Study population.The data used in this study is from the 2014 China Longitudinal Aging Social Survey (CLASS). It is a national and continuous large-scale social survey project conducted by the China Survey and Data Center, Renmin University of China, Among the Chinese aged 60 and above, the social and economic background of the elderly and the situation of their children are collected regularly and systematically. The purpose of CLASS is to find the issues facing by the elderly during aging and to provide data base for the study and solve of the problem of aging in China. Because CLASS obtained very detailed informations on the socio-economic status of elderly with different numbers of children and their children in different ranks, it is particularly appropriate to study the relationship between intergenerational socio-economic status and the health of elderly.
The survey adopted the multi-layer and multi-stage probability sampling method, covering 29 provinces, autonomous regions or municipalities, which include 134 counties, districts and 462 villages, with a sample size of 11,511. This research mainly concerns about the aspects of CLASS such as the education, income, health status of the elderly and the education and economic conditions of their children. After excluding the 1227 elderly whose annual income data was null and those have missing values of other variables, 9745 of the 11,201 elderly who have given birth were finally selected for analysis. Among them, 1192, 1588 and 2534 valid samples in urban areas and 305, 1055 and 3071 in rural areas have one child, two children, and three or more children respectively.
Health of the elderly.The self-evaluation of the elderly on their physical and relative health status is a more comprehensive reflection of their health condition, which includes not only the combination of past and present health condition, but also the future health, resistance to disease and the extent to concern about the health (Yip et al., 2007; Read et al., 2016)[32, 33]. It has also been pointed out that subjective health assessment is more important than actual medical measurements (Maddox et al., 1973; Ocampo, 2010)[34, 35], therefore, the self-rated health and relative health were used to measure the health status of the elderly. The self-rated health was based on comprehensive evaluation of their own health status by the interviewees, and the relative health of the interviewees was scored from 1 to 5 relative to the health status of other people of the same age. The higher the score, the healthier the elderly.
The quality of children and the socioeconomic status of the elderly. The quality of children is generally expressed by their socio-economic status (Shi Zhilei, 2015). Economic level and educational level are used as the measurement variables in this study.
On a scale of 1 to 5, the economic conditions of children in the CLASS survey were "very difficult (poverty)", "relatively difficult", "basically adequate", "relatively rich" and "very rich", respectively, representing the degree of economic condition of children from poverty to affluence. The educational attainment scores of the elderly and their children ranged from low to high: 1. Can't read, 2. Primary School (private school or literacy class), 3. Middle School, 4. High School or Technical Secondary School, 5. Junior college or above.
On one hand, all the variables in the model are in order of Grade 5, and the same measurement standard is more helpful to compare the variables in the model with different number of children, on the other hand, income data is often obtained with a fuzzy feature, and income and health is not a simple linear relationship, research income for each additional 1 unit, a few additional units of health, is not very significant, only by comparing the health of different income groups can policies be made and implemented (Fang Fuqian, Lv Wenhui, 2009). In this paper, the scores of the income level of the elderly are divided according to the quantiles of 20, 40, 60 and 80 of the total sample income. The final scores from low to high are as follows: Below 2000 yuan (less than 20 deciles) is the low income level, and the score is 1; The median income level is 7200 yuan (between 20-40th quartile) with a score of 2; the median income level is 20000 yuan (between 40-60th quartile) with a score of 3; and the median income level is 32164 yuan (between 60-80th quartile) with a score of 4; more than 32164 yuan (more than 80th percentile) is the high income level, the score is 5.
Control variable.The most commonly used age in related studies were selected as control variables in this paper. In addition, in examining the intergenerational relationship of Chinese families and the health status of the elderly, the living arrangement of children and the family size of the daily life of the elderly are also factors that need to be considered. It reflects the organization of family life and determines the interaction of family members at the structural level, especially the interaction between the elderly and their children (Chen Junming, Chen Qi, 2016). Therefore, this study takes whether to live with their children as a control variable.
In order to avoid the possibility of regional differences in the number of different children of the elderly, we chose the residential location as the control variable. This variable is an ordered class variable, and the scores from 1 to 5 are "the central city of the city/county", "the edge city of the city/county", "the urban-rural fringe of the city/county", and "town outside city/county", "rural areas".
In addition, to distinguish differences in provincial economic development level, we chose provincial GDP per capita as a control variable.
Statistical analyses.Descriptive statistical analysis combined with structural equation model (SEM) has more advantages in dealing with the overall problem of measurement variables and group comparison (Kuklys, 2005). In this study, the measurement models of health status, children's education level and children's economic conditions of the elderly with one, two and more children were analyzed by multi-factor confirmatory analysis. The composition reliability of all measurement models was greater than 0.6, the average extraction of variance (AVE) was greater than standard (0.5), the factor loading of the observed variables was greater than 0.6, and the reliability coefficient (SMC) was greater than 0.36, All measurement models (CFA) had good reliability and validity, which were suitable for SEM analysis. The final fitness indexes (X2/DF < 5, FGI > 0.90, AGFI P > 0.90, CFI P > 0.9, RMSER < 0.08) met the criteria, which shown that the model had good fitness.