5 The direction of effects is family-specific 155 2019) in Mplus 8.5. This relatively novel analytical technique combines the strengths of structural equation modeling, multilevel modeling, and N = 1 time series analyses – and can yield both insights into within-family effects at the group level (i.e., averaged effects) as well as at the level of the individual family (i.e., family-specific effects). Preliminary analyses confirmed that the data met the assumption of weak stationarity because time (i.e., days in the study) explained little-to-no variance (0.0%–0.1%) in the parenting and affect variables. Eight lag-1 multilevel vector autoregressive (ML-VAR(1)) models (see Fig. 4) were estimated: 4 (parenting dimensions) × 2 (affect dimensions). The withinfamily bi-variate cross-lagged effects were specified as random effects to estimate these (family-specific) effects for each individual family separately. The within-person coupling reliability (WPCR) of the family-specific parenting-affect couplings ranged between .72 and .97 for the couplings concerning positive affect, and between .45 and .75 for couplings concerning negative affect(Neubauer et al., 2020). To account for unequal time intervals between measurements due to missing data, the option TINTERVAL was set to 1 (i.e., 1 day). All data points were placed in this equal day-to-day time interval and missing data were inserted into time intervals without data. Due to the Kalman filter implemented in DSEM, all available observations were used in the DSEM analyses (Hamaker et al., 2018; McNeish & Hamaker, 2019) Model convergence was inspected using two criteria: (1) PSR lower than 1.1 (potential scale reduction factor) and (2) whether the trace plots of the parameters look like fat caterpillars, especially the plots of the cross-lagged parameters (Hamaker et al., 2018). We used 40,000 iterations and a thinning factor of 10 in our final models. If the models did not converge with all random effects, fixed autoregressive effects were estimated. Inference Criteria We extracted the family-specific standardized cross-lagged effects (i.e., STDYX standardization) from the ML-VAR(1) models by using the R package “Mplus Automation”(Hallquist & Wiley, 2018). As pre-registered (https://osf.io/7n2jx/), these standardized effects were interpreted based on the smallest effect size of interest (SESOI) of .05 (Boele, Bülow, de Haan et al., 2023; Lakens et al., 2018). A standardized within-family cross-lagged effect of .05 can be considered a small(-to-moderate) effect according to recent guidelines (Orth et al., 2022). Hence, we interpreted standardized family-specific cross-lagged effects smaller than .05 as null effects (-.05 > β < .05), effects with a size of β ≥ .05 as positive effects, and effects with a size of β ≤ -.05 as negative effects.
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