David A. Kenny

In this article, we attempt to distinguish between the properties of moderator and mediator variables at a number of levels. First, we seek to make theorists and researchers aware of the importance of not using the terms moderator and mediator interchangeably by carefully elaborating, both conceptually and strategically, the many ways in which moderators and mediators differ. We then go beyond this largely pedagogical function and delineate the conceptual and strategic implications of making use of such distinctions with regard to a wide range of phenomena, including control and stress, attitudes, and personality traits. We also provide a specific compendium of analytic procedures appropriate for making the most effective use of the moderator and mediator distinction, both separately and in terms of a broader causal system that includes both moderators and mediators.

1. Basic Definitions and Overview Nonindependence Basic Definitions Data Organization A Database of Dyadic Studies 2. The Measurement of Nonindependence Interval Level of Measurement Categorical Measures Consequences of Ignoring Nonindependence What Not to Do Power Considerations 3. Analyzing Between- and Within-Dyads Independent Variables Interval Outcome Measures and Categorical Independent Variables Interval Outcome Measures and Interval Independent Variables Categorical Outcome Variables 4. Using Multilevel Modeling to Study Dyads Mixed-Model ANOVA Multilevel-Model Equations Multilevel Modeling with Maximum Likelihood Adaptation of Multilevel Models to Dyadic Data 5. Using Structural Equation Modeling to Study Dyads Steps in SEM Confirmatory Factor Analysis Path Analyses with Dyadic Data SEM for Dyads with Indistinguishable Members 6. Tests of Correlational Structure and Differential Variance Distinguishable Dyads Indistinguishable Dyads 7. Analyzing Mixed Independent Variables: The Actor-Partner Interdependence Model The Model Conceptual Interpretation of Actor and Partner Effects Estimation of the APIM: Indistinguishable Dyad Members Estimation of the APIM: Distinguishable Dyads Power and Effect Size Computation Specification Error in the APIM 8. Social Relations Designs with Indistinguishable Members The Basic Data Structures Model Details of an SRM Analysis Model Social Relations Analyses: An Example 9. Social Relations Designs with Roles SRM Studies of Family Relationships Design and Analysis of Studies The Model Application of the SRM with Roles Using Confirmatory Factor Analysis The Four-Person Design Illustration of the Four-Person Family Design The Three-Person Design Multiple Perspectives on Family Relationships Means and Factor Score Estimation Power and Sample Size 10. One-with-Many Designs Design Issues Measuring Nonindependence The Meaning of Nonindependence in the One-with-Many Design Univariate Analysis with Indistinguishable Partners Univariate Estimation with Distinguishable Partners The Reciprocal One-with-Many Design 11. Social Network Analysis Definitions The Representation of a Network Network Measures The p1 12. Dyadic Indexes Item Measurement Issues Measures of Profile Similarity Mean and Variance of the Dyadic Index Stereotype Accuracy Differential Endorsement of the Stereotype Pseudo-Couple Analysis Idiographic versus Nomothetic Analysis Illustration 13. Over-Time Analyses: Interval Outcomes Cross-Lagged Regressions Over-Time Standard APIM Growth-Curve Analysis Cross-Spectral Analysis Nonlinear Dynamic Modeling 14. Over-Time Analyses: Dichotomous Outcomes Sequential Analysis Statistical Analysis of Sequential Data: Log-Linear Analysis Statistical Analysis of Sequential Data: Multilevel Modeling Event-History Analysis 15. Concluding Comments Specialized Dyadic Models Going Beyond the Dyad Conceptual and Practical Issues The Seven Deadly Sins of Dyadic Data Analysis The Last Word

Given that the root mean square error of approximation (RMSEA) is currently one of the most popular measures of goodness-of-model fit within structural equation modeling (SEM), it is important to know how well the RMSEA performs in models with small degrees of freedom ( df). Unfortunately, most previous work on the RMSEA and its confidence interval has focused on models with a large df. Building on the work of Chen et al. to examine the impact of small df on the RMSEA, we conducted a theoretical analysis and a Monte Carlo simulation using correctly specified models with varying df and sample size. The results of our investigation indicate that when the cutoff values are used to assess the fit of the properly specified models with small df and small sample size, the RMSEA too often falsely indicates a poor fitting model. We recommend not computing the RMSEA for small df models, especially those with small sample sizes, but rather estimating parameters that were not originally specified in the model.