......Page 150 Test (and Other) Bias......Page 151 Aptitude–Treatment Interactions......Page 159 Steps for Testing for ATIs......Page 160 ANCOVA......Page 162 CAVEATS AND ADDITIONAL INFORMATION “Effects” of Categorical Subject Variables......Page 163 Further Probing and Figural Display of Statistically Significant Interactions......Page 164 SUMMARY......Page 167 EXERCISES......Page 168 Notes......Page 169 Effects of TV Time on Achievement......Page 170 CURVILINEAR REGRESSION......Page 177 Curvilinear Effects of Homework on GPA......Page 178 EXERCISES......Page 184 Note......Page 185 MODERATION......Page 186 MEDIATION......Page 188 Baron and Kenny (Causal Steps)......Page 189 Bootstrapping and PROCESS......Page 190 Mediation Example......Page 191 COMMON CAUSE......Page 196 A FURTHER COMMENT ON LANGUAGE......Page 201 SUMMARY......Page 202 EXERCISES......Page 203 SUMMARY “Standard” Multiple Regression......Page 204 Explanation and Prediction......Page 206 Three Types of Multiple Regression......Page 207 Categorical and Continuous Variables, Interactions, and Curves......Page 208 Moderation, Mediation, and Common Cause......Page 209 Assumptions Underlying Regression......Page 210 Regression Diagnostics......Page 211 SAMPLE SIZE AND POWER......Page 225 PROBLEMS WITH MR?......Page 230 Note......Page 234 Related Methods......Page 235 Predicting Optimism Versus Pessimism......Page 236 Problems With the MR Analysis......Page 237 Logistic Regression: Transforming the Dependent Variable to Log Odds......Page 241 Conducting the Logistic Regression and Understanding the Output......Page 244 Categorizing a Continuous Variable......Page 248 Appropriate Uses of Logistic Regression......Page 249 MULTILEVEL MODELING......Page 250 Multiple Regression Analysis......Page 251 Multilevel Analysis of the Effect of SES on Achievement......Page 254 SUMMARY......Page 261 EXERCISES......Page 262 --- SEM......Page 264 Path Modeling......Page 265 INTRODUCTION TO PATH ANALYSIS A Simple Model......Page 266 Cautions......Page 270 Jargon and Notation......Page 272 Steps for Conducting Path Analysis......Page 274 Interpretation: Direct Effects......Page 277 Indirect and Total Effects......Page 279 SUMMARY......Page 283 EXERCISES......Page 286 Notes......Page 287 Path Analysis......Page 289 THE DANGER OF COMMON CAUSES......Page 290 A Research Example......Page 292 Common Causes, Not All Causes......Page 294 Intervening (Mediating) Variables......Page 296 OTHER POSSIBLE DANGERS Paths in the Wrong Direction......Page 297 DEALING WITH DANGER......Page 299 REVIEW: STEPS IN A PATH ANALYSIS......Page 300 SUMMARY......Page 301 EXERCISES......Page 302 Notes......Page 303 SEM PROGRAMS......Page 304 Amos and Mplus......Page 305 REANALYSIS OF THE PARENT INVOLVEMENT PATH MODEL......Page 306 Estimating the Parent Involvement Model via Amos......Page 307 ADVANTAGES OF SEM PROGRAMS Overidentified Models......Page 311 Comparing Competing Models......Page 320 MORE COMPLEX MODELS Equivalent and Nonequivalent Models......Page 323 Nonrecursive Models......Page 330 Longitudinal Models......Page 331 ADVICE: MR VERSUS SEM PROGRAMS......Page 333 Evaluating a Single Model......Page 334 SUMMARY......Page 336 EXERCISES......Page 338 Notes......Page 340 Error......Page 342 EFFECTS OF UNRELIABILITY The Importance of Reliability......Page 343 Effects of Unreliability on Path Results......Page 344 EFFECTS OF INVALIDITY The Meaning and Importance of Validity......Page 347 Accounting for Invalidity......Page 348 LATENT VARIABLE SEM AND ERRORS OF MEASUREMENT......Page 351 The Latent SEM Model......Page 352 SUMMARY......Page 354 Notes......Page 355 FACTOR ANALYSIS: THE MEASUREMENT MODEL......Page 356 AN EXAMPLE WITH THE DAS-II......Page 357 Structure of the DAS-II......Page 358 The Initial Model......Page 359 Standardized and Unstandardized Results: The Initial Model......Page 361 Testing a Standardized Model......Page 362 Testing Plausible Cross-Loadings......Page 366 A Three-Factor Combined Nonverbal Model......Page 368 Modification Indexes......Page 371 Residuals......Page 374 Values......Page 376 HIERARCHICAL MODELS Higher-Order Model Justification and Setup......Page 377 Higher-Order Model Results......Page 378 Bifactor Model Justification and Setup......Page 381 Bifactor Model Results......Page 382 Comparing the Hierarchical Models......Page 384 ADDITIONAL USES OF MODEL CONSTRAINTS......Page 387 SUMMARY......Page 392 EXERCISES......Page 393 Notes......Page 395 Putting it all together......Page 397 AN EXAMPLE: EFFECTS OF PEER REJECTION Overview, Data, and Model......Page 399 Results: The Initial Model......Page 403 COMPETING MODELS......Page 407 Other Possible Models......Page 408 MODEL MODIFICATIONS......Page 410 SUMMARY......Page 412 EXERCISES......Page 413 Note......Page 416 SINGLE INDICATORS AND CORRELATED ERRORS A Latent Variable Homework Model......Page 417 Competing Models......Page 427 Model Modifications......Page 429 Latent Variable Panel Models......Page 432 A MultiGroup Homework Model Across Ethnic Groups......Page 434 Omitted Common Causes......Page 443 Path in the Wrong Direction......Page 445 SUMMARY......Page 446 EXERCISES......Page 447 Notes......Page 451 Latent Means in SEM......Page 452 PREPARATORY WORK Displaying Means and Intercepts in SEM......Page 453 Estimation of Means and Intercepts in Single Group SEM Models......Page 456 OVERVIEW: TWO METHODS TO TEST FOR DIFFERENCES IN LATENT MEANS......Page 462 EXAMPLE: HYPNOSIS FOR HOT FLASHES Single Group/Dummy Variable Approach......Page 464 MG-MACS Approach......Page 468 Comparing the Two Methods......Page 474 Other Technical Issues......Page 478 SUMMARY......Page 479 EXERCISES......Page 481 Notes......Page 482 INVARIANCE TESTING WITH MEANS......Page 483 Measurement Invariance Steps......Page 486 Alternative Model Specification......Page 502 Invariance Testing Without Means......Page 507 Higher-Order Models......Page 508 SINGLE-GROUP, MIMIC MODELS......Page 513 SUMMARY......Page 517 EXERCISES......Page 518 Notes......Page 520 Latent Growth Models......Page 521 UNCONDITIONAL, SIMPLE GROWTH MODEL......Page 525 CONDITIONAL GROWTH MODEL, OR EXPLAINING GROWTH......Page 532 ADDITIONAL ISSUES Data Requirements......Page 536 Variations in Model Specifications......Page 537 OTHER METHODS OF ANALYZING GROWTH DATA......Page 538 SUMMARY......Page 539 EXERCISES......Page 540 Note......Page 541 INTERACTIONS BETWEEN CONTINUOUS VARIABLES......Page 542 Testing Curvilinear Effects......Page 547 MULTILEVEL MODELING IN SEM......Page 552 Effects of Homework on Achievement......Page 554 A Non-ML SEM Alternative......Page 565 SUMMARY......Page 567 EXERCISES......Page 568 Summary......Page 569 SUMMARY Path Analysis......Page 570 Error......Page 573 Confirmatory Factor Analysis......Page 574 Latent Variable SEM......Page 575 SEM With Mean Structures......Page 578 CFA With Latent Means and Invariance......Page 580 Latent Growth Modeling......Page 581 Missing Values......Page 582 Sample Size, Number of Parameters, and Power......Page 586 Longitudinal Models......Page 587 Causality and the Veracity of Models......Page 588 More Advanced Resources......Page 589 Reporting SEM Results......Page 590 Cautions......Page 591 Data Files......Page 593 Review of Basic Statistics Concepts......Page 595 Partial & Semipartial Correlation......Page 613 Symbols......Page 621 Formulas......Page 623 Ref......Page 625 Index......Page 636