Social Capital and Health - Findings from the Scottish Health Survey and Scottish Social Attitudes Survey

Annex A - Regression models

1. Regression analysis aims to summarise the relationship between a 'dependent' variable and one or more 'independent' explanatory variables. It shows how well we can estimate a respondent's score on the dependent variable from knowledge of their scores on the independent variables. This technique takes into account relationships between the different independent variables (for example, between education and income, or social class and housing tenure). Regression is often undertaken to support a claim that the phenomena measured by the independent variables cause the phenomenon measured by the dependent variable. However, the causal ordering, if any, between the variables cannot be verified or falsified by the technique. Causality can only be inferred through special experimental designs or through assumptions made by the analyst.

2. All regression analysis assumes that the relationship between the dependent and each of the independent variables takes a particular form. This report was informed by logistic regression analysis - a method that summarises the relationship between a binary 'dependent' variable (one that takes the values '0' or '1') and one or more 'independent' explanatory variables. The tables in this annex show how the odds ratios for each category in significant explanatory variables compares to the odds ratio for the reference category (always taken to be 1.00).

3. Taking Model 1 (below) as an example, the dependent variable is self-assessed health. If the respondent rated their own health as fair, bad or very bad, the dependent variable takes a value of 1. If they rated their health as good or very good, it takes a value of 0. An odds ratio of above 1 means that, compared with respondents in the reference category, respondents in that category have higher odds of saying their health is fair/bad/very bad. Conversely, an odds ratio of below 1 means they have lower odds of saying this than respondents in the reference category. The 95% confidence intervals for these odds ratios are also important. Where the confidence interval does not include 1, this category is significantly different from the reference category. If we look at age in Model 1, we can see that those aged 35-44 have an odds ratio of 2.32, indicating that they have higher odds of saying standards in the health service have fallen compared with 16-24 year-olds (who are the reference category). The 95% confidence interval for this age group (1.07-5.02) does not include 1, indicating this difference is significant.

4. The significance of each independent variable is indicated by 'P'. A p-value of 0.05 or less indicates that there is less than a 5% chance we would have found these differences between the categories just by chance if in fact no such difference exists, while a p-value of 0.01 or less indicates that there is a less than 1% chance. P-values of 0.05 or less are generally considered to indicate that the difference is highly statistically significant, while a p-value of 0.06 to 0.10 may be considered marginally significant. The models below show the odds ratios and 95% confidence intervals for those variables with P-values of less than or equal to 0.10 only; other variables are simply listed with their P-values.

5. The models below were produced using the Complex Survey command (CS Logistic) in PASW. Unlike forward stepwise models, CS Logistic models can account for complex sample designs (in particular, the effects of clustering and associated weighting) when calculating odds ratios and determining significance.

Model 1: Factors associated with rating own health as fair/bad/very bad rather than good/very good (SHeS 2009)

Nagelkerke R2 = 38.4%

Model 2: Factors associated with rating own health as fair/bad/very bad rather than good/very good (SSA 2009)

Nagelkerke R2 = 34.8%

Model 3: Factors associated with below average WEMWBS score (SHeS 2009)

Nagelkerke R2 = 25.1%