*2.5. Research Model*

Previous study dichotomized output variable and used binominal logistic regression to estimate the effect of social capital. The benefit of the approach was to facilitate the interpretation of regression coefficient as the likelihood to report better or worse health condition. However, [39,56,57] argued that such a dichotomization of a continuous variable was often arbitrary, which could fail to provide complete information about the actual distribution of the dependent variable or even cause misleading results. Therefore, in this study, we have kept the outcome variable, i.e., self-rated mental health as continuous and used a series of two-level linear regressions to examine the effect of individual and community social capital on an individual's mental health. Following the approaches of [58,59], and [21], we have specified the following basic model:

$$MH\_{\rm ij} = \beta\_{0\rm j} + \beta\_1 \left( SC\_{\rm ij} - SC\_{\rm j} \right) + \beta\_2 SC\_{\rm j} + \beta\_3 X\_{\rm ij} + \mu\_{0\rm j} + \varepsilon\_{\rm ij} \tag{1}$$

where *MH* is the mental health status for individual *i* (level 1) in community *j* (level 2); *SC* is the set of social capital variables measured at both the individual and community levels; and *X* is a vector of socioeconomic-demographic variables. This model estimated the fixed *β* parameters, which represented the overall relationships between individual social capital variables, covariates and mental health. There were also two random parameters *μ*0*j* (community level) and *εij* (individual level), which were assumed to follow a normal distribution and represent the differences from the corresponding means at both individual and community levels. The variance between-community and the variance between-individual within a given community were used to calculate the variance partition coefficient (VPC), which represented the deviation in mental health across individual and community levels [60]. That is to say, the proportion of the total residual variation that is due to differences between communities. As the community-level social capital variables were aggregated from those at the individual level, the value of individual social capital was group-centered in order to alleviate the multicollinearity problem (i.e., *SCij* − *SCj*) [21,61,62].

Our research model is illustrated in Figure 1.

**Figure 1.** Research model.

We have followed the nested modeling strategy of previous multilevel health studies (e.g., [16,21,42,56,63]) to account for the hierarchical structure of our dataset. We first estimated two variance components models (Model 0-Rural and 0-Urban) that include only random intercepts. Then we estimated Model 1-Rural and 1-Urban to include random intercepts and human capital variables. Finally, we estimated Models 2a–2e that include random intercepts, human capital variables, the five individual-level social capital variables (i.e., the aggregated SCI, CP, CT, PP, and PT) and the five community-level social capital variables (i.e., the aggregated SCI-Dist, CP-Dist, CT-Dist, PP-Dist, and PT-Dist), respectively.
