Analyzing Mixed-Dyadic Data Using Structural Equation Models

Abstract

Mixed-dyadic data, collected from distinguishable (nonexchangeable) or indistinguishable (exchangeable) dyads, require statistical analysis techniques that model the variation within dyads and between dyads appropriately. The purpose of this article is to provide a tutorial for performing structural equation modeling analyses of cross-sectional and longitudinal models for mixed independent variable dyadic data, and to clarify questions regarding various dyadic data analysis specifications that have not been addressed elsewhere. Artificially generated data similar to the Newlywed Project and the Swedish Adoption Twin Study on Aging were used to illustrate analysis models for distinguishable and indistinguishable dyads, respectively. Due to their widespread use among applied researchers, the AMOS and Mplus statistical analysis software packages were used to analyze the dyadic data structural equation models illustrated here. These analysis models are presented in sufficient detail to allow researchers to perform these analyses using their preferred statistical analysis software package.

Keywords:

• distinguishable
• dyadic
• exchangeable
• indistinguishable
• mixed

Notes

¹This article used generated hypothetical data to demonstrate the procedures involved in various dyadic data analyses using SEM, not to evaluate dyadic data analysis models. Model fit statistic values are presented “as is”; no judgments as to the quality of the fit of the model to the data are made and no theoretical conclusions should be drawn from the hypothetical results presented.

²No consensus currently exists, either in the empirical literature or across statistical analysis software packages, as to whether exogenous variable covariances should be estimated in a null model (see Widaman & Thompson, 2003). For all null models used here (e.g., Figures 4, 8, and 11), all analysis variable covariances were manually fixed to zero in Mplus and AMOS.

³Depending on the statistical analysis software package used, researchers might need to take additional steps to avoid estimation errors. See the Additional Caveats.docx file in the online Appendix materials.

⁴Many researchers consider the estimation of an unconditional model (i.e., omitting the psychological maltreatment covariates from Figure 7) prior to a conditional model a prudent testing step. An unconditional model was fit to the Newlywed data; that model showed the following fit indexes (χ² ₄ = 4.95, p > .05; CFI & TLI = 1, RMSEA = .02). The intercept and slope variance estimates for both husbands (ψ _IH = 7.69, p < .01; ψ _SH = 2.35, p < .01) and wives (ψ _IW = 11.00, p < .01; ψ _SH = 1.59, p < .01) were statistically significant.

⁵For both distinguishable and indistinguishable dyadic longitudinal models, the issue of whether unique variances and covariances should be freely estimated (e.g., distinguishable) or constrained to equality (e.g., indistinguishable) between dyad members should be treated as a hypothesis to be tested rather than viewed as a dyadic methodological requirement (e.g., Kashy et al., 2008).

⁶An unconditional model (i.e., omitting the self-reported fear covariates from Figure 9) was also fit to the SATSA data. After removing arbitrary designation misfit (49.43 – 42.85 = 6.58; 17 – 12 = 5; χ² ₅ = 6.58, p > .05), the unconditional model showed the following fit indexes: CFI = .99, TLI = .98, RMSEA = .03. Results also showed twins had an expected life satisfaction that differed significantly from zero in 1987 (45.96, p < .01), but decreased significantly per year (−.30, p < .01). Results further showed twins' intercept variance (ψ _T = 42.76, p < .01) and slope variance (ψ _S = .33, p < .01) estimates were statistically significant.