For the love of my child: How parents’ relative extrinsic aspirations for children and interdependent self-construal predict their relational well-being

Self-determination theory suggests that holding extrinsic aspirations (e.g., getting rich) over and above other aspirations bears negative implications for one’s relational well-being. The present research examined whether this pattern generalizes to the aspirations people hold for significant others and more specifically whether parents’ extrinsic aspirations for children (AFC), relative to other AFC, predict their well-being in their relationships with children. We also examined whether this relationship varies depending on parents’ interdependent self-construal. Results of four correlational studies (N = 998 parents) revealed that, overall, relative extrinsic AFC predicted lower relational well-being. However, this relationship was attenuated among parents high (vs. low) in interdependent self-construal. This pattern of moderation was observed among U.S. parents at different stages of parenthood and partially replicated among a sample of Chinese parents. The findings suggest that interdependent self-construal could buffer against the negative implications of prioritizing extrinsic AFC for parental well-being.


Introduction
Contemporary societies often emphasize monetary success as a pathway to happiness (Derber, 1979;Ownby, 1999).According to Pew Research Center (2007), most people born in the U.S. between 1981 and 1988 identify wealth and fame as two of the most important goals for their generation.There may be good reasons for this: after all, wealth can be highly instrumental to the fulfillment of many other goals.
Even so, research suggests that excessive pursuits of goals that emphasize being rich, famous, and physically attractive-goals that are labeled as extrinsic aspirations-can be detrimental to psychological well-being and interpersonal relationship functioning (Bradshaw et al., 2023;Kasser & Ryan, 1993, 1996, 2001).This occurs when such aspirations are given more weight than aspirations that are said to be intrinsic to well-being (e.g., the pursuit of meaningful relationships, personal growth, and community contributions).
The popularity of extrinsic aspirations implies that people may hold such aspirations for significant others, such as for their children (AFC; Hollmann et al., 2016Hollmann et al., , 2018;;LeVine, 1980; see also Ryff et al., 1994).Existing research suggests holding extrinsic AFC may bear implications for one's children.For example, when children perceive their parents as promoting extrinsic (vs.intrinsic) aspirations, they tend to report less positive school functioning (Mouratidis et al., 2013) and higher social dominance orientation (i.e., preference for social inequalities, Duriez et al., 2007Duriez et al., , 2008)).This suggests that parental AFC may be relevant to children's welfare and how they view the world.
Meanwhile, relatively little attention has been dedicated to parents' perceptions of their own AFC and the implications of those perceptions on parents themselves (but see Kaiyuan Chen and Jinhyung Kim contributed equally to the project (i.e., study design, data collection and analyses, manuscript writing).Hollmann et al., 2016 for an exception).The lack of attention is surprising because there are good reasons to believe relative extrinsic AFC (i.e., a focus of parents on extrinsic AFC over other AFC) may have implications for parents' relational well-being.

Extrinsic aspirations and relational well-being
Aspirations are life goals that involve desirable states in the future (Emmons, 1989).However, not all "desirable states" are equally beneficial.According to self-determination theory (SDT, Deci & Ryan, 2000, 2014), intrinsic aspirations (e.g., pursuits of personal growth, social affiliation, and community involvement) are inherently satisfying and psychologically healthy.This is because they directly fulfill basic psychological needs: autonomy (i.e., feeling volitional in ones' behaviors), competence (i.e., feeling effective in ones' behaviors), and relatedness (i.e., feeling close to others in interpersonal relationships).In contrast, extrinsic aspirations (e.g., pursuits of wealth, popularity, and image) are pursued as a means to other desirable ends.These aspirations, though not unhealthy per se, do not inherently satisfy basic needs.As such, to the extent these aspirations are prioritized over and above other aspirations (in particular, intrinsic aspirations), people may become distracted from pursuits and activities that otherwise satisfy basic needs and promote well-being (Bradshaw et al., 2023;Kasser & Ryan, 1993, 1996).This is especially the case within interpersonal relationships.SDT argues that flourishing interpersonal relationships are contingent on the satisfaction of all three basic needs (Deci & Ryan, 2014).Through prioritizing extrinsic aspirations, people are said to be prompted into viewing their partners and relationships as mere instruments for their extrinsic aspirations (e.g., as a vehicle to gain fame).This renders a relationship superficial and not satisfying for basic needs.Consistent with this reasoning, an early study suggests that a relative focus on extrinsic aspirations was related to lower-quality romantic relationships (Kasser & Ryan, 2001).A more recent study similarly found that contrary to intrinsic aspirations that predicted increased need satisfaction within romantic relationships, extrinsic aspirations predicted decreased need satisfaction (Leung & Law, 2019, Study 2).Finally, within parent-children relationships, research suggested fathers' relative extrinsic aspirations negatively predicted their own need satisfaction and the need satisfaction of their children (Nishimura et al., 2021).
In sum, empirical research supports SDT's prediction that prioritizing extrinsic aspirations could undermine one's relational well-being.While the majority of the work focused on the aspiration one holds for oneself, one study (Rodriguez et al., 2015) looked into the ideals people hold for their romantic partners.The researchers found that satisfaction of intrinsic ideals predicted relation well-being more strongly than satisfaction of extrinsic ideals.This suggests SDT's analysis of aspiration for self could apply to the aspirations one holds for significant others (e.g., children).
We thereby hypothesize that relative extrinsic AFC should predict reduced relational well-being.Insofar as extrinsic AFC focuses on issues extrinsic to parent-children relationships, prioritizing such AFC should direct parents' attention away from need satisfaction in their relationships with children.For example, parents who wish their children to be famous may focus overly on whether other people approve of their children, as opposed to engaging with their children in an intrinsically satisfying manner.Their relationship with children may therefore be more strained than would be otherwise (Hollmann et al., 2016).Nevertheless, we also note that there is reason to believe that some parents may fare better against relative extrinsic AFC.As we contend below, the relationship between relative extrinsic AFC and relational well-being may be attenuated among parents high (vs.low) in interdependent self-construal.

Interdependent self-construal as a buffer against relative extrinsic AFC
The concept of self-construal refers to "a constellation of thoughts, feelings, and actions concerning one's relationship to others, and the self as distinct from others" (Singelis, 1994, p. 581).Researchers commonly distinguish between independent self-construal and interdependent self-construal.While these two types of self-construal have historically been treated as distinct categories that describe differences between cultural groups (e.g., West vs. East), recent research suggests these are related but different continuums that vary across individuals within a given culture (Cross et al., 2011).People high in independent self-construal tend to see themselves as autonomous entities, unique and somewhat separate from others.In contrast, people high in interdependent self-construal tend to view themselves as entities intertwined with significant others through group affiliation and harmonious interpersonal relationships.
We propose that interdependent self-construal should buffer the cost of relative extrinsic AFC on parent-children relationships.This proposal is guided by the idea that extrinsic AFC may reflect not only an individual affinity toward extrinsic values, but also deeply rooted other-oriented concerns.To elaborate, the desired ends of extrinsic AFC (e.g., wealth) are considered meaningful measures of success by many societies (Derber, 1979;Ownby, 1999).In this sense, it is possible that, at least for some parents, a wish for their children to be rich is, at its core, a wish for the best interests of their children.That is, extrinsic AFC may not be a mere wish for wealth for wealth's sake (a wish extrinsic to parent-children relationships), but a genuine wish for one's children to be successful and happy (a wish intrinsic to parent-children relationships) as well.
We contend that this other-focused, motivationally more intrinsic aspect of "extrinsic" AFC should be especially prevalent among parents high in interdependent selfconstrual.These parents think and behave in ways that are attentive to significant others (Markus & Kitayama, 1991).Such an other-oriented way of thinking is by nature prosocial and in conflict with the self-centeredness typically entailed by extrinsic values (Burroughs & Rindfleisch, 2002;Yoo et al., 2021).We therefore reason that interdependent selfconstrual should prompt parents to see extrinsic AFC as nurturing, other-oriented endeavors (i.e., expressing parental love and fulfilling caregiver duties to help children achieve success).For parents high (vs.low) in interdependent self-construal, extrinsic AFC is thereby motivationally more intrinsic to parent-children relationships.Under such conditions, prioritizing "extrinsic" AFC (i.e., high relative "extrinsic" AFC) should not disrupt relational well-being as much as would be expected otherwise.
Consistent with this idea, Yoo et al. (2021) found that materialistic goal-pursuits predicted well-being less negatively in national groups that tend to be relatively interdependent (e.g., Chinese, Japanese) than in national groups that tend to be relatively independent (e.g., European Americans).They also found evidence that this difference was driven by materialistic goal-pursuits being more motivated by social motives in interdependent national groups.In other words, people from interdependent national groups are more likely to pursue materialistic goals to attain positive social relationships.This, in turn, explains why materialistic goalpursuits are less negatively predictive of well-being among these groups.Extending the work of Yoo and colleagues, we applied the same analysis to aspirations for children using individual differences in interdependent self-construal.

The current research
The goal of the current research is to examine whether and how parents' relative extrinsic AFC predicts their relational well-being.Drawing from research on SDT and self-construal, we advanced the following two predictions: H1 Relative extrinsic AFC should, in general, negatively predict parents' relational well-being.

H2
Relative extrinsic AFC should predict relational wellbeing less negatively among parents high (vs.low) in interdependent self-construal.
We conducted four studies to test these hypotheses.Studies 1a and 1b were both cross-sectional survey studies where we tested H1 and H21 among online adult samples.The sample sizes were not pre-determined.We had sought to recruit at least 140 participants given the availability of lab resources.Sensitivity tests via the software G*Power (Faul et al., 2007) revealed that our obtained sample sizes had a minimum detectable effect size of f2 = 0.05 at p = 0.05 (assuming power as 0.80).
In Studies 2 and 3, we took a more confirmatory approach, pre-registered, 23 the two studies, and determined the sample size a priori.Study 2 was a direct replication of Study 1b with a high-powered sample.Study 3 tested the generalizability of our findings among parents from U.S. and China who had older offspring.Research suggests that SDT's conceptualization of extrinsic/intrinsic aspiration is valid across different nations (e.g., Grouzet et al., 2005;Ryan et al., 1999;Tang et al., 2008).We expected that our hypothesized main effect of extrinsic AFC (H1) and its interaction with interdependent self-construal (H2) would be observed among both U.S. and Chinese parents.We also included the potential three-way interaction (national group × relative extrinsic AFC × interdependent self-construal) in our analyses to account for the fact that the samples came from two different nations; however, we did not have any reason to expect it would be significant.

Participants
One hundred and forty-eight U.S. parents were recruited from Amazon Mechanical Turk (MTurk) in exchange for $1.We removed two cases because they had identical IP addresses.This resulted in a final sample of 1 3 N = 146 (60 male, 85 female, 1 gender nonconforming; M age = 38.53years, SD = 11.13;117 White, 12 Black or African-American, 9 Asian, 1 American Indian/Alaska Native, 1 Native Hawaiian or other Pacific Islander, 2 more than one race, 4 other).On average, participants reported having children around 10 years old (M = 10.71,SD = 9.10).

Measures and procedure
The whole procedure was delivered via Qualtrics software.Participants completed an online survey where they first completed measures of self-construal4 and AFC (order of the two measures randomized), followed by measures of well-being (order of the measures randomized).After that, participants reported their demographics, including their annual income (see supplemental materials), before being debriefed and compensated for participation.
Interdependent Self-Construal.Interdependent self-construal was measured by nine items selected from the selfconstrual scale (Singelis, 1994, e.g., "My happiness depends on the happiness of those around me", 1 = strongly disagree, 7 = strongly agree).Responses were averaged into composite scores (see Table 1 for reliability coefficients).
Relative Extrinsic AFC.We adapted the Aspiration Index (Kasser & Ryan, 1996).As a measure of aspirations for self, the original scale presents participants with 35 life goals and has participants to rate how important each goal is to them.The 35 goals assess seven broader categories: the extrinsic aspirations of wealth, fame, and image; the intrinsic aspirations of personal growth, meaningful relationships, and community contribution; and health (considered neither extrinsic nor intrinsic).To measure AFC, we similarly presented participants with the life goals5 but asked them to rate how important each goal was to them for their son(s) or daughter(s) on a 7-point scale (1 = not at all, 7 = very).For each category, Cronbach's αs and McDonald's ωs both ranged from 0.76 to 0.91 (see supplemental materials).Example items include "To be a very wealthy person" for wealth and "To work for the betterment of society" for community contribution.
Past research has provided ample evidence of the validity of the Aspiration Index (e.g., Grouzet et al., 2005;Ryan et al., 1999;Tang et al., 2008).Similar findings have been reported for scales adapted to measure parental AFC (Hollmann et al., 2018).For all our samples, we performed exploratory factor analyses on this measure.The results generally supported a two-factor solution (see OSF), with extrinsic subscales loaded on one factor and non-extrinsic subscales loaded on the other, providing evidence of construct validity.
To capture relative extrinsic AFC as parents' attempts to prioritize extrinsic AFC over other AFC, we followed Kasser andRyan (1993, 1996) and computed relative centrality scores: first, we calculated mean-corrected importance scores for each AFC category by subtracting the grand mean of the scale from each of the category scores-doing so allowed us to control for individual differences in global AFC strivings (i.e., being engaged with AFC vs. not being engaged with AFC).We then collapsed the mean-corrected scores of the three extrinsic goal categories into one composite.Higher scores on this composite indicate stronger orientations towards extrinsic AFC over other AFC.On average, participants scored lower than zero on this measure (see Table 1), suggesting that they generally placed more importance on non-extrinsic AFC over extrinsic AFC.
Relational Well-Being.We assessed two indices of relational well-being: relationship satisfaction and perceived relationship quality.To access relationship satisfaction, we adapted the 5-item Satisfaction with Life Scale (SWLS, Diener et al., 1985).SWLS is a validated measure of global life satisfaction (see Pavot & Diener, 2008 for a review).The original scale items ask people whether they agree with statements like "In most ways my life is close to my ideal."We took a relatively exploratory approach and reworded the items to assess satisfaction in family context (e.g., "In most ways my life with my family is close to ideal", 1 = absolutely untrue, 7 = absolutely true).Participants' responses were internally consistent (see Table 1) and were averaged into one composite.We similarly conducted exploratory factor analyses for this measure (see OSF).In support of scale validity, only one factor was extracted across our samples.
To measure perceived relationship quality, we used the Family Quality of Life Scale (FQOL, Hoffman et al., 2006), a validated measure.The 16-item scale consists of three subscales6 : family interactions (e.g., "My family enjoys spending time together"), parenting (e.g., "Family members help the children with schoolwork and activities"), and emotional well-being (e.g., "My family has the support we need to relieve stress").Though some of the items concern family life in general, FQOL taps into ambient and behavioral aspects of parent-children relationships (e.g., parenting, family interactions).We included this measure as an indirect index of relational well-being that involves less subjective evaluation (compared to relationship satisfaction).Participants rated their agreement with the items on a 7-point Likert scale (1 = strongly disagree, 7 = strongly agree).We found good reliabilities for each subscale (αs > 0.70; ωs > 0.71).Given subscale scores were inter-correlated (rs > 0.62), we collapsed them into one composite that represents overall perceived relationship quality.

Results
Descriptive statistics and correlations among key variables are presented in Table 1.Relative extrinsic AFC was significantly and negatively correlated with perceived relationship quality.The correlation between relative extrinsic AFC and relationship satisfaction was negative, but nonsignificant.We proceeded by conducting hierarchical linear regression analyses (Aiken & West, 1991) to examine the potential interaction between relative extrinsic AFC and interdependent self-construal.Scores of relational well-being indices were regressed onto mean-centered relative extrinsic AFC, mean-centered interdependent self-construal (both entered at Step 1) and their interaction term (entered at Step 2).We predicted a significant main effect of relative extrinsic AFC (H1) and a significant two-way interaction between relative extrinsic AFC and interdependent self-construal (H2).
For relationship satisfaction, the analysis To probe this interaction, we performed simple slope analyses by regressing perceived relationship quality onto relative extrinsic AFC respectively for those high (1 SD above the mean) and low (1 SD below the mean) in interdependent self-construal.We then generated the predicted scores from the mean-centered relative extrinsic AFC (see Fig. 1).As can be seen, for parents low in interdependent self-construal, relative extrinsic AFC significantly predicted lower perceived relationship quality, b = −0.73,SE = 0.11, p < 0.001, 95% CI [−0.95, −0.52].In contrast, for those high in interdependent self-construal, relative extrinsic AFC did not significantly predict perceived relationship quality, b = −0.17,SE = 0.10, p = 0.08, 95% CI [−0.36, 0.02].This is consistent with both H1 and H2.

Discussion
Study 1a provides partial support for our hypotheses.We found patterns consistent with H1 and H2 on one of the two indices of relational well-being: perceived relationship quality.Relative extrinsic AFC in general predicted lower perceived relationship quality.Nevertheless, parents high (vs.low) in interdependent self-construal suffered less from relative extrinsic AFC.We did not find support for our predictions on relationship satisfaction, the other index of relational well-being.The mixed finding could be due to the fact that the wording of relationship satisfaction items made no explicit reference to parent-children relationships (i.e., participants were asked to evaluate their life satisfaction with their "family," which may reflect satisfaction with their spouse, parents, or even pets).It is also possible that our predicted interaction is limited to perceived relationship quality.To address these possibilities, we designed Studies 1b and 2 to replicate the initial findings with a revised relationship satisfaction measure.

Participants
One hundred and fifty U.S. parents from MTurk participated in the study in exchange for $1. Two cases were removed for having the same IP addresses.This resulted in a final sample of N = 148 (63 male, 85 female; M age = 35.30years, SD = 10.03;119 White, 12 Black or African-American, 10 Asian, 1 American Indian/Alaska Native, 1 Native Hawaiian or other Pacific Islander, 1 Indian, 1 more than one race, 3 other).On average, the parents reported they had children around 9 years old (M = 9.23, SD = 7.21).

Measures and procedure
The procedure was identical to Study 1a.Participants completed the same measures of self-construal, AFC (Cronbach's αs ranged from 0.77 to 0.89; McDonald's ωs ranged from 0.78 to 0.89) and relational well-being (SWLS and FQOL, αs > 0.78; ωs > 0.78 for FQOL subscales)-only that the items of SWLS were reworded to refer more specifically to parent-children relationships (e.g., "In most ways my life with my child(ren) is close to ideal").The measures were all internally consistent (see Table 2 and supplemental materials).As in Study 1a, we collapsed the subscales of FQOL, given they were inter-correlated (rs ≥ 0.67).

Results
Descriptive statistics and correlations among major measured variables are presented in Table 2. Relative extrinsic AFC was significantly and negatively correlated with both perceived relationship quality and relationship satisfaction.We repeated the analyses as in Study 1a.For relationship satisfaction, the analysis (Step 1 R 2 = 0.12; Step 2 R 2 = 0.

Discussion
Study 1b provides additional evidence for our hypotheses.Consistent with H1, overall, relative extrinsic AFC significantly and negatively predicted relational well-being.In line with H2, this relationship was attenuated among parents high (vs.low) in interdependent self-construal.This pattern went beyond perceived relationship quality (as in Study 1a) and was also evident when predicting relationship satisfaction, likely owing to the fact that we adjusted the wording of the measure to refer specifically to parent-children relationships.Nevertheless, in neither of the studies was the sample size determined a priori.It is possible that both studies were underpowered.We conducted Study 2 as a more rigorous, pre-registered replication with sample size determined by a priori power analyses.

Participants
Three hundred and sixty-four U.S. parents recruited from MTurk completed the online survey in exchange for $1.
To ensure the data quality, three attention-check items were embedded into the survey (e.g., "For quality control purpose, please select 'Somewhat Agree'").In addition, we included a seriousness-check item at the end of the survey (Aust et al., 2013) that asked participants whether or not they had taken the study seriously.A total of twentythree cases were removed because they failed to pass more than two attention-check items and/or to report having taken the study seriously.Another 19 cases were removed because they had duplicate IP addresses.The final sample consisted of 322 participants (188 male, 133 female, 1 preferring not to say; M age = 34.52 years, SD = 9.55; 190 White, 98 Black or African-American, 16 Asian, 10 American Indian/Alaska Native, 3 more than one race, 2 Native Hawaiian or other Pacific Islander, 2 Indian, 1 other).On average, participants reported having children about 8 years old (M = 8.32, SD = 7.30).
The sample size of Study 2 was determined by two a priori power analyses.The first power analysis, based on G*Power, revealed that a minimum of 296 participants would be needed to detect an expected effect size of f 2 = 0.04, with power of 0.80 at p = 0.01 (see OSF for more details).We conducted another a priori power analysis that took into account the uncertainty of estimated effect size as recommended by Anderson et al. (2017).We used a t-value of 2.69 for the interaction term predicting one outcome measure with a sample size of 150, 0.60 of desired level of assurance to correct the uncertainty (no publication bias correction considered) and 0.80 of a statistical power at an alpha level of 0.01.This analysis revealed a minimum sample size of 301 for detecting our predicted relationships.Taken together,

Procedure and materials
The materials of Study 2 were identical with those of Study 1b.Participants completed the same measures of self-construal, AFC (αs of AFC categories ranged from 0.82 to 0.92; ωs ranged from 0.84 to 0.92), and relational well-being (i.e., SWLS and FQOL; αs > 0.72, ωs > 0.72 for FQOL subscales).Once again, the measures were internally consistent (see Table 3).We collapsed the FQOL subscales, given they were inter-correlated (rs > 0.70).

Results
Descriptive statistics and correlations among major variables are presented in Table 3. Relative extrinsic AFC was significantly and negatively correlated with perceived relationship quality.The correlation between relative extrinsic AFC and relationship satisfaction, however, was not significant.We repeated the analytical procedure in previous studies.For relationship satisfaction, the analysis (Step 1 R 2 = 0.38; Step 2

Discussion
In Study 2, we observed remarkably similar results as in our early studies (especially Study 1b): while relative extrinsic AFC negatively predicted both relational well-being indices (relationship satisfaction and perceived relationship quality), these relationships were attenuated (in fact, statistically nonsignificant) among parents high (vs.low) in interdependent self-construal.These findings provided strong support for both of our hypotheses.Moreover, the fact that Study 2 was pre-registered with sample size pre-determined addresses concerns of statistical power and lends even more credence to our findings.Still, so far, our findings were based entirely on U.S. parents recruited online who reported they had children about 8-10 years old of age.It is unclear whether the hypothesized interaction generalizes to parents outside of U.S. and/or parents with older offspring.In Study 3-which we also preregistered with sample size pre-determined-we aimed to demonstrate the generalizability of our work in two aspects: First, we reached out to parents via college students to examine whether the findings would be replicated among parents with older offspring (relative to Studies 1a, 1b, and 2).Second, we included a Chinese parent sample to look into the generalizability of our findings in a different national context.

Participants
Participants were 176 U.S. parents (60 male, 114 female, 1 gender nonconforming, 1 preferring not to say; M age = 49.85 years, SD = 6.06; 162 White, 2 Black or African-American, 2 more than one race, 1 Asian, 1 American Indian/Alaska Native, 1 Native Hawaiian or other Pacific Islander, 5 other, 2 missing) and 206 Chinese parents (66 male, 139 female, 1 other; M age = 45.99 years, SD = 5.49) recruited through their children (i.e., college students, see supplemental materials for details).U.S. parent participants received an entry into a random drawing for $20 Starbucks gift cards in compensation for their participation.Chinese parent participants received an entry into a random drawing of 50 CNY cash reward (roughly equivalent to $8) for their participation.
The sample size of Study 3 was determined by a power analysis using G*Power.Since we do not have the basis to estimate effect size for Chinese parents, we only estimated the required sample size for U.S. parents and used it as a guideline for collecting data in China.The analysis yielded that a minimum of 150 participants was needed to detect an expected effect of f 2 = 0.08, at p = 0.01 with power of 0.80 (for one group).We initially planned to recruit at least 400 participants (200 participants per group) and ended up recruiting slightly less than that.

Measures and procedure
The study materials were the same as in Studies 1b and 2. Past research has translated the Aspiration Index into Chinese and found evidence for its validity (Tang et al., 2008).In the current research, the adapted AFC scale and other measures were translated into Chinese by a native Chinese speaker who was fluent in English and blind to the hypotheses.The materials were then back-translated into English by the authors and compared to the original version.Minor changes in wording were made to ensure the quality of translation.Measurement invariance was then evaluated and ensured (see the next section).
For each scale, we first specified a model in which only the general factor structure was held equivalent across groups (i.e., the configural model); the means and variances 1 3 of the latent factors were fixed to 0 and 1 for both groups.Then we estimated a second model in which factor loadings were constrained to equality across groups with one group's factor variance allowed to freely estimate (i.e., the metric model).The second model was compared to the configural model using the chi square difference test for nested models.If the metric model did not fit significantly worse than the configural model (chi square p > 0.05), the assumption of metric invariance was supported.
For any scale evincing non-invariance, we identified the item with the most prominent discrepancy between groups based on the rank ordering and absolute magnitude of factor loadings in the configural model.We then estimated a partially constrained model that allowed the non-invariant item's factor loading to vary across groups (the factor loading of the remaining items remained constrained).This model was compared with the configural model.If no significant fit degradation was observed, partial invariance was achieved.If a significant drop in fit was still observed, we repeated the whole process until fit degradation was no longer significant.
Overall, metric invariance was supported in most of the scales.We only detected non-invariance in the interdependent self-construal scale.We identified two non-invariant items and removed them before conducting the analyses.

Primary analyses
Table 4 presents descriptive statistics and correlations among key variables.To our surprise, relative extrinsic AFC was not significantly correlated with relationship satisfaction and perceived relationship quality among U.S. parents.This is inconsistent with what we observed in our other studies.
In testing H1 and H2, we took into account the possibility of a three-way interaction among relative extrinsic AFC, interdependent self-construal, and national group (U.S. vs. China).To this end, we adopted a multi-group structural equation modeling approach (Green & Thompson, 2012) similar to the multi-group confirmatory factor analyses we had performed: Using Mplus 7.31, we first estimated a completely unconstrained model where scores of relational well-being indices were predicted by relative extrinsic AFC, interdependent self-construal (both grand-mean centered), and their interaction term.Intercepts and residual variances were allowed to freely vary.One at a time, we constrained each of the two interaction paths (i.e., from the interaction term to relationship satisfaction/perceived relationship quality) to equality across groups and compared the two constrained models to the unconstrained model.A significance decrease in model fit (chi square difference: p < 0.05) suggests meaningful differences between Chinese and U.S. parents on the path constrained.
Constraining the path resulted in significant degradation in model fit predicting relationship satisfaction, Δχ 2 (1) = 7.98, p = 0.005, but not predicting perceived relationship quality, Δχ 2 (1) = 0.04, p = 0.84.In other words, the interaction between relative extrinsic AFC and interdependent self-construal differed between Chinese and U.S. groups in relationship satisfaction but not perceived relationship quality.A final model was estimated with the path of interaction term predicting relationship satisfaction unconstrained and the path of interaction term predicting perceived relationship quality constrained.Given this analysis involved essentially two structural equation models (one for each national group) and a large number of estimates, we briefly report what is most relevant to our investigation (see supplemental materials and OSF for more details).
The analyses revealed a significant main effect of relative extrinsic AFC only in predicting perceived relationship quality among Chinese parents, b = −0.23,SE = 0.07, p = 0.002, 95% CI [−0.37, −0.09].The main effect of interdependent self-construal was significant for both relational well-being We proceeded by probing these interactions.Given that the interactions did not differ between Chinese and U.S. parents in predicting perceived relationship quality, we looked into Chinese and U.S. samples as a whole for this variable.As seen in Fig. 4 For relationship satisfaction, the interaction differed significantly between Chinese and U.S. parents: whereas the interaction was not significant among Chinese parents, it was significant among U.S. parents: as seen in Fig. 5, the relationship between relative extrinsic AFC and relationship satisfaction was more positive (though not statistically significant) among U.S. parents high in interdependent self-construal (1 SD above the grand mean), b = 0.31, SE = 0.17, p = 0.07, 95% CI [−0.02, 0.63], compared to the more negative relationship among those low in interdependent self-construal (1 SD below the grand mean), b = −0.19,SE = 0.13, p = 0.14, 95% CI [−0.45, 0.06].This pattern is broadly in line with H2, suggesting parents high (vs.low) in interdependent self-construal fare better against relative extrinsic AFC.

Discussion
In Study 3, we only observed patterns consistent with H1 on perceived relationship quality among Chinese parents.For H2, however, we successfully replicated the essential pattern of interaction when predicting relationship satisfaction (among U.S. parents only) and perceived relationship quality (among both U.S. and Chinese parents).The fact that we found support for H2 despite a lack of evidence for H1-in particular, on U.S. parents' relationship satisfaction-was surprising to us.A closer look at the simple slopes suggested this could have something to do with the interaction between relative extrinsic AFC and interdependent selfconstrual.Among those high in interdependent self-construal, the relationship between relative extrinsic AFC and relationship satisfaction is, though not significant, somewhat positive (compared to a "flat" null relationship in Studies 1b and 2).This may have "canceled" out the more negative link between relative extrinsic AFC and relationship satisfaction among those low in interdependent self-construal, resulting in an overall null relationship.We see several potential explanations for the discrepancy between this finding and what we found in other studies.We will explore this issue in the General Discussion.
Overall, the findings of Study 3 suggest that our H2 can be observed even in the absence of H1.Even when relative extrinsic AFC is tangentially related or unrelated to relational well-being, parents high (vs.low) in interdependent self-construal could still hold an advantage in relational well-being while pursuing such goals.

General discussion
Throughout the four studies, we found evidence for our hypotheses.In general, we found parents' relative extrinsic AFC predicted lower parent-children relational wellbeing-especially in terms of perceived relationship quality and to a lesser extent, relationship satisfaction.This supports H1.This relationship was, for the most part, less negative among those high (vs.low) in interdependent self-construal, which is consistent with H2.The pattern of interaction was replicated among several U.S. parent samples at different stages of parenthood (as indicated by the age of their children) and among a sample of Chinese parents (with the exception of relationship satisfaction).Our findings extend existing research on life aspirations and interpersonal relationships.Research on SDT suggests that pursuing extrinsic goals, such as goals of oneself to be rich, famous and physically attractive, over and above other goals predicts lower relational well-being (Kasser & Ryan, 2001;Leung & Law, 2019;Nishimura et al., 2021).However, the implications of holding similar aspirations for significant others in general-and for children in specific-have received relatively little attention.Our work represents one of the first attempts to directly look into these relationships.Along with other emerging research (Hollmann et al., 2016(Hollmann et al., , 2018) ) and in line with SDT, our findings suggest parental AFC could play an important role in the functioning of parent-children relationships-parents' endorsement of extrinsic (over nonextrinsic) aspirations for children specifically seems to negatively predict their self-report relational well-being.
Still, we also found this relationship to be attenuated by interdependent self-construal.Past research suggests that extrinsic pursuits tend to entail self-centered values that are in conflict with the collective orientations entailed by interdependence (Burroughs & Rindfleisch, 2002).A more recent study suggests that interdependence may instead prompt people to leverage the typical extrinsic goals to fulfill their collective orientations (as opposed to self-centered motives) and this brings benefits (Yoo et al., 2021).Our finding is broadly consistent with these studies, suggesting that cultivating interdependence may be one way to combat or even undo the potential negative influences of excessive extrinsic pursuits.

Limitations and future directions
Future research should try to address one general limitation of our work: the exclusive usage of cross-sectional designs.Dittmar et al. (2014) noted that research was lacking in using experimental and longitudinal methods to study the relationship between materialism and well-being.It remained somewhat open whether materialism causes well-being, vice versa; or the relationship is bidirectional or is even emerging due to a third variable.Echoing Dittmar and colleagues' concern, we call for follow-up research to utilize experimental or longitudinal designs.
Though we consider it less conceivable that relational well-being causes parents' relative extrinsic AFC, experimentally manipulating AFC should help establish causality.Longitudinal methods, on the other hand, could not only elucidate the direction of our hypothesized relationships but also potentially integrate our work with broader developmental theories.For example, the theory of generativity (Erikson, 1950) suggests that efforts to contribute to the well-being of the next generation play a key role in healthy personality development.Our research could suggest some efforts (e.g., towards the fulfillment of intrinsic AFC) may be more important than others.Along these lines, it would be interesting to examine the interaction between relative extrinsic AFC and interdependent self-construal over time to see if the effect is temporally stable.
Future research should also explore why the findings in our Study 3, especially with regard to relationship satisfaction, diverged from those in our other studies.Specifically, in Study 3 we observed that U.S. parents high (vs.low) in interdependent self-construal fared better against relative extrinsic AFC even when the latter was in general unrelated to relationship satisfaction, a pattern in support of H2 but not H1.One possible account is that this finding is explained by ceiling effects or restricted range of responses.As reflected in descriptive statistics, most of our participants rated themselves as higher than the scale midpoint on relationship satisfaction.This might have contributed to the positive yet nonsignificant simple slope observed among U.S. parents high in interdependent self-construal in that study (see Fig. 5).
Fig. 5 Relationship satisfaction as predicted by interdependent self-construal and relative extrinsic AFC for U.S. and Chinese parents in study 3. Note.AFC aspiration for children.ISC interdependent self-construal.Relative extrinsic AFC is a grand mean-centered variable; thus, the zero value on the x-axis indicates the grand mean (SD = 0.74).Ribbons around the slopes for high and low ISC indicate 95% confidence bands Another possible account is that the U.S. parents in Study 3 had older offspring who were in college (compared to young adolescents in our other studies).For these parents, extrinsic AFC may already have been to some degree attained (e.g., my kid is going to a "prestigious" college).This may have conferred some additional psychological benefits on parents (thereby "evening" the otherwise negative slope), particularly for those high in interdependent self-construal whose life satisfaction is contingent on social appraisals (Suh et al., 2008).More research is needed to examine the implications of relative extrinsic AFC on parents whose offspring have fulfilled (vs.not fulfilled) their AFC.
Meanwhile, it may be tempting to attribute the inconsistencies to our U.S. parents in Study 3 having higher SES than the rest of our samples (see supplemental materials).Nevertheless, across the samples, parental SES (measured by income) was not correlated with interdependent selfconstrual, nor did it interact with relative extrinsic AFC in predicting relational well-being.The three-way interaction among parental SES, interdependent self-construal and relative extrinsic AFC was mostly not significant.These findings suggest that the relationship between relative extrinsic AFC and relational well-being (and our predicted moderation of interdependent self-construal) was not subject to parental SES.
Finally, it is worth noting that among Chinese parents, we only partially replicated our predicted interaction.The interaction was significant and in predicted direction for perceived relationship quality, but not for relationship satisfaction.Given we only had one Chinese parent sample, it is difficult to pin down why this mixed finding occurred and to what extent the finding applies to other national groups.We encourage future research to replicate our work with a broader variety of national groups (and relational well-being indices) and explore nation-level boundary conditions.

Conclusion
SDT (Bradshaw et al., 2023;Deci & Ryan, 2000, 2014;Kasser & Ryan, 1993, 1996) contends that people's wellbeing can be compromised when they aspire to be rich, famous and physically attractive above all else.Our work extends this analysis of aspirations for self to the aspirations parents hold for their children.We suggest parents may want to examine what they wish for their children to attain, as some of these wishes (e.g., wishing for their children to be rich), if held above others, could hurt their relational wellbeing.Despite that, an interdependent self-construal, or the belief that one's self is intertwined with significant others, could be an antidote to such negative implications.Our work highlights not only the utility of applying SDT to a broader variety of goals (i.e., goals parents hold for children) but also how nuances in the way people construe their selves may alter the implications of goal-pursuits.

Fig. 2
Fig. 2 Relational well-being indices as predicted by interdependent self-construal and relative extrinsic AFC in study 1b.Note.AFC aspiration for children.ISC interdependent self-construal.Relative extrin-

Fig. 4
Fig. 4 Perceived relationship quality as predicted by interdependent self-construal and relative extrinsic AFC in study 3. Note.AFC aspiration for children.ISC interdependent self-construal.Relative extrinsic AFC is a grand mean-centered variable; thus, the zero value on the x-axis indicates the grand mean (SD = 0.74).Ribbons around the slopes for high and low ISC indicate 95% confidence bands

Table 1
Descriptive statistics and correlations for measured variables in study 1aISC interdependent self-construal, AFC aspirations for children, N/A not applicable

Table 3
Descriptive statistics and correlations for measured variables in study 2ISC interdependent self-construal, AFC aspirations for children, N/A not applicable

Table 4
Descriptive statistics and correlations for measured variables in study 3Numbers above the diagonal represent descriptive statistics and correlations of variables within the U.S. sample and numbers below the diagonal represent descriptive statistics and correlations of variables within the Chinese sample ISC interdependent self-construal, AFC aspirations for children, N/A not applicable