Parental Child-Rearing Styles and Subjective Well-Being of Children Involved in Bullying

This study aims to examine how parental child-rearing styles contribute to subjective well-being of three groups: bullying victims, bullying perpetrator-victims, and those uninvolved in bullying. These groups were categorized based on the children’s self-reported bullying incidents. This study used quantitative approach with cross-sectional design. The participants were 781 4th to 6th-grader students (51.98% boys, 48.02% girls), consists of 329 bullying victims, 197 were both bullying perpetrators and victims, and 255 were uninvolved in bullying. Parental child-rearing styles were measured using The Egna Minnen Beträffande Uppfostran for Children (EMBU-C), while subjective well-being was measured using the Children’s Worlds Subjective Well-Being Scale 5 items (CW-SWBS5). Data were analysed using structural equation modelling. The results revealed that the warmth of fathers and mothers made significant and direct contributions to the subjective well-being of children uninvolved in bullying, where the father’s warmth negatively contributed, while the mother’s warmth positively contributed. Similar results did not appear in the subjective well-being of victims or perpetrator-victims.


Introduction
Parental child-rearing is known to be an important determinant of children's development. Parental child-rearing styles are parents' attitudes toward the child that create an emotional climate on how the child perceived parents' rearing style (Muris et al., 2003). Parental child-rearing style is a contextual variable that may be perceived differently by the child over time.
In Indonesian contexts, child development is influenced by different parental child-rearing styles compared to Western countries. In Indonesia,

Parental Child-Rearing Styles and Subjective Well-Being of Children Involved in Bullying
authoritarian parental child-rearing is considered to be the best parental style in practice (Riany et al., 2017). In Indonesia's major ethnic groups -Javanese and Sundanese -fathers apply an authoritarian approach in rearing their children (Zevalkink & Riksen-Walraven, 2001). As an expression of authoritarian parental child-rearing, Indonesian fathers keep physical distance from their children as a way to instill politeness in their children.
The fathers are unwilling to show emotions or affection to their children (Eisenberg et al., 2001;Riany et al., 2017). In contrast, Indonesian mothers tend to be more permissive towards their children (Zevalkink & Riksen-Walraven, 2001). They also tend to show affection to their children, display more warmth than fathers, and support their children as a means to stimulate their social and emotional development (Zevalkink & Riksen-Walraven, 2001). Warmth describes parents who give special attention to their children and express affection for them (Zevalkink & Riksen-Walraven, 2001). Although fathers and mothers tend to practice different styles of parental child-rearing, both styles are nevertheless traditionally considered to optimize child development (Riany et al., 2017).
According to Hussein (2010), children from collectivistic cultures such as Indonesia may be more vulnerable to bullying involvement due to the authoritarian parental child-rearing style. However, some studies showed different results in diverse collectivistic cultures. A study in Iran showed that authoritarian parental child-rearing significantly predicts bullying perpetration (Alizadeh Maralani et al., 2019). A study in Japan showed that children had more conflict and more relationally aggressive parenting experiences with their mothers than their fathers, but also had more intimate relationships with mothers than fathers (Kawabata & Crick, 2016). In contrast, a study in Taiwan showed that authoritarian parental child-rearing did not relate to school bullying victimization or perpetration (Hokoda et al., 2006), and overprotective parental child-rearing was also found to be unrelated to victimization (Hokoda et al., 2006). A study among U.S.born Asians showed that fathers' noninvolvement was found to be positively associated with bullying victimization, and authoritarian parenting was positively associated with perpetration (Hong et al., 2021). Some studies have pointed out that adolescents from a collectivistic culture who perceived parental control and authoritarian parental child-rearing still reported positive development outcomes (Keshavarz & Baharudin, 2012;Kim, 2005).
In Indonesian contexts, the authoritarian parental child-rearing style has been known as typical of the father's parental child-rearing style (Abubakar et al., 2015;Riany et al., 2017), while mothers were perceived to be more authoritative (Abubakar et al., 2015) or permissive (Riany et al., 2017). Although according to Riany et al. (2017), Indonesian children perceive parental control as a positive and warm expression from parents, bullying cases in Indonesia have increased over the years (Borualogo & Casas, 2021b;. These results were in line with Hussein's (2010) statement about the risk of children from collectivistic cultures becoming involved in bullying. Only a few studies have investigated parental childrearing in collectivistic cultures, particularly in Indonesia, and its correlation with bullying. The present study intends to contribute to filling this gap in non-Western countries.
The relationship between parental child-rearing styles and children's subjective well-being (SWB) is still unclear, although several studies have investigated its relationship (Gherasim et al., 2017;Wu et al., 2021). Studies showed a positive, negative, and even no correlation between the two variables depending on a variety of factors, e.g., age, gender, or personality of parents and children (Fan et al., 2020;Horton, 2021).
Following the pioneering, the Children's Worlds project on children's SWB, research on the topic has expanded in recent years, often to scrutinize factors that correlate and contribute to children's SWB. Children's SWB is defined as children's cognitive and affective evaluations about their lives, the circumstances affecting their lives, and the social contexts in which they live (Savahl et al., 2019). For clarification, Diener (2000) explained that cognitive evaluation refers to an individual's perceptions and understanding of his or her global and domain-specific life satisfaction, whereas affective evaluation refers to his or her positive and negative affect. Among the predictors of children's SWB, three have been pointed out as particularly relevant: bullying, safety, and feel listened to, respected, and taken into account (Casas, 2016).
International data presented by Progress in International Reading Literacy Study in 2016 showed that 29% of students reported being bullied on monthly basis and 14% on a weekly basis (Mullis et al., 2017). The Global School-based Student Health Survey (GSHS) in 2015 reported that 20.6% of Indonesian children experienced being bullied in the past month (CDC, 2016). The Program for International Student Assessment (PISA) revealed that 41.1% of Indonesian children reported being bullied (OECD, 2019). This high percentage of bullying victimization incidents puts Indonesia in the fifth highest position out of 78 countries (OECD, 2019).
Bullying incidents in Indonesia have become quite worrying . A study showed that 27.1% of children reported they had been bullied physically by other children at school at least twice and more in the last month, 36.7% of children reported they had been bullied verbally by other children at school at least twice and more in the last month, and 26.5% of children reported they had been bullied emotionally by other children in class at least twice and more in the last month . Data also showed that Kota Bandung is among the highest bullying frequency in West Java Province Borualogo et al., 2020a). Studies have shown that Indonesian children who have been bullied display lower SWB scores than those who have not (Borualogo et al., 2020b;Borualogo & Casas, 2021a). This agrees with the findings of a multinational study on bullying and SWB by Savahl et al. (2019).
Despite the need to analyze whether children's perceptions of their parents' rearing styles display any relationship with their SWB when involved in bullying (as perpetrators, victims, or both), we were unable to identify any studies on parental child-rearing styles and their relation with SWB in Asian countries, particularly in Indonesia. Several studies on bullying have focused on explaining the effects of bullying on children's SWB (Borualogo, 2021;Borualogo & Casas, 2021a, 2021b. Other studies have explained the effects of the parent-child relationship on children's involvement in bullying (Elledge et al., 2019;Stavrinides et al., 2015). However, none of these studies have explained the direct influence of different parental childrearing styles on children's SWB separately, depending on whether they are bullying victims, perpetrators, both, or uninvolved. Therefore, the ultimate goal of this study is to support activities aimed to raise awareness about the contribution of parental child-rearing styles to increase SWB in children involved in bullying. We included the uninvolved in the analysis as a comparison to the involved ones. This applied developmental study explores perceived parental child-rearing styles that contribute to SWB of children involved in bullying to help children's positive development.
The aims of this paper are: (a) to determine whether a set of child-reported variables regarding their parents' rearing styles have effects on the subjective wellbeing of Indonesian children; and (b) to determine whether said effects are different depending on the fact that the child has reported being uninvolved in bullying, a victim of bullying, or both a bullying victim and a bullying perpetrator.

Methods
This study used a cross-sectional design with self-reported questionnaires. The study population was elementary students in Kota Bandung, in West Java Province, Indonesia. Kota Bandung has been reported to have the highest bullying frequency in Indonesia . To obtain a sample of children in Kota Bandung, this study used a stratified cluster sampling procedure. Strata were the type of schools in Indonesia: public, private, religious-based, and non-religious-based. The sampling frame included all elementary schools in Kota Bandung. Eleven elementary schools were randomly chosen, and all of them agreed to participate in this study. Clusters were classrooms randomly chosen in each school, and all students from each chosen classroom were taken as participants. Eighty students in grades 4-6 from each school were chosen. All agreed to participate and obtained parental consent. In the data depuration process following the recommendation from Casas (2016), cases with three or more missing values in the SWB scale used here were excluded from the data analysis (N= 71). Of the participants (N = 781), 51.98% were boys, and 48.02% were girls.

Categorization of Children Based on Bullying Incidents
Children in the sample were classified regarding bullying incidents they reported in the questionnaires. Children can answer the questionnaires because these questionnaires have been tested in more than 35 countries in three waves of international surveys (Borualogo & Casas, 2021a, 2021bCasas & González-Carrasco, 2021;Rees et al., 2020;Savahl et al., 2019;Tiliouine, 2015;Varela et al., 2020). A set of questions for measuring bullying victimization and perpetration were administered, providing four response options: "never", "once", "two or three times", and "more than three times".
We defined bullying as repeated aggressive behavior intended to harm another person, involving a disparity of power between the perpetrator and the victim (Olweus, 1997;Volk et al., 2014). This criterion was used for victims of bullying and perpetrators of bullying in repeated bullying incidents. Bullying includes physical aggression (e.g. hitting), verbal aggression (e.g. name-calling) and emotional aggression (e.g. social exclusion) (Borualogo & Casas, 2021a). Children who reported being bullied two or more times in any of the three categories of bullying (i.e. physical, verbal and emotional) in the last month were considered victims; children who bullied other children two or more times in the last month in any of the three categories of bullying were considered perpetrators. The sample size of those who were only perpetrators was too small (28 students) for multi-group structural equation modeling (SEM), and consequently, this group was not included in our data analysis. Preliminary exploration of the data of only perpetrators displayed a very different pattern of answers than the other groups; thus, it is advisable in the future to get a bigger sample to carry out separate data analysis for this group. Therefore, the groups analyzed here were the victims, the perpetrator-victims (perpetrators who were also victims), and the uninvolved. Details of the categorization are presented in table 1.

Ethical Approval
The ethical committee approved the proposal to conduct a research project with children. Parents' written consent was obtained as a requirement for children to participate in the study. Children were also informed that their data would be treated confidentially and that they were free not to answer any questions. The questionnaire was self-administered using pencil and paper. Data were collected in 2019 and anonymously. Data collection was obtained in the classroom, with two researchers observing the process.

Victim Items
Three items measuring being bullied at school were taken from the Children's Worlds project (www.isciweb.org) and translated into Indonesian following the guidelines for the translation and cultural adaptation of instruments . The items measured physical bullying ("How often in the last month have you been hit by other children at school?"), verbal bullying ("How often in the last month have you been called unkind names by other children in school?") and emotional bullying ("How often in the last month have you been left out by other children in your class?"). The items were scored on a fourpoint frequency scale with four response options (0 = "never", 1 = "once", 2 = "two or three times", and 3 = "more than three times").

Perpetrator Items
Ten items measuring perpetrators' actions were adopted from Cole et al. (2006) and translated into Indonesian. The items measured the frequency of engaging in bullying behavior with peers at school in the last month. Four of the items measured the perpetration of physical bullying (e.g. "I intentionally hit other kids"). Another four measured the perpetration of verbal bullying (e.g. "I called other children bad names"), and the remaining two items measured the perpetration of emotional bullying (e.g. "I prevented other children from joining in activities that I do"). Those items were scored on a four-point frequency scale using four response options (0 = "never", 1 = "once", 2 = "two or three times", and 3 = "more than three times").

Children's World Subjective Well-Being Scale Five Items (CW-SWBS5)
The CW-SWBS5 has been used and validated in 35 countries that participated in the Children's Worlds international survey (Casas & González-Carrasco, 2021). The CW-SWBS5 has been validated and translated into Indonesian  using an 11-point scale from 0 (Do not agree at all) to 10 (Totally agree). The items are (1) "I enjoy my life", (2) "My life is going well", (3) "I have a good life", (4) "The things that happen in my life are excellent", and (5) "I am happy with my life". For Indonesia, the original fit indices for 10-year-olds were χ 2 = 75.17, df = 5, p = .000, comparative fit index (CFI) = .995 and root mean square error of approximation (RMSEA) = .043 (.035 -.052) , and for 12-year-olds were χ 2 = 93.79, df = 5, p = .000, CFI = .995 and RMSEA = .047 (.039 -.056) . Cronbach's alpha for this study = .902. The Egna Minnen Beträffande Uppfostran for Children (EMBU-C) (Muris et al., 2003) is a modified version of the original EMBU that measures children's perceptions of their parents' child-rearing behavior. The instrument's 40 items measure four types of parental child-rearing from the child's perspective: overprotective (e.g. "When you come home, you have to tell your parents what you have been doing"), emotionally warm (e.g. "When you are unhappy, your parents console you and cheer you up"), rejective (e.g. "Your parents tell you that they don't like your behavior at home"), and anxious (e.g. "Your parents worry about what you are doing after school"). Each subscale includes ten items. The scale includes 40 items for the mother and 40 items for the father. Children answered each question to separately assess their father's and mother's child-rearing behavior. The items used a four-point Likert-scale (1 = "never", 2 = "sometimes", 3 = "often", 4 = "most of the time").

Data Analysis
Data were analyzed using SEM with Amos 24.0 (Byrne, 2016). A hypothesized model was drawn based on the theoretical assumption that the parental styles perceived by children may have direct influences on their SWB. Analyzing data using SEM involves estimating the parameters of the relationship between variables and assessing the model's fitness about the data (Hooper et al., 2008). Thus, this work used maximum likelihood estimation. Of the several indices recommended for assessing an SEM's fitness (Hooper et al., 2008), we used CFI and RMSEA. Following Arbuckle (2010.) and (Byrne, 2016), scores exceeding .950 for CFI and less than .05 for RMSEA were considered to be excellent. Scores up to .08 for RMSEA were considered to be acceptable errors of approximation (Byrne, 2016;Marsh et al., 2010). Any CFI value greater than .90 was considered to reflect an acceptable fit to the data (Marsh et al., 2010).
Data analysis involved using a new variable generated using children's answers to the victim items and perpetrator items with three categories equivalent to the groups of children classified as victims, perpetrator-victims, or uninvolved in bullying events. Multi-group models were tested to compare the results between the three categories after being checked for factor invariance to ensure that the items measured the same constructs across groups. If factor invariance was not supported, then the differences between the measured variables could not be interpreted.
Initially, the pooled data model was tested to estimate correlations among all parental child-rearing variables and its factor weights on SWB, including gender and grade, for the overall sample. Next, three steps were developed to test for factor invariance in the multi-group models. In the first step, configure factor invariance was tested. It assesses an unconstrained multigroup model in which the parameters are freely estimated. Second, metric factor invariance, which is a requisite for comparing covariance, correlations, or regression coefficients, was tested by constraining the factor loadings of the baseline model. Finally, scalar factor invariance (requisite for comparing mean scores across groups) was tested by constraining the factor loadings and intercepts. For each additional constraint, the fit indices were checked to not decrease more than .01 in terms of CFI (Cheung & Rensvold, 2001) or .015 in terms of RMSEA (Chen, 2007).
Squared multiple correlations (SMC) were obtained for each model to indicate how accurately each variable was predicted by the other variables in the model (Arbuckle, 2010;Byrne, 2016). Additionally, the remaining variance in percentage was accounted for by its unique factor error. If the error represented a measurement error only, then the variable's estimated reliability was assumed to be the value displayed for each variable's SMC. Therefore, each SMC value was estimated from the lower band of reliability relating to its variable (Arbuckle, 2010;Byrne, 2016). Table 2 displays descriptive data of SWB and perceived parental child-rearing styles according to EMBU-C subscales by gender for the three groups: the uninvolved, the victims, and the perpetrator-victims. SWB scores were significantly different across groups, with the highest observed in the uninvolved group and the lowest in the perpetrator-victims. While SWB in the two first groups did not show significant gender differences, in the perpetrator-victims group, girls' SWB appeared to be significantly lower than that of boys.

Descriptive Statistics
At this stage, it was important to check for significant differences across the perceived parental child-rearing styles subscales between the bullying incidents groups. The perception of a rejective parent (both father and mother) was significantly different between groups in all cases. For the uninvolved group, the perception of both a rejective father (p < .001) or mother (p < .001) was significantly lower than for the victim's group and lower than the perpetrator-victims group (p < .001), while it was significantly lower for the victims than for the perpetrator-victims (p < .001). Additionally, the perception of a warm father was significantly higher for the For the three groups, the highest mean scores of a perceived parental child-rearing style for both girls and boys were observed for a warm mother. The perpetrator-victim girls and the victim boys displayed the lowest SWB scores across the three groups.
For children uninvolved in bullying, boys and girls displayed significant differences in their perceptions of having an overprotective mother, overprotective father, rejective mother, rejective father, anxious mother, or anxious father. Girls showed significantly higher mean scores than did boys in perceiving their mothers and fathers to be both overprotective and anxious.
However, boys displayed significantly higher mean scores than did girls in perceiving their mothers and fathers to be rejective.
For the victims, mean scores for a rejective father or mother were significantly higher than for the uninvolved group. In this group, girls displayed significantly higher mean scores than boys in perceiving their fathers to be warm or anxious.
The perpetrator-victims displayed no significant gender difference in the perception of their parents' rearing styles as measured by the EMBU-C subscales. Additionally, they showed higher mean scores for perceiving a rejective parental child-rearing style for both their mothers and their fathers than the two other groups, with boys showing the highest mean scores.

Structural Equation Modelling
SEM was performed with a model relating gender, grade, and all of the parental child-rearing subscales to the CW-SWBS5 latent variable (i.e. SWB). Therefore, we analyzed the contribution of each parental child-rearing variable for both mothers and fathers on the SWB of children in the three groups (i.e. victims, perpetrator-victims, and uninvolved). The model using the pooled sample (Model 1) presented an excellent fit, as displayed in figure 1 and table 3.
Loadings for the CW-SWBS5 items on its latent variable were high (between .72 and .88), as expected. The results showed that the subscales measuring parental childrearing styles contributed to the CW-SWBS5 with an SMC of .15, which means that parental child-rearing contributed 15% (i.e. on the lower band) to the explained variance of the SWB indicator.
We next tested this model as a multigroup model by bullying incidents, and its fit statistics were excellent (Models 2-4, table 3). With each additional constraint, the CFI did not display any decrease greater than .01. Therefore, these results support measurement invariance (both metric and scalar invariance), which means that correlations, regressions, and mean scores are comparable across the three groups.
Results obtained with Model 4 (i.e. with constrained loadings and intercepts) are displayed in table 4. As expected, very high correlations are observed between the perceived rearing styles of the father and the mother when we analyze the same subscale of the EMBU-C for each parent. These results suggest that when the mother is perceived as overprotective, warm, rejective, or anxious, the father tends to be perceived as having a similar rearing style. When observing the pooled sample results, all possible correlations are shown as significant at some level; that is to say, all combinations seem to be possible among Indonesian children.
However, it is interesting to observe that many of the less-expected correlations are not significant in the uninvolved group and are only significant in the groups of victims or perpetrator-victims. The combination of a rejective parent with a warm parent mainly appears in the victim's group; the combination of a rejective mother with either an anxious mother or father only appears in the perpetrator-victims group, while a rejective father with either anxious mother or father only appears in the victim's group; the combination of a rejective parent with an overprotective parent mainly appears in the perpetrator/ victims group.
Using the pooled sample, gender and grade do not display direct effects on SWB. However, gender shows significant effects on the SWB of the perpetrator-victims group. Only four perceived parental childrearing subscales show a significant direct contribution to SWB using the pooled sample: "Overprotective father" and "Warm mother" display a significant positive contribution to SWB, while "Rejective mother" and "Overprotective mother" display a significant negative one. While perceiving a warm mother displays highly significant effects on the SWB indicator for the uninvolved, its effects did not reach signification for the other groups. No perceived parental style has significant effects on SWB both for the victims and for the perpetrator-victims groups. Both a perceived rejective mother  Note. CFI = comparative fit index; RMSEA = root-mean square error of approximation; CI = confidence interval and perceived warm father show significant .716 *p < .05; **p < .01; ***p < .001 CW-SWBS5 = Children's Worlds Subjective Well-Being Scale 5 items negative effects on the SWB of the uninvolved, but not in the other two groups.
Most items of the CW-SWBS5 have a similar high contribution to its latent variable for the three types of bullying incidents. However, four of the five items display slightly higher contribution among the victims and the perpetrator-victims groups than among the uninvolved.
The explained variance of all the perceived parental styles subscales on the SWB (measured using SMC) is clearly lower for the perpetrator-victims group than for the other two groups, which suggests that other factors influence SWB of the perpetrator-victims.
In order to determine whether a set of child-reported variables on their parents' rearing styles affects the subjective wellbeing of Indonesian children (our first aim), we explored correlations between variables and their effects on an SWB latent variable using the CW-SWBS5 as an SWB indicator. Analysis of the correlations was important to confirm whether the EMBU-C subscales display similar correlations in Indonesia as in other countries, provided parental styles of the father and mother are expected to be perceived as very different in this country. Very high correlations were observed, as expected when the parental child-rearing styles of the father and the mother were perceived to be the same. Specifically, among children in our sample, when the mother is perceived as overprotective, warm, rejective, or anxious, the father tends to be perceived as having the same childrearing style. However, in our sample, many of the less-expected correlations did not appear in the uninvolved group and only appeared in the group of victims or perpetrator-victims. We did not find reports on these significant combinations of perceptions of apparently inconsistent parental child-rearing styles in other countries (e.g. a father being perceived as warm and rejective at the same time, a mother being perceived as overprotective and rejective at the same time, perceiving a rejective mother and an anxious father) (table 4). These significant correlations suggest that the three major parental styles as defined by Baumrind (1991) are not observed in their "pure" profiles in many Indonesian familiesa mixture of perceptions about inconsistent father's and mother's parenting styles and behaviors being frequent, particularly in families with children involved in bullying incidents.
On the other hand, findings revealed different contributions of some parental child-rearing styles variables on the SWB of children depending on their situations as victims, perpetrator-victims, or uninvolved in bullying.
Neither gender nor grade displayed significant direct effects on SWB when using the pooled sample. In the international literature, results on the relationship between gender and SWB are contradictory and depend on age. While it has been pointed out that in children between 10 and 15 years of age, SWB scores tend to decrease with age in most countries (Casas & González-Carrasco, 2019), we did not observe any significant decrease in our sample. This is consistent with previous findings using samples of Indonesian children (Borualogo & Casas, 2021b).
In our sample, "Overprotective father" and "Warm mother" displayed a significant positive contribution to SWB, while "Rejective mother" and "Overprotective mother" displayed a significant negative contribution, confirming that relationships between parents and children have direct effects on children's SWB. However, our results also indicate that any other combination of perceptions of parental child-rearing styles by a child did not exert a direct contribution to his or her SWB, even though the contribution could be indirect.
It seems surprising that an overprotective father has positive effects on SWB, while an overprotective mother has negative effectsalthough this was not unexpected among Indonesian children. Indonesian fathers are perceived as the heads of the family who have important roles in protecting and controlling their children (Zevalkink & Riksen-Walraven, 2001).
Therefore, perceiving an overprotective father may have a positive effect on children's SWB because the children may believe that their fathers are controlling them to ensure their positive development. In contrast, in Indonesia, mothers are perceived as warm and tend to be permissive in rearing their children (Zevalkink & Riksen-Walraven, 2001). Consequently, perceiving a mother as overprotective may have a negative effect on the child's SWB.
For children uninvolved in bullying, the mother's perceived warmth made a highly significant positive contribution to SWB, whereas the father's perceived warmth made a significantly negative one. As said in the introduction, warmth describes parents who give special attention to their children and express affection for them (Zevalkink & Riksen-Walraven, 2001). Parental warmth allows children to share their feelings and experiences with them and invites children to approach their parents when they need to. Parents should be encouraged to give their children attention and make their children feel they are being heard. A mother's warmth promotes feelings of self-worth among children and helps them develop social competence (Laible & Carlo, 2004). In the Indonesian context, mothers and fathers play different roles in raising their children and optimizing their children's development.
Mothers have more responsibility for taking care of children; they tend to be warmer and express more affection towards their children (Zevalkink & Riksen-Walraven, 2001).
Mothers in Indonesia have also been observed to be more supportive of children by stimulating their social and emotional development (Zevalkink & Riksen-Walraven, 2001). Therefore, children feel more secure and safe in sharing feelings with their mothers than with their fathers in the parent-child relationships at home.
Mothers who express warmth and support towards children can signal that their children are valued and loved, which tends to make them feel secure, safe, and listened to. Those feelings have been associated with decreased behavioral problems and increased SWB (Casas, 2016). Results regarding warm mothers in our study strengthen previous findings that explain the contribution of warm parental child-rearing on children's SWB (Garbarino, 2014).
However, in Indonesia's patriarchal culture (Koentjaraningrat, 2005), the father is an authoritarian figure who does not express warmth or affection to his children (Riany et al., 2017) but sets and implements rules and boundaries at home. In their relationships with their father, children value the role of their fathers but distance themselves from them in terms of affection. Therefore, it was expected that a father's warmth could negatively contribute to SWB for many Indonesian children. A study in Western culture showed that warm fathers contributed positively to children's wellbeing (Shewark & Blandon, 2015). In contrast, perceiving a father as warm may have no significant effect on the child's SWB because it is not expected by most children in Indonesia (Koentjaraningrat, 2005). High frequent positive and warm emotions expressed by fathers may be viewed as silly (Eisenberg et al., 2001), which may explain why Indonesian fathers tend to constrain their expression of warm emotions.
Perceptions of mothers as being rejective have a significant negative effect on the SWB of children uninvolved in bullying. Because Indonesian mothers are expected to be warm and a source of affection for their children (Zevalkink & Riksen-Walraven, 2001), being perceived as rejective represents an unexpected and undesirable mother's parenting style, and it negatively affects the SWB of children uninvolved in bullying.
The second aim of this article was to determine whether the effects are different depending on whether the child has reported being uninvolved in bullying, a bullying victim, or a bullying perpetrator-victim.
Previous research in Indonesia using a sample of 8 to 12-year-old children from West Java Province showed significant effects of gender on the SWB of bullied victims, with girls displaying significantly higher SWB mean scores than boys (Borualogo & Casas, 2021a). Descriptive results in the present study point out nonsignificant gender differences for the pooled sample, using t-tests (table 2), even though scores for girls are higher than for boys in the victim and uninvolved groups, like previous findings in Indonesia. However, results are the opposite for the perpetratorvictims group, where girls display significantly much lower scores than boys. While using a more powerful statistical instrument such as SEM allows us to include all variables and statistical relationships together in one model that includes the measurement errors, gender for children who were both victims or uninvolved in bullying shows no statistically significant contribution to SWB, but it does for the perpetrator-victims (table 4). These results point out a very serious problem with the SWB of girls who are bullying perpetratorvictims, which needs particular attention.
Although our results point out that perceiving a warm mother appears to be the most important positive fact for the SWB of all Indonesian children, perceiving a warm mother does not show significant effects on the SWB of the bullying victims or perpetrator-victims. On the other hand, perceiving a rejective mother or a warm father appears as a negative factor for the SWB of Indonesian children. Again, this only happens for those uninvolved in bullying because these negative effects are not observed in the other two groups. Additionally, four of the five items of the CW-SWBS5 display a slightly higher contribution among the victims and the perpetrator-victims groups, than among the uninvolved, suggesting most of the factors contributing to SWB are more important when a child is involved in bullying incidents. These results are in line with Casas' (2016) statement that bullying was a predictor of SWB. Other studies also support that children involved in bullying display lower SWB than the uninvolved (Borualogo & Casas, 2021a, 2021bSavahl et al., 2019;Tiliouine, 2015).
When analyzing the pooled sample's results (table 4), it becomes obvious that the reader may misunderstand the contribution of perceived child-rearing styles on the SWB of Indonesian children if we do not take into account the different effects that can be observed in the bullying victims or bullying perpetrator-victims compared to those uninvolved in bullying.
The explained variance (measured using SMC) of all the perceived parental style subscales on the SWB indicator used here is lower for the perpetrator-victims group than for the other two groups, which suggests that the SWB of the perpetratorvictims is influenced by other factors, probably related to peer group belonging, acceptance and support. The highest variance explained by the latent variable was for "I have a good life" and the lowest for "I enjoy my life" for both victims and perpetrator-victims.
In contrast, it respectively was for "My life is going well" and "Things in my life are excellent" for the uninvolved, supporting that influences on the SWB components may differ depending on the bullying situation.
Across the three groups, the victims displayed the highest explained variance (15.7%) of parental child-rearing items on the CW-SWBS5. Four correlations between perceived parental child-rearing items appeared to be significant only for the group of victims (table 4): between "Warm father" and "Rejective mother", between "Warm father" and "Rejective father", between "Warm mother" and "Rejective father", and between "Rejective father" and "Anxious mother", suggesting problems in the parental child-rearing styles in their families.
Finally, none of the parental childrearing variables contributed to SWB for the perpetrator-victims, while explained variance on the SWB was the lowest across groups (12.8%). The findings suggest that these children somehow "protect" their SWB from their parents' influences, and other variables influence their SWB. The highest correlation observed in that group was between the perceived anxious mother and anxious father (.845). The correlation between perceiving an overprotective mother and an anxious mother among perpetrator-victims exhibited the highest score in all groups (.747).
Perceived lack of parental warmth may be associated with a child's sense of being rejected and insufficiently nurtured by parents. Children may perceive that their parents do not give them enough attention when they need it, and they do not feel comfortable sharing their feelings and experiences with their parents when they experience being bullied at school; they may doubt that their parents will listen to them. Such circumstances in practice indicate that parents are not efficiently protective in front of bullying events of their children, and that situation makes it easier for the children to become repeat victims of bullying or perpetrator-victims. Previous research conducted in Indonesia has shown that children tend to tell their parents if they have been bullied at school before they tell their teachers (Borualogo et al., 2020b). Upon perceiving that their parents are not warm and do not listen to them, victims and perpetrator-victims may feel they lack the resources to express their bullying experiences at school. Such situations may cause them to feel rejected and may negatively affect their SWB.
Several studies have suggested that perpetrators of bullying come from families in which parents practice corporal discipline and reject their children (Demaray & Malecki, 2003). Perpetrators and victims of bullying are not demonstrated to be mutually exclusive categories, and like in previous research (Haynie et al., 2001), most of the perpetrators in our sample reported being victims as well. Future research needs to separately investigate children who are victims, perpetrators, and perpetratorvictims in Indonesian contexts. Non-victim perpetrators come from families in which parents are less involved with their children. According to Cummins (2014), having opportunities to develop good relationships with their parents is a factor that acts as a buffer from stressors and helps children maintain their SWB.
Findings from this study shall be implemented in helping positive development for children involved in bullying.
Parents, teachers, and policymakers shall be aware that children involved in bullying need to have warm parents to help them increase their SWB.
This study has several limitations. It focused exclusively on elementary-school students and therefore did not include secondary-school students who were still rarely studied in Indonesia. Therefore, for future studies, it is suggested to include secondary school students. It did not collect information from parents and, therefore did not test whether parents make any contribution to improving the SWB of bullying victims and perpetrator victims as they enter adolescence.
In addition, the number of perpetrators in the sample of the current study was too small. In our sampling procedure, we only identified 28 children who were perpetrators only. This made it impossible to analyze them separately as a different group because the sample size was too small for SEM multi-group testing.
Finally, each of the two categories of victims and perpetrator-victims included a mixture of physical, verbal, and emotional bullying. These should be analyzed separately in the future using larger samples to clarify whether the perceived parental child-rearing styles differ depending on the kind of bullying involved.

Conclusion
This study's findings demonstrated the Indonesian cultural uniqueness in how mothers' and fathers' rearing styles contributed to children's SWB while children were involved in bullying. These findings showed how non-Western cultures on child-rearing, particularly Indonesian culture, contributed differently to parentschild relationships. For example, in Indonesia perceiving an overprotective father displays positive effects on SWB, while an overprotective mother shows negative effects. In contrast, studies in Western literature have demonstrated that overprotective fathers contributed to children's problem development (Brussoni & Olsen, 2013), and warm fathers contributed positively to children's wellbeing (Shewark & Blandon, 2015).
Unlike among children uninvolved in bullying, none of the parental rearing variables showed any contribution to the SWB of victims or perpetrator-victims. Both victims and perpetrator-victims do not perceive warmth from their parents to a degree that affects their SWB. Parents of these children need support and resources to improve their children's SWB, which is at risk of serious decrease if other buffering factors do not work (e.g. support from other adults or friends) (Cummins, 2014). Perceived warmth of the mother has been related to higher SWB scores only among children who were uninvolved in bullying at school. On the contrary, the warmth of the father had a significant negative effect on most Indonesian children's SWB, except if they were involved in bullying events. Indonesian fathers are seen as authoritarian figures who set the rules and boundaries at home, and thus most children do not expect warmth from their fathers.
Girls from the perpetrator-victims group display significantly lower SWB scores compared to boys and all other girlsboth the uninvolved and the victims. This finding should be taken into account by parents, teachers, and policymakers because the SWB of the perpetrator-victim girls faces a most serious challenge, and its potential serious negative consequences need to be addressed and prevented.
The analysis presented here by dividing the sample into three categories of bullying incidents is the main strength of this study because it allowed us to focus on how SWB differs among children depending on their recent experience with bullying events (or not).