Social Networks and Subjective Well-Being: A Comparison of Australia, Britain, and China

The different number of categories between Australia and Britain may, at first sight, suggest some serious difficulties for the analysis, with the former having four and the latter ten categories. However, on closer scrutiny, the problem is not particularly severe. If we were to re-code the British data into a four-category variable, then the responses in the current 5th category would go up and those in the 6th category would go down, resulting in 1.1, 10.8, 54.5 and 33.6% respectively, a pattern very similar to that found for Australia. Given this and our standardization procedure, we would believe that the approach we have taken is a reasonable one in the absence of strictly comparable data. We thank the Associated Editor and one of the Reviewers for alerting the issue to us.

Australian and British datasets separate relatives from friends but the Chinese dataset combines the two. To make them comparable with each other, we combine relatives and friends in the Australian and British datasets.

In our case, the set of variables for formal social networks meets the criteria better than does that for informal networks but for consistency, we use the IRT modeling in both formal and informal domains. Under the IRT, a single continuous factor is posited to underlie responses to items within a set but this factor is ‘measured’ subject to error by each item. A continuous score thus underlies each item, the sum of a true score contribution and an error. The distribution of this score is divided up by a set of ordered thresholds, with each section of the distribution being associated with observing one of the possible ordered categorical responses. A respondent’s categorical score is therefore determined by their continuous score falling within a particular range of values defined by an adjacent pair of thresholds. Since the continuous score is not directly observable, it is commonly considered to be a latent variable.

As different items may have different characteristics, they are allowed to differ in two ways. Firstly, items may have different threshold parameters. This allows, for example, fewer people to have memberships in political organizations than in sports clubs in Britain or Australia. Secondly, items may have different loading parameters. This allows items to be strongly or weakly related to the underlying factor, or correspondingly to vary in the extent to which they measure the underlying factor rather than something else. Choosing a proportional odds ordinal logistic parameterization allows the model to be specified by

\(\ln \left( {{\raise0.7ex\hbox{${pr(Y_{ij} \le k)}$} \!\mathord{\left/ {\vphantom {{pr(Y_{ij} \le k)} {pr(Y_{ij} > k)}}}\right.\kern-0pt} \!\lower0.7ex\hbox{${pr(Y_{ij} > k)}$}}} \right) = \alpha_{iK} + \lambda_{i} \eta_{j}\)

where \(Y_{ij}\) is the response to item i from individual j, \(\eta_{j}\) is the score of individual j on the latent factor, \(\lambda_{i}\) is the factor loading for item i, \(\alpha_{iK}\) is the threshold for a response of K or above. For an item with K categories, 1 to K, \(\alpha_{iK} = \infty\). It is also usual to make some parametric assumption about the distribution of the latent variable in the population. We have assumed this to be normally distributed. The models were estimated by maximum likelihood in STATA using Generalized Linear Latent and Mixed Models (gllamm) (Rabe-Hesketh and Skrondal 2012). The details of IRT loadings are available on request and we show the minimum and maximum scores obtained via the Expected A Posteriori (EAP) method (Zheng and Rabe-Hesketh 2007) in Table 2.

There are sizeable missing data on education in the British sample: 18% were excluded from the analysis as they had not completed full-time education yet and 3.4% had ‘unknown’ levels of education. The missing cases in Australia and urban and rural China are minimal, all within 1.0%. There are also missing cases on class in the range of 3.0–9.3% for the four societies. Following Greenland and Finkle (1995), we omitted the missing cases in the analysis. Including the missing as dummy variables does not have any substantial change on the effects of formal and informal social networks on subjective well-being in the four societies. We also conducted a separate analysis using ordinal logit (ologit) regressions and the pattern is essentially the same as shown in Table 3, with informal social networks having significant and positive effects for all four societies and formal networks being positively and significantly associated with SWB for only Britain and urban China (full details of ologit models are available upon request).