TABLE 2.

Research Questions That Can Be Answered by the Various Modeling Approaches Considered in This Study for Our Example

Type of Research Questions	Related Parameters to Be Estimated and Tested	How to Deal With the Data From Two Members of a Dyad
		(1) Separate Modeling	(2) Simultaneous Modeling With a Default Error Covariance Structure	(3) Simultaneous Modeling With a Dependent Error Covariance Structure
1. How do mothers’ (or fathers’) reports of marital satisfaction change over time, on average?	Fixed effects (e.g., β10 in Equation 2 and β20 in Equation 3)	Y	Y	Y
2. How do mothers (or fathers) differ in changes in marital satisfaction over time?	Level 2 variance components (e.g., ${\sigma }_1^2$and ${\sigma }_2^2$ in Equation 5)	Y	Y	Y
3. How do mothers differ from fathers in changes in marital satisfaction over time, on average?	Fixed effects (e.g., β30 in Equation 9 and β40 in Equation 10)	N	Y	Y
4. How do couples differ in the mother versus father differences in changes over time?	Level 2 variance components (e.g. ${\sigma }_3^2$ and ${\sigma }_4^2$ in Equation 11)	N	Y	Y
5. How do mothers’ changes relate to fathers’ changes? Or how do mothers’ changes relate to mother versus father differences in the changes?	Level 2 covariances (e.g., covariances in Equation 11)	N	Y	Y
6. How much average intraindividual variability is there for mothers (or fathers) after controlling the individual fitted trends?	Level 1 residual variances (e.g., ${\sigma }_e^2$ in Equations 4 or 12; ${\sigma }_m^2$ and ${\sigma }_f^2$ in Equation 13)	Y	Y	Y
7. How much difference in the average intraindividual variability is there between mothers and fathers after controlling the individual fitted trends?	Difference in Level 1 residual variances (e.g., compare ${\sigma }_m^2$ and ${\sigma }_f^2$ in Equation 13)	N	N	Y
8. How do intraindividual fluctuations of mothers relate to those of fathers after controlling the individual fitted trends?	Level 1 residual covariance (e.g., σmf in Equation 13)	N	N	Y

Note. Each model can be fitted in either the multilevel modeling or structural equation modeling framework. Y = the research question can be answered by the approach; N = the research question cannot be answered by the approach. For the statistical tests, the Wald test can be used for testing the fixed effects and covariances. For testing the variances, we recommend the specific one-sided Wald test or the generalized likelihood ratio test (see Ke & Wang, 2015, for more details).