Social Capital and Self-rated Health Amongst Older People in Western Finland and Northern Sweden: A Multi-level Analysis

To check for robustness, we tried a number of alternative ecometrics specifications: (1) without accounting for “difficulty” bias and (2) a two-level model that uses the same individual-level social capital variables as are later used in the substantive models. For all specifications, we also performed sensitivity checks for the number of integration points and the adaptive quadrature methods employed in GLLAMM vis-à-vis the Stata command xtmelogit (the latter command results in Empirical Bayes modal predictions instead of the posterior means reported by GLLAMM). The municipal-level social capital variables resulting from these ecometrics analyses all correlate very highly with each other, and the results in the substantive models (Table 3) are comparable to the reported results. Thus, our results are robust to a variety of alternative specifications and estimation methods. This corresponds to earlier research (see footnotes 12 and 14 in [41]).

We compared the model fits for alternative specifications of these control variables, such as a categorical predictor of a variety of income levels. Model fit was optimal using the reported specification, and model outcomes in Table 3 are substantively similar.

The estimated equation mimics the ecometrics multi-level model. Y _ij takes on a value of unity if a respondent i reports high health in municipality j, with Y _ij  = 0 if not. Then, m _ij is the probability that Y _ij  = 1, and the log-odds (η _ij ) of this probability is estimated as the two-level model: η _ij  = γ + γ ₁ X _ij  + γ ₂ Z _j  + u _j  + ε _ij . In this example, we only introduce two covariates, X _ij and Z _j , although we, of course, introduce more covariates in each model (see Table 3). The γ is the grand-mean of self-rated health across all municipalities; X _ij is an individual-level predictor (which has a different value for each individual i in municipality j), and γ ₁ reflects the parameter estimate of that predictor; similarly, Z _j is a municipality-level predictor and γ ₂ refers to the parameter estimate of this predictor; u _j refers to municipality-level random effect and ε _ij refers to residual error. In several explorative models, we tested for random coefficients and cross-level interactions. Analytically, random coefficients are modelled by introducing a new interaction term between a specific covariate and group-level residuals of the slope of the individual explanatory variables. Cross-level interactions add the interaction term between individual-level and municipality-level covariates.