Fitting the Longitudinal Actor-Partner Interdependence Model as a Dynamic Structural Equation Model in Mplus

Abstract

Though the Actor-Partner Interdependence Model (APIM) has been extended to accommodate longitudinal data in the multilevel modeling (MLM) and structural equation modeling (SEM) frameworks, intensive longitudinal dyadic data with many (20+) timepoints provide technical challenges for researchers that neither framework fully addresses. We provide an overview of the strengths and weaknesses of MLM and SEM for intensive longitudinal APIMs, then discuss how dynamic structural equation models (DSEMs) are a more general form of both methods and can address their weaknesses in longitudinal APIM analyses. We illustrate how to fit a longitudinal APIM as a DSEM in Mplus with three examples from a daily diary study of heterosexual couples. Specifically, we show (1) when the MLM, SEM, and DSEM will produce similar results, (2) how DSEM can address research questions that traditional MLM and SEM cannot accommodate, and (3) how to specify increasingly complex longitudinal APIMs as DSEMs in Mplus.

Keywords:

• intensive longitudinal data
• multilevel modeling
• structural equation modeling

Notes

1 Annotated Mplus scripts and output can be accessed on the Open Science Framework page associated with this project, https://osf.io/vamku/?view_only=4f5b4c39fb294b0281566b94b61198da

2 Indistinguishable dyads are also appropriate for an APIM, see Ledermann and Kenny (2017) and Kenny et al. (2006, Chapter 7) for a discussion on the pros and cons of using MLM or SEM in this case. The DSEM framework can also accommodate indistinguishable dyads, though is not the focus of this manuscript.

3 Gistelinck and Loeys (2019) note similar issues (p. 335) but propose a method that was able to converge with data containing 21 repeated measures.

4 With wide data, there are ways to imply random slopes in some cases but this is not synonymous with permitting random slopes generally. For instance, a growth factor in a latent growth model can imply a random slope by creating a stand-alone latent variable with basis coefficients constrained to values of time, but this is not a true random slope whereby a coefficient is modeled as a latent variable. A multilevel model has a true random slope because the coefficient associated with the effect of time on the outcome is modeled as a latent variable. In growth modeling this distinction is often moot. However, in time-series modeling with ILDs random coefficients other than growth and that are more related to moment-to-moment dynamics are often of interest (e.g., autoregressive effects or time-varying covariate effects). Random slopes on these coefficients are more difficult to imply with wide data.