This was a cross-sectional study that utilized the 8th Panel Study on Korean Children [Fig. 1].
We included parents and their children who participated in the 8th Panel Study on Korean Children (2015). The Panel Study was a review of the newborns born in 2008, their mothers, and the community environment (the date are publicly available). The Panel Study, conducted by the Korea Institute of Child Care and Education, included all households of newborns (excluding those who refused to participate) born between April and July 2008 from surveyed medical institutes with more than 500 or more annual births per year. The exclusion criteria were mothers who could not communicate in Korean, mothers with poor health after giving birth, newborns with serious diseases, mothers with serious diseases, newborns awaiting adoption, multiple births, and mothers aged ≤18 years.
The Panel Study recruited a pilot sample of 2563 households, from which 2150 households were selected as the final sample. Stratified multistage sampling was applied: the first stage included selecting medical institutes where childbirth occurs, the second stage included extracting households with newborns born in selected medical institutes as a pilot sample, and the third stage included establishing a sample from the pilot sample with households who wished to participate in the panel. The sample retention rate proposed by the Panel Study’s research team for the validity of this study sample was 74.3%.
In the current study, among all children who participated in the Panel Study and health questionnaire survey, 161 fathers and 161 mothers raising seven-year-old children, treated for AD within the last year, were selected as the final study participants [Fig. 2]. The Korean Children’s Panel Survey requested the Asan Medical Center to develop a questionnaire related to children’s health and verified the presence of atopy from the parents of the children through trained surveyors. The presence of children with AD was confirmed by using questions such as, “Has your child been diagnosed with AD by a doctor?,” “When was your child first diagnosed with atopy?,” and “Has your child been treated owing to AD (also known as “congenital fever” or “eczema”)?”
In the structural equation model, the minimum recommendation for the sample size is 10 times the free parameter, and the ideal size is 150–400 participants ; therefore, 161 participants constituted a sufficient sample size to analyze actor and partner effects using the structural equation model.
For the parenting stress survey, “burden and distress from carrying out parents’ role,” among the subfactors of the parenting stress scale developed by Kim and Kang , was extracted by the Panel Study’s research team, and a tool with 11 questions—confirmed through a preliminary survey from 2007—was used. Eleven questions were based on a five-point scale, and higher scores signified higher parenting stress. Concerning tool reliability, Cronbach’s alpha was .86 in a previous study , and .88 (fathers) and .90 (mothers) in this study.
The confirmatory factor analysis revealed that the goodness-of-fit of fathers’ parenting stress model was χ2 = 26.24, df = 24, goodness-of-fit index (GFI) = .93, adjusted GFI (AGFI) = .90, normed fit index (NFI) = .92, comparative fit index (CFI) = .94, root mean squared error of approximation (RMSEA) = .02. The goodness-of-fit of mothers’ parenting stress model was χ2 = 70.49, df = 24, GFI = .93, AGFI = .90, NFI = .92, CFI = .94, RMSEA = .05.
Co-parenting is a conceptual term that refers to the ways that parents and/or parental figures relate to each other in the role of a parent. For the co-parenting survey, the measurement tool developed by Mchale  was translated by the Panel Study’s team, and 16 questions (four subcategories: family unity, discipline, criticism, conflict) were selected. Questions were answered with a seven-point scale. Higher scores signified a higher level of co-parenting. In Mchale’s study , Cronbach’s alphas ranged .59–.82; in this study, Cronbach’s alphas .88 (fathers) and .86 (mothers). The confirmatory factor analysis revealed that the goodness-of-fit of the fathers’ co-parenting model was χ2 = 34.23, df = 21, GFI = 95, AGFI = .91, NFI = .94, CFI = .96, RMSEA = .05. The goodness-of-fit of mothers’ co-parenting model was χ2 = 31.13, df = 21, GFI = .97, AGFI = .92, NFI = .97, CFI = .98, RMSEA = .06.
For marital conflict, the measurement tool developed by Markman et al.,  was translated and revised by the Panel Study’s research team. It comprised eight questions that were answered using a five-point scale. Cronbach’s alphas for fathers and mothers were .91 and .93, respectively. The confirmatory factor analysis revealed that the goodness-of-fit of fathers’ marital conflict model was χ2 = 49.55, df = 20, GFI = .93, AGFI = .90, NFI = .94, CFI = .96, RMSEA = .03. The goodness-of-fit of mothers’ marital conflict model was χ2 = 56.32, df = 20, GFI = .92, AGFI = .90, NFI = .95, CFI = .97, RMSEA = .04.
The 8th Panel Study on Korean Children was approved by the institutional review board of the Korea Institute of Child Care and Education (no. KICCEIRB-2015-03). The current work was also conducted after review by the Institutional Review Board of C University (no. 1040271-201811-HR-030).
Data collection and analysis
The data were obtained from the Panel Study on Korean Children’s website (http://panel.kicce.re.kr/kor/publication/02.jsp). For data use, the study protocol was submitted to the Panel Study’s research team and reviewed. After obtaining approval, the corresponding data were downloaded. The collected data were analyzed using IBM SPSS Statistics for Windows, Version 22.0 (IBM Data solution, Seoul, Korea) and IBM SPSS AMOS, Version 20.0 programs (IBM Data solution, Seoul, Korea). Descriptive statistics were used for participants’ general characteristics and descriptive statistics of the measurement variables. Skewness and kurtosis of the measurement variables were verified for the normality of the data. For each measurement variable, the absolute value of skewness (− 0.65 to 0.81) did not exceed 2, and the absolute value of the kurtosis (− 0.17 to 1.15) did not exceed 4. AMOS was used to confirm multivariate normality. In this study, the univariate normality of each measurement variable satisfied the normal distribution condition by showing the absolute value of the skewness and the kurtosis ranging less than 2; however, multivariate normality was not satisfied at the significance level of .05 with multivariate index = 4.10 and CR = 6.10. If multivariate normality is not satisfied, there may be a problem of upward biasing the threshold when estimating the parameters. However, even if the multivariate normality is not assumed, it is reported that the estimated parameter is reliable when using the maximum likelihood method and when the sample size is ≥120. Therefore, the model was estimated without converting the data.
In addition, the correlations and multicollinearity of each construct and the measurement variables were confirmed by Pearson’s correlation coefficient, and the reliability of the tool was confirmed by Cronbach’s alpha coefficient. To confirm the actor and partner effects of parenting stress and co-parenting on marital conflict, the AMOS structural equation model was used. Furthermore, measurement invariance was conducted to confirm the homogeneity of fathers’ and mothers’ data within one measurement tool. To verify this, four competing models were compared. The first model was the baseline model, the second constrained the factor loading, the third constrained the covariance of the error, and the fourth constrained the factor loading and covariance of the error.
To verify the goodness-of-fit of our model, maximum likelihood method was used, and a confirmatory factor analysis was conducted to confirm the validity of latent variables for model analysis. For the goodness-of-fit of the model, the absolute fit indices of χ2, χ2/df, RMSEA, SRMR, GFI, AGFI, CFI, NFI and the Tucker-Lewis Index (TLI) were used. Direct effects, indirect effects, and total effect significance were confirmed using bootstrapping. To test structural model invariance across groups, an analysis technique that examines the difference in path coefficients between measurement models was used to compare the critical ratios of the free and constrained models.