Measurement of loneliness
Loneliness, the main outcome variable, was assessed by a single question in line with previous studies [11, 13, 25]. Participants were asked the question “Do you have the feeling of loneliness?” with answers ranging from “often, sometimes, and never”. We dichotomized this variable into two categories (yes, no) by combining “often and sometimes” as the presence of loneliness, while “never” as the absence of loneliness, which was in line with other studies [11, 13, 34]. Details about the measurement of loneliness please refer to Additional file 1.
Measurement of social capital
Social capital, the main independent variable, included six dimensions: social participation, social connection, social support, trust, cohesion, and reciprocity. Social capital was measured with a five-point Likert scale and 22 items, which was adapted from the World Bank’s Social Capital Assessment Tool  and validated by our previous works [33, 36]. The Cronbach’s alpha was 0.919, denoting an excellent internal consistency. More information about the measurement of social capital can has been published elsewhere  and can be found in the Additional file 1.
Subjects were asked to respond to each item with answers ranging from 1 = “never”, 2 = “seldom”, 3 = “usually”, 4 = “often”, and 5 = “more often”, where each number indicated the associated score accordingly. The score ranges for each dimension were obtained by summarizing answers to each item as follows; social participation (4–20), social support (4–20), social connection (3–15), trust (3–15), cohesion (5–25), reciprocity (3–15). A higher score denoted a better social capital. During analysis, binary variables (high and low level) were generated by dichotomizing each dimension into two categories according to their relative median value, which was in accordance with other studies [23, 37].
Measurement of other variables
Data were collected on the demographic and health-related variables, including age, gender, body mass index (BMI, kg/m2), living status, residence (urban, rural), marital status, education level, functional ability, smoking status, drinking status, and the number of diseases. Functional ability was measured through a scale comprised of 14 items including both the Activities of Daily Living (ADL) and Instrumental Activities of Daily Living (IADL), adapted from Lawton and Brody  and validated by our previous work . Based on the physical health section of the Older Americans Resources and Services (ORAS) , participants were asked to report their diagnosis history of the following diseases or conditions: high blood pressure, diabetes, heart disease (coronary or valve disease), hyperlipidemia, angina, chronic bronchitis (emphysema), cerebral infarction (stroke), coronary heart disease(CHD), cataract, arthritis, cancer, liver or kidney-related diseases. The data were ranked into four categories: 0, 1, 2, > 2 .