The Longitudinal Relationship Between Parenting and Self-Control Needs Reconsideration: A Commentary on Li et al. (2019)

The relationship between parenting and self-control has been a highly debated topic. Recently, Li et al. (2019) conducted a timely multilevel meta-analysis that summarized the overall relationship between parenting and self-control and explored a number of potential moderators. Specifically, Li et al. (2019) identified a cross-sectional association between parenting and adolescent self-control of r = .204, p < .001; a longitudinal association between parenting and subsequent self-control of r = .157, p < .001; and a longitudinal association between adolescent self-control and subsequent parenting of r = .155, p < .001. These effect sizes were invariant across ethnicities, cultures, age of adolescents, and gender of parents and adolescents. On the basis of these results, Li et al. (2019) concluded that “throughout adolescence, parenting continues to affect the development of adolescent self-control and adolescent self-control continues to affect parenting” (p. 990).

It is well known that cross-sectional correlations provide limited information for causality, and only experimental designs can directly inform causal inferences. Longitudinal studies are better than cross-sectional studies because they tap the issue of temporal precedence. That is to say, although longitudinal studies cannot be used to establish causality, they can inform the question of whether the purported cause comes before the effect, therefore helping researchers move one step closer to understanding causality. Apparently, Li et al. (2019) aimed to provide evidence for temporal precedence such that parenting at Time 1 can predict the change of adolescent self-control from Time 1 to Time 2 and adolescent self-control at Time 1 can predict the change of parenting between Time 1 and Time 2. However, their methods did not fully support them in achieving this goal. Specifically, Li et al. (2019) utilized bivariate correlations between the predictor at Time 1 and the outcome at Time 2 to estimate the longitudinal association. Because these correlations were confounded by the stability of the outcome, it is very likely that their estimated longitudinal association mainly reflected the extent to which the strong cross-sectional association between the predictor and the outcome at Time 1 (r = .204) was sustained via the temporal stability of the outcome rather than the extent to which the predictor at Time 1 was related to the change of the outcome between Time 1 and Time 2 (Harris & Orth, 2020; Sowislo & Orth, 2013). Therefore, it is necessary to control for the stability of the constructs to address temporal precedence (Locascio, 1982; Rogosa, 1980).

Currently, the most commonly used method addressing temporal precedence in longitudinal studies is the cross-lagged panel model (CLPM), which controls for the stability of the constructs through the inclusion of the autoregressive effects (i.e., the prior levels of the constructs; Finkel, 1995). When meta-analyzing effect sizes derived from the CLPM, the longitudinal relationship is often estimated by the standardized regression coefficient. When this coefficient is not available, the cross-lagged association ( r C . L . ) can be calculated as a semipartial correlation as suggested by Cohen et al. (2014) and Aloe (2014):

r C . L . = r Y 1 − r Y 2 r 12 1 − r 12 2 .

When parenting is the predictor and adolescent self-control is the outcome variable, r C . L . represents parenting at Time 1 on self-control at Time 2, adjusting for self-control at Time 1. The prospective correlation between the predictor and the outcome variable is r Y 1 (i.e., the association between parenting at Time 1 and self-control use at Time 2), which was the correlational estimate used by Li et al. (2019); the autocorrelation between the outcome variable and itself across time (i.e., self-control at Time 1 and Time 2) is denoted by r Y 2 ; and the correlation of parenting at Time 1 with self-control at Time 1 is r 12 . The same equation was also used to calculate a semipartial correlation for self-control at Time 1 as a predictor of parenting at Time 2 adjusting for parenting at Time 1.

Because the standardized regression coefficient in the CLPM is available only for a few articles in Li et al.’s (2019) data set, we extracted the three parameters ( r Y 1 , r Y 2 , and r 12 ) in all articles and reestimated the overall effect sizes on the basis of the semipartial correlation. Because there is no cross-lagged data in some studies (i.e., the outcome variable was measured only once at Time 2), we ended up including fewer studies than Li et al. (2019). To rule out the possibility that the difference between our results (based on the cross-lagged association) and Li et al.’s (2019) results (based on the bivariate correlation) is due to the number of studies included, we first analyzed our current data set on the basis of the bivariate correlation to ensure that the current data set and Li et al.’s (2019) data set were comparable. Results showed that the current data set was comparable to Li et al.’s (2019) data set in all facets: overall effect size, moderating variables, multiple-moderator analysis results, and publication bias (for details, see the Supplemental Materials available online). Then we reanalyzed the longitudinal relationship between parenting and self-control by using the cross-lagged association.

Based on the cross-lagged association, the overall effect size of longitudinal P → SC was statistically significant, ES _Z = 0.059, SE = 0.010, t = 5.723, p < .001, 95% confidence interval (CI) = [0.039, 0.080], with substantial heterogeneity, Q_E(246) = 892.839, p < .001; the longitudinal association of measuring parenting first and self-control later was r = .059, 95% CI = [0.039, 0.080]. The results of the regression test showed a significant asymmetry (z = 2.793, p = .005), suggesting publication bias in longitudinal P → SC. A trim-and-fill procedure was performed to produce an adjusted effect size of ESz = 0.037, SE = 0.005, 95% CI = [0.027, 0.048], p < .001, r = .037, 95% CI = [0.027, 0.048]. Based on the cross-lagged association, the overall effect size of longitudinal SC → P was also statistically significant: ESz = 0.062, SE = 0.012, t = 5.159, p < .001, 95% CI = [0.038, 0.086], r = .062, 95% CI = [.038, .086], with substantial heterogeneity, Q_E(184) = 487.675, p < .001. The results of the regression test showed a marginally significant asymmetry (z = 1.776, p = .076). A trim-and-fill procedure was performed to produce an adjusted effect size of ESz = 0.048, SE = 0.005, 95% CI = [0.038, 0.058], p < .001, r = .048, 95% CI = [.038, .058]. On the basis of the distribution of 1,028 CLPM effect sizes in four subfields of psychology, researchers proposed to use .03 (small effect), .07 (medium effect), and .12 (large effect) as benchmark values when interpreting the size of cross-lagged effects (Orth et al., 2022). According to this guideline, we found a small to medium level of effect size for both longitudinal P → SC and SC → P.

Note that we are not saying that estimating the longitudinal relationship with the cross-lagged association is a foolproof method that is immune to biases. Actually, the CLPM has been criticized for not distinguishing the within-person variance and the between-person variance (Hamaker et al., 2015). That is, if the stability of the construct is to some extent of a trait-like, time-invariant nature, the inclusion of the autoregressive effect may not adequately control for this. Therefore, many latent variable-type models were developed to adjust for unmeasured time-invariant confounding factors by including additional latent variables. A recent article compared the CLPM and three latent variable-type models from a causal-inference perspective by using potential outcome notation to define causal estimand (i.e., the cross-lagged effect; Lüdtke & Robitzsch, 2022). The three latent variable-type models were the random-intercepts cross-lagged panel model (RI-CLPM) that decomposes the longitudinal associations between two constructs into stable between-person associations and temporal within-person dynamics, the observation-level model that includes the stable trait factors at the level of all observed scores, and the fixed-effects dynamic panel model that models only the process of the outcome but is agnostic about the process of the predictor. Simulation studies confirmed that the CLPM provided biased estimates of the cross-lagged effect if there were unmeasured confounding factors. However, the latent variable-type models also produced biased estimates under different data-generating scenarios. That is, the latent variable-type models strongly depend on their specific parametric assumptions. If these assumptions did not correspond with the data-generating model, the latent variable-type models provided biased estimates of the cross-lagged effect. For example, if the data were assumed to be generated by the observation-level model with a single latent variable, although the observation-level model with a single latent variable produced unbiased estimates, all other models provide positively or negatively biased estimates of the cross-lagged effect.

Although both the CLPM and the latent variable-type models have limitations, they can still provide important information regarding the cross-lagged effect if they fit well with the actual data and produce consistent estimates. Researchers recently compared the CLPM with six latent variable-type models by assessing the frequency of convergence problems, the fit of the models, and the consistency of parameter estimates across 10 longitudinal samples (Orth et al., 2021). The CLPM and the RI-CLPM were demonstrated to be the most reliable methods in terms of convergence, fit statistics, and consistency of parameter estimates compared with other methods currently available such as the autoregressive latent trajectory model and the latent curve model with structured residuals. Because the RI-CLPM has a short history and requires at least three waves of data, it has never been adopted in studies included in Li et al.’s (2019) meta-analysis, which made it impossible to meta-analyze effect sizes derived from the RI-CLPM. Therefore, although our CLPM-based results may also be biased, currently there is no other way that can better address temporal precedence when meta-analyzing the longitudinal relationship between parenting and adolescent self-control.

Finally, it is very important to correctly interpret the results from the CLPM and the RI-CLPM. Because the RI-CLPM separates the within-person variance from the between-person variance, it can better answer questions focusing on within-person effects (e.g., whether the same adolescent who experiences more positive parenting than usual at Time 1 will show a subsequent increase in self-control at Time 2). However, the RI-CLPM does not provide any information about time-lagged between-person effects because the between-person differences are relegated to the random-intercept factors. Instead, just because the CLPM does not distinguish the within-person variance and the between-person variance, the cross-lagged effects tested in the CLPM are also based on the between-person variance, which can provide important information about time-lagged between-person effects. Therefore, the CLPM can better address questions focusing on between-person effects (Orth et al., 2021). In the current context, our results suggest that adolescents who experience more positive parenting at Time 1, relative to those who experience more negative parenting at Time 1, will be more likely to develop high self-control at Time 2. Likewise, adolescents with higher self-control at Time 1, relative to those with lower self-control at Time 1, will be more like to experience positive parenting at Time 2.