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Multiple Regression and Beyond offers a conceptually oriented introduction to multiple regression (MR) analysis, along with more complex methods that flow naturally from multiple regression: path analysis, confirmatory factor analysis, and structural equation modeling. By focusing on the concepts and purposes of MR and related methods, rather than the derivation and calculation of formulae (the "plug and chug" approach), students learn more clearly, in a less threatening way. As a result, they are more likely to be interested in conducting research using MR, CFA, or SEM -- and are more likely to use the methods wisely. This is undoubtedly the most readable book about multiple regression I have ever used. My students found it clear and understandable. Keith writes in a clear style that is designed to engage students rather than alienate them. The emphasis is on conceptual understanding rather than mathematical proofs. Formulas are used when necessary, but Keith takes care not to drown students in a sea of algebra. The aim throughout is to empower students to make the decisions that they will need to make in thier own research.Larry Greil, Alfred University Keith's approach is a "conceptually oriented introduction" to multiple regression.None of the negative connotations of that phrase apply here. Keith's coverage de-emphasizes complex mathematics yet is committed to a rigorous, model-building use of multiple regression in research data analysis...Material that can be quite difficult and confusing for students is covered with sufficient depth and clarity so that many issues will make considerably more sense to students than they usually do. Robert J. Crutcher, University of Dayton
Contents
Preface.a. The orientation of this book.i. Data.ii. Computer Analysis.b. Overview of the book.I. MULTIPLE REGRESSION.1. Introduction and Simple (Bivariate) Regression.a. Simple (Bivariate) Regression.i. Example: Homework and Math Achievement.1. The Data.2. The Regression Analysis.3. The Regression Equation.a. Interpretation.4. The Regression Line.5. Statistical Significance of Regression Coefficients.6. Confidence Intervals.7. The Standardized Regression Coefficient.b. Regression in Perspective.i. Relation of Regression to Other Statistical Methods.ii. Explaining Variance.iii. Advantages of Multiple Regression.c. Other Issues.i. Prediction versus Explanation.ii. Causality.d. Review of Some Basics.i. Variance and Standard Deviation.ii. Correlation and Covariance.e. Working with Extant Data Sets.f. Summary.g. Exercises.2. Multiple Regression: Introduction.a. A New Example: Regressing Grades on Homework and Parent Education.i. The Data.ii. The Regression.1. Multiple R.2. Regression Coefficients.3. Interpretation(s).a. Formal.b. Real World.b. Questions.i. Controlling for...1. Partial and Semipartial Correlations.ii. b versus .iii. Comparison Across Samples.1. Cautions.c. Direct Calculation of b and R2.d. Summary.e. Exercises.3. Multiple Regression: More Detail.a. Why R2 r2 + r2 .b. Predicted Scores and Residuals.i. Regression Line.c. Least Squares.d. Regression Equation = Creating a Composite?e. Assumptions of Regression and Regression Diagnostics.f. Summary.g. Exercises.4. Three and More Independent Variables and Related Issues.a. Three Predictor Variables.i. Regression Results.ii. Interpretation.b. Rules of Thumb: Magnitude of Effects.c. Four Independent Variables.i. Another Control Variable.ii. Regression Results.iii. Trouble in Paradise.d. Common Causes and Indirect Effects.e. The Importance of R2.f. Prediction and Explanation.g. Summary.h. Exercises.5. Three Types of Multiple Regression.a. Simultaneous Multiple Regression.i. The Analysis.ii. Purpose.iii. What to Interpret.iv. Strengths and Weaknesses.b. Sequential Multiple Regression.i. The Analysis.ii. Comparison to Simultaneous Regression.1. The Importance of Order of Entry.2. Why is order of entry so important?3. Total effects.iii. Problems with R2 as a Measure of Effect.iv. Other Uses of Sequential Regression.1. Interpretation of regression coefficients.2. Block entry.3. Unique variance.4. Interactions and curves.v. Interpretation.vi. Summary: Sequential Regression.1. Analysis.2. Purpose.3. What to interpret.4. Strengths.5. Weaknesses.6. Conclusion.c. Stepwise Multiple Regression.i. The Analysis.1. How are variables added to the equation?2. How does the program decide what variable to add at each step?ii. Danger: Stepwise regression is inappropriate for explanation.iii. A Predictive Approach.iv. Cross-Validation.v. Adjusted R2.vi. Additional dangers.1. Degrees of freedom.2. Not necessarily the best predictors.3. Lack of generalizability.vii. Alternatives to Stepwise Regression.viii. Summary: Stepwise Regression.1. Analysis.2. Purpose.3. What to interpret.4. Strengths.5. Weaknesses.d. The Purpose of the Research.i. Explanation.ii. Prediction.e. Combining Methods.f. Summary.g. Exercises.6. Analysis of Categorical Variables.a. Dummy Variables.i. Simple Categorical Variables.ii. More Complex Categorical Variables.iii. False Memory and Sexual Abuse.1. ANOVA and Follow-Up.2. Regression Analysis with Dummy Variables.3. Post Hoc Probing.a. Dunnett's test.b. Other post hoc tests.4. Demonstration of the Need for Only g-1 Dummy Variables.5. Was Multiple Regression Necessary?b. Other Methods of Coding Categorical Variables.i. Effect Coding.ii. Criterion Scaling.c. Unequal Group Sizes.i. Family Structure and Substance Use.1. Dummy Variable Coding and Analysis.2. Effect Variable Coding and Analysis.d. Additional Methods and Issues.e. Summary.f. Exercises.7. Categorical and Continuous Variables.a. Sex, Achievement, and Self-Esteem.b. Interactions.i. Testing Interactions in MR.1. Centering and Cross-Products: Achievement and Sex.2. The MR Analysis.ii. Interpretation.c. A Statistically Significant Interaction.i. Does Achievement Affect Self-Esteem? It Depends.ii. Understanding an Interaction.1. Further Analysis.iii. Extensions and Other Examples.iv. Testing Interactions in MR.d. Specific Types of Interactions Between Categorical and Continuous Variables.i. Test (and Other) Bias.1. Predictive Bias.2. Research Example: Investigating Test Bias.3. Predictive Bias: Steps.ii. Aptitude-Treatment Interactions.1. Verbal Skills and Memory Strategies.2. Testing for ATIs.iii. ANCOVA.e. Caveats and Additional Information.i. "Effects" of Categorical Subject Variables.ii. Interactions and Cross-Products.iii. Further Probing of Statistically Significant Interactions.f. Summary.g. Exercises.8. Continuous Variables: Interactions and Curves.a. Interactions between Continuous Variables.i. Effects of TV Time on Achievement.1. The Data: Centering and Cross-Products.2. The Regression.3. Probing an Interaction Between Continuous Variables.4. Points to Consider.b. Moderation, Mediation, and Common Cause.i. Moderation.ii. Mediation.iii. Common Cause.c. Curvilinear Regression.i. Curvilinear Effects of Homework on GPA.1. The Data: Homework and Homework2.2. The Regression.3. Graphing the Curve.4. Controlling for Other Variables.5. Testing Additional Curves.d. Summary.e. Exercises.9. Multiple Regression: Summary, Further Study, and Problems.a. Summary.i. "Standard" Multiple Regression.ii. Explanation and Prediction.iii. Three Types of Multiple Regression.iv. Categorical Variables in MR.v. Categorical and Continuous Variables, Interactions, and Curves.b. Assumptions and Regression Diagnostics.i. Assumptions Underlying Regression.ii. Regression Diagnostics.1. Diagnosing Violations of Assumptions.a. Non-Linearity.b. Non-Independence of Errors.c. Homoscedasticity.d. Normality of Residuals.2. Diagnosing Data Problems.a. Distance.b. Leverage.c. Influence.d. Uses.3. Multicollinearity.c. Topics for Additional Study.i. Sample Size and Power.ii. Related Methods.1. Logistic Regression & Discriminant Analysis.2. Hierarchical Linear Modeling .d. Problems with MR?e. Exercises.II. BEYOND MULTIPLE REGRESSION.10. Path modeling: Structural equation modeling with measured variables.a. Introduction to Path Analysis.i. A Simple Model.ii. Cautions.iii. Jargon and Notation.1. Recursive and Non-Recursive Models.2. Identification.3. Exogenous and Endogenous Variables.4. Measured and Unmeasured Variables.b. A More Complex Example.i. Steps for Conducting Path Analysis.1. Develop the Model.2. Check the Identification Status of the Model.3. Measure the Variables in the Model.4. Estimate the Model.ii. Interpretation: Direct Effects.iii. Indirect and Total Effects.1. Using Sequential regression to Estimate Total and Indirect Effects.2. Interpretation.c. Summary.d. Exercises.11. Path Analysis: Dangers and Assumptions.a. Assumptions.b. The Danger of Common Causes.i. A Research Example.ii. Common Causes, Not All Causes.1. True Experiments and Common Causes.c. Intervening (Mediating) Variables.d. Other Possible Dangers.i. Paths in the Wrong Direction.1. Reciprocal Causal Relations?ii. Unreliability and Invalidity.e. Dealing with Danger.f. Review: Steps in a Path Analysis.g. Summary.h. Exercises.12. Analyzing Path Models Using SEM Programs.a. SEM programs.i. Amos.1. Basics of SEM Programs.b. Re-analysis of the Parent Involvement Path Model.i. Estimating the Parent Involvement Model Via Amos.c. Advantages of SEM programs.i. Over-Identified Models.1. Correlations versus Covariances.2. Model Fit and Degrees of Freedom.3. Other Measures of Fit.ii. Comparing Competing Models.d. More Complex Models.i. Equivalent and Non-Equivalent Models.1. Equivalent Models.2. Directionality Revisited.ii. Non-Recursive Models.iii. Longitudinal Models.e. Advice: MR versus SEM Programs.f. Summary.g. Exercises.13. Error: The Scourge of Research.a. Effects of Unreliability.i. The Importance of Reliability.ii. Effects of Unreliability on Path Results.b. Effects of Invalidity.i. The Meaning and Importance of Validity.ii. Accounting for Invalidity.c. Latent Variable SEM and Errors of Measurement.i. The Latent SEM Model.1. Understanding the Model.d. Summary.e. Exercises.14. Confirmatory Factor Analysis.a. Factor Analysis or the Measurement Model.b. An Example with the DAS.i. Structure of the DAS.ii. The Initial Model.iii. Standardized Results: The Initial Model.iv. Testing a Standardized Model.c. Testing Competing Models.i. A Three-Factor No Memory Model.ii. A Three-Factor Combined Nonverbal Model.d. Hierarchical Models.i. Model Justification & Setup.ii. Hierarchical Model Results.1. Total Effects.e. Model Fit and Model Modification.i. Modification Indices.ii. Standardized Residuals.iii. Adding Model Constraints & z-Values.iv. Cautions.f. Additional Uses of CFA.g. Summary.h. Exercises.15. Putting It All Together: Introduction to Latent Variable SEM.a. Putting the Pieces Together.b. An Example: Effects of Peer Rejection.i. Overview, Data, & Model.1. Measurement Model.2. Structural Model.ii. Results: The Initial Model.1. Standardized Results.2. Unstandardized Findings.3. Mediation.4. Total Effects.c. Competing Models.i. Other Possible Models.d. Model Modifications.e. Summary.f. Exercises.16. Latent Variable Models: More Advanced Topics.a. Single Indicators and Correlated Errors.i. A Latent Variable Homework Model.1. Single-Indicator Latent Variable.2. Correlated Errors.3. Results.4. Interpretation.5. Unstandardized Coefficients.6. Effects on Homework, Indirect and Total Effects.ii. Competing Models.iii. Model Modifications.b. Multi-Sample Models.i. A Multi-Sample Homework Model Across Ethnic Groups.1. Constraining Parameters Across Groups.2. Measurement Constraints.3. Does Homework Have the Same Effect Across Groups?4. Other Effects.5. Summary: Multi-Sample Models.c. Replication and Cross-Validation.i. Using One Sample to Set Constraints in Another.1. Multi-Sample versus Replication Models.2. Model Development.d. Dangers, Revisited.i. Omitted Common Causes.ii. Path in the Wrong Direction.iii. Incomplete Knowledge.e. Summary.f. Exercises.17. References.
