Conceptual framework

Within the conceptual framework of this study, our primary focus is on examining the distributional relationship between parenting style, parents' relationship, socioeconomic status (SES), and the mental health of children and adolescents. The framework combines eco-social theory and the social production of disease theory [58, 59]. The core of this paradigm is upon the recognition that individuals with lower socioeconomic status (SES) tend to experience higher levels of emotional distress as parents. This distress is typically marked by feelings of despair, worry, anger, and detachment. The distress may cause heightened disputes in the parental connection, which could lead to more severe, distant, or inconsistent parenting methods. The changes in parenting styles are essential in our framework since they have a direct correlation with the mental well-being of children and adolescents, as illustrated in Fig. 1.

Fig. 1

Conceptual framework socioeconomic status, parental style, parents couple relationship and mental health in children and adolescents

Study setting and study design

This study utilized data from waves one to seven of the LSAC dataset. LSAC is an ongoing, comprehensive, and multidisciplinary national representative survey that focuses on parenting, family relationships, education, employment, child health, and development. This survey used a multistage cluster sampling technique to collect the data. The data were collected from parents or caregivers (biological mother in 95% cases) of the children of participating households and from children themselves (from the age of 12 onward) through different methods (e.g., face-to-face interviews, self-reported questionnaires) with skilled interviewers. The detailed methodology for LSAC is available elsewhere [33]. In this study, we only used the K-cohort from Wave 1 to Wave 7 (i.e., aged 4–18 years) because of data availability. The baseline observation (n) of this cohort was 4953 and was followed up until wave 7 (n = 3014).

However, in the current study, children from single-parent families, adopted parents, stepparents, foster parents, aunts, and uncles were excluded from the analyses (Additional file 2). In this study, we only included children and adolescents from intact biological parent families. This decision stems from the understanding that children from step-blended or single-parent families often encounter unique challenges, including potential mental health burdens and socioeconomic inequalities that are not typically present in intact biological families. Across all seven waves, therefore, a total of 3014 children met these inclusion criteria for final analysis.

Measure of mental health status

The mental health status of the children and adolescents was the outcome variable of this study. To measure mental health status, this study used the Strength and Difficulties Questionnaire (SDQ). The SDQ is a valid and reliable tool to measure the mental status of children and adolescents [34, 35] and has been used extensively to measure mental health status in children and adolescents [36,37,38,39]. The SDQ scores are based on five domains: hyperactivity, emotional problems, conduct problems, peer problems, and prosocial behaviours [40,41,42]. In this study, we used all domains except pro-social behaviors because of the unavailability of this variable in all waves of LSAC. Each of the four domains covered five items; for example, the hyperactivity scale (i.e., not being able to stay still, constantly fidgeting, being distracted, stopping to think before acting, good attention span), the conduct problems scale (i.e., temper, obeys requests, often fights, argumentative with an adult, spiteful to others), the emotional problems scale (i.e., complaints of headaches, seemed worried, unhappy, nervous, fearful), and the peer problems scale (i.e., solitary, liked by other children, bullied by children, gets on better with adults, has at least one good friend). These four domains were used to generate a total SDQ, and their response scales ranged from 0 to 40 [36]. Higher SDQ scores implied a negative mental health status (i.e., mental health difficulties/distress), whereas lower scores reflected a positive mental health status in children and adolescents.

Measure of parental style

Parenting style is referred to as a collection of beliefs, values, and attitudes held by a parent regarding the health and development of children and teenagers [43,44,45]. A good parenting style (e.g., warm, consistent, supportive) has positive effects on a child's development; however, experiences of overprotection, rejection, and restriction by parents increase the risk of mental health issues in children and adolescents [46,47,48]. Thus, good parenting styles play a crucial role in the social-emotional development of children and adolescents [49, 50]. Based on established survey methods and theories, the LSAC integrated eight distinct parenting dimensions into their dataset: anger, inductiveness, consistency, over-protectiveness, parenting self-efficacy, monitoring, warmth, and hostility. However, our analysis omitted five of these dimensions: over-protectiveness, parenting self-efficacy, monitoring, warmth, and hostility, due to their limited availability in only one or two waves, which conflicts with our aim of conducting a comprehensive longitudinal study. Therefore, this study specifically focused on three dimensions: anger, consistency, and inductiveness in parenting. By examining the interplay between anger, warmth, and consistency, this approach aligns with Baumrind's 1991 framework in defining classic parenting styles [12]. Angry Parenting was measured using four questions, while Consistent Parenting and Inductive Parenting were measured using five and two questions, respectively. We calculated the frequency of exhibiting anger, consistency, or inductiveness towards children by computing the mean of the responses to the relevant questions on a 5-point Likert scale (1 = never, 5 = always) for each parenting style. Additional file 1 provides details of the questions used to measure parenting styles.

Measure of parent’s relationship

A positive relationship between parents is defined as nurturing and investing in meaningful relationships for overall happiness and success which can be beneficial for the family psychological adjustment [51, 52]. However, negative relationships between parents increase conflict among family members and decrease emotional warmth, which has been significantly linked to developing emotional and behavioral problems in children and adolescents [17, 53,54,55]. Thus, a friendly home environment and a pleasant relationship between parents are important predictors of children’s health and development [56]. In this study, we used two indicators derived from LSAC data to measure the quality of parents’ couple relationships: the argumentative relationship scale and the degree of happiness in the relationship. The argumentative relationship scale is a four-question scale that assesses the level of conflict in a relationship, with higher values indicating a more argumentative relationship. The degree of happiness in a relationship is a single question that assesses the overall level of satisfaction with the relationship, with higher values indicating a happier relationship. For further details on the questions related to the parent-couple relationship, please refer to Additional file 1.

Measure of income

Income was calculated as the sum of all members of a household's reported weekly income from all sources, which is referred to as disposable household income. We then used the Organization for Economic Co-operation and Development (OECD) equivalence scale to calculate equivalent household income [57]. Household income was used to measure SES and was constructed as the income component of the concentration index (CI). Equation (1) is used to calculate equivalent household income:

$$} = \frac}\,}\,}}}}\,} + 0.5 \times }\,} + 0.3 \times }\,}}}.$$

(1)

Other variables

Mothers’ education and employment status within household income were used to control for other characteristics of the socioeconomic status of a household. Age, gender, and place of residence were also used as control variables in this analysis. The descriptive statistics of all the variables are provided in Table 1.

Table 1 Descriptive statistics of variablesPotential bias

Although cohort studies are generally less susceptible to bias than other observational methods, such as cross-sectional studies, it is crucial to acknowledge three specific types of potential bias in cohort studies: selection bias, informational bias, and confounder bias [58]. The LSAC data collection methods strictly adhere to the top international guidelines for longitudinal cohort studies, aiming to minimize biases related to geographical location and nonresponses [59, 60]. Although identifying every potential confounder bias is challenging, in this study, we used both crude and adjusted regression models to examine the influence of potential confounders (i.e., demographics) on the relationships between parenting style, parental couple relationship, SES, and mental health status.

Statistical analysis

First, we employed descriptive statistics (frequency, mean, and standard deviation) to summarize the study variables. Second, using longitudinal data, we performed a wave-wise regression analysis to measure elasticities and examine the relationships between parenting style, parental couple relationships, and the mental health of children and adolescents. Subsequently, a concentration index (CI) was used to measure socioeconomic health inequalities in child and adolescent mental health. In addition, we applied the decomposition method to identify the factors contributing to the mental health status of children and adolescents (Additional file 2: Fig. S1). Furthermore, this study encountered some missing data that were addressed using a simple imputation method. All statistical analyses were conducted using R.

Concentration index (CI)

The concentration index (CI) is a standard tool used to measure and quantify socioeconomic inequalities in health variables. It ranges from − 1 to 1 and indicates thea relationship between health variables and the standard of living. A negative (positive) value of concentration index (CI) exhibited that the health variable was more concentrated towards poor individuals (better off) and indicated a pro-poor (pro-rich) distribution. CI is calculated using the following equation [61, 62].

$$2\sigma_r^2 \left( }} \right) = \alpha + \beta r_i + \varepsilon_i$$

(2)

Here, \(\sigma^2\) is the variance of the fractional rank, \(h\) is the health variable interest of the study (i.e., mental health) population, \(\overline\) is the mean of health variable of interest, and \(r_i \, = \frac\) is fractional rank of the study population rank by income or other indicators of socioeconomic status (i.e., \(i = 1\) for poorest and \(i = N\) richest).

Decomposition analysis

To identify the contribution of each independent variable to socioeconomic inequalities in mental health status, this study used the Wafstaff, Doorslaer, and Watanabe approach to a decomposed the CI [63]. Wagstaff et al. [65] demonstrated that when health is considered as a linear function of various factors, demographics, parenting style, and socioeconomic status (SES), the concentration index (CI) can be expressed as a weighted sum of the socioeconomic inequalities observed in these factors. Therefore, the CI can be broken down based on the regression model. Equation (3) can be used to decompose the CI.

$$h_i = \alpha + \sum_i^k + \varepsilon_i }$$

(3)

where \(\alpha\) is the intercept, \(\beta\) is the coefficient, \(X_k\) is a predictor, and \(\varepsilon\) signifies the error terms. According to Wagstaff et al. [65], \(CI\) of \(h_i\) can be decomposed into the contribution of each predictor, which would explain its contribution to the distribution of mental health inequalities [63].

$$CI = \sum_k CI_k + GC_u /\mu$$

(4)

where \(\mu\) is the mean of the health variable, \(\eta_k = \,\frac = elasticity\), which measures the effect (positive and negative) of independent variables, \(CI_k\) denotes the concentration index of each independent variable, and \(GC_e\) denotes the error terms. Equation (4) gives the total contribution of socioeconomic inequalities explained by the model, where the error term shows the unexplained socioeconomic inequalities. The contribution percentage is calculated by \(\left( / }} \right) \times 100\). Furthermore, in this study, decomposition of the concentration index was calculated based on the following: first, we ran the multiple regression model (e.g., every wave from wave 1 to wave 7) by adjusting the parenting style, parent’s relationship, age of children and adolescents, gender, place of residence, mother’s education, mother’s employment, and household income. Secondly, we calculate the mean of the study variable, then the calculated mean of each variable was multiplied by the coefficient which was obtained from the regression model and got the elasticity. Thirdly, the concentration index was calculated using the library (rineq) packages in R, and the calculated concentration index was multiplied by the calculated elasticity to obtain the contribution of the variables. Moreover, for the pooled regression model, we applied the same steps as described above.

Decomposition of concentration index change

This method analyses how the concentration of a particular variable changes over time. Therefore, in this study, we applied the Oaxaca and Blinder type decomposition approach to explain the differences in inequalities over a particular period [64, 65]. Although Wafstaff et al. [66] used this approach to investigate the factors that could change the health inequalities over the time. Applying the Oaxaca method to Eq. (4) yields the following equation:

$$\Delta CI = \sum_k } \left( - C_ } \right) + \sum_k } \left( - \eta_ } \right) + \Delta \left( /\mu_t } \right)$$

(5)

where \(t\) is the time period, \(\Delta\) signifies the first differences, and the first and second terms indicate the extend of change in CI due to change in inequalities in the determinants of health and changes in their elasticity, respectively. The third term is residuals components. Moreover, the calculation of the decomposition of the concentration index change was based on the Oaxaca and Blinder approach: (i) estimate all elasticities and concentration indices of each using the prior methods, (ii) subtract all factors of current elasticities and concentration index from prior periods that gives the change in concentration index, (iii) each factor multiplies (wave wise) with changes in concentration indices and current period elasticities, and (iv) finally, by adding the current elasticity and concentration index, the total contribution to factor changes over the time period. The results are presented in an Additional file 1: Table S3.