Confounding and collinearity in regression analysis: a cautionary tale and an alternative procedure, illustrated by studies of British voting behaviour.

Many ecological- and individual-level analyses of voting behaviour use multiple regressions with a considerable number of independent variables but few discussions of their results pay any attention to the potential impact of inter-relationships among those independent variables-do they confound the regression parameters and hence their interpretation? Three empirical examples are deployed to address that question, with results which suggest considerable problems. Inter-relationships between variables, even if not approaching high collinearity, can have a substantial impact on regression model results and how they are interpreted in the light of prior expectations. Confounded relationships could be the norm and interpretations open to doubt, unless considerable care is applied in the analyses and an extended principal components method for doing that is introduced and exemplified.

Coming together in a rightward direction: post-1980s changing attitudes to the British welfare state.

Major changes in the British welfare state were initiated during the 1980s in response to the 1970s' stagflation, rapid globalisation and the government's inability to ensure full employment: the relatively unrestricted payment of unemployment benefits was replaced by a jobseekers' allowance with applicants obliged to seek work actively and, if required, undergo training. Public support for this shift lagged behind the policy introductions, but from 1997 on there was a major change in attitudes towards welfare beneficiaries. Analysis of social attitude survey data for 1983-2011 shows this change occurred during the decade of relative prosperity under the New Labour governments. There was a growing concentration of anti-welfare attitudes across all social groups, regions and supporters of the main political parties.

Ethnic Residential Segregation: A Multilevel, Multigroup, Multiscale Approach Exemplified by London in 2011.

We develop and apply a multilevel modeling approach that is simultaneously capable of assessing multigroup and multiscale segregation in the presence of substantial stochastic variation that accompanies ethnicity rates based on small absolute counts. Bayesian MCMC estimation of a log-normal Poisson model allows the calculation of the variance estimates of the degree of segregation in a single overall model, and credible intervals are obtained to provide a measure of uncertainty around those estimates. The procedure partitions the variance at different levels and implicitly models the dependency (or autocorrelation) at each spatial scale below the topmost one. Substantively, we apply the model to 2011 census data for London, one of the world's most ethnically diverse cities. We find that the degree of segregation depends both on scale and group.

London's changing ethnic landscape, 2001-2011: a cartographic exploration.

London population became increasing more diverse ethnically over the decade 2001-2011, a period when the White population declined, with many commentators suggesting that there has been 'White flight' from some districts in the face of 'invasion' by members of ethnic minority groups. To examine how extensively the city's ethnic landscape changed during that period--and whether suggestions of the operation of 'invasion and succession processes' are valid--this article reports on statistical mapping of small area data for the two censuses. The results identify clearly-defined, substantial blocks of territory within the urban residential fabric where members of each of the main census respondent self-identified ethnic groups are concentrated. These have expanded outwards, into areas from which the White population has clearly withdrawn, though in most cases the rate of cluster areal expansion has been less than the groups' numerical growth.

The performance of automated case-mix adjustment regression model building methods in a health outcome prediction setting.

We have previously described a system for monitoring a number of healthcare outcomes using case-mix adjustment models. It is desirable to automate the model fitting process in such a system if monitoring covers a large number of outcome measures or subgroup analyses. Our aim was to compare the performance of three different variable selection strategies: "manual", "automated" backward elimination and re-categorisation, and including all variables at once, irrespective of their apparent importance, with automated re-categorisation. Logistic regression models for predicting in-hospital mortality and emergency readmission within 28 days were fitted to an administrative database for 78 diagnosis groups and 126 procedures from 1996 to 2006 for National Health Services hospital trusts in England. The performance of models was assessed with Receiver Operating Characteristic (ROC) c statistics, (measuring discrimination) and Brier score (assessing the average of the predictive accuracy). Overall, discrimination was similar for diagnoses and procedures and consistently better for mortality than for emergency readmission. Brier scores were generally low overall (showing higher accuracy) and were lower for procedures than diagnoses, with a few exceptions for emergency readmission within 28 days. Among the three variable selection strategies, the automated procedure had similar performance to the manual method in almost all cases except low-risk groups with few outcome events. For the rapid generation of multiple case-mix models we suggest applying automated modelling to reduce the time required, in particular when examining different outcomes of large numbers of procedures and diseases in routinely collected administrative health data.

Trustful societies, trustful individuals, and health: An analysis of self-rated health and social trust using the World Value Survey.

This study analyses the relationships between self-rated health and both individual and mean national social trust, focusing on a variant of Wilkinson's hypothesis that individuals will be less healthy the greater the lack of social cohesion in a country. It employs multilevel modelling on World Values Survey data across 69 countries with a total sample of 160,436 individuals. The results show that self-rated health are positively linked to social trust at both country and individual levels after controlling for individual socio-demographic and income variables plus individual social trust; increased trust is associated with better health. Moreover, this analysis of social trust gives some insight into distinctive results for the former Soviet Bloc countries, which have high reported levels of poor health, alongside the Scandinavian countries which have high levels of trust and better health situations. Our results support and extend the Wilkinson hypothesis that the level of trust, an indicator of social cohesion, is predictive of individuals' health.

Global variations in health: evaluating Wilkinson's income inequality hypothesis using the World Values Survey.

This international comparative study analyses individual-level data derived from the World Values Survey to evaluate Wilkinson's [(1996). Unhealthy societies: The afflictions of inequality. London: Routledge; (1998). Mortality and distribution of income. Low relative income affects mortality [letter; comment]. British Medical Journal, 316, 1611-1612] income inequality hypothesis regarding variations in health status. Random-coefficient, multilevel modelling provides a direct test of Wilkinson's hypothesis using micro-data on individuals and macro-data on income inequalities analysed simultaneously. This overcomes the ecological fallacy that has troubled previous research into links between individual self-rated health, individual income, country income and income inequality data. Logic regression analysis reveals that there are substantial differences between countries in self-rated health after taking account of age and gender, and individual income has a clear effect in that poorer people report experiencing worse health. The Wilkinson hypothesis is not supported, however, since there is no significant relationship between health and income inequality when individual factors are taken into account. Substantial differences between countries remain even after taking account of micro- and macro-variables; in particular the former communist countries report high levels of poor health.

Compositional and contextual approaches to the study of health behaviour and outcomes: using multi-level modelling to evaluate Wilkinson's income inequality hypothesis.

Much research into health behaviour and outcomes involves evaluating compositional and contextual hypotheses: the former suggest that behaviour/outcomes are a function of the individual's characteristics alone, whereas the latter argue for the importance of contextual/environmental influences. Wilkinson has presented a contextual argument relating inter-country variations in mortality rates to income inequalities; Gravelle has countered this arguing that Wilkinson's findings are a statistical artefact and that a compositional approach, relating mortality to individual income, is sufficient. Discriminating between these two cases requires a methodology combining the two approaches. Multi-level modelling is proposed and applied to two data sets. The results sustain Gravelle's case, emphasising the role of compositional rather than contextual variables in accounting for inter-country variations in health status.

On referee bias, crowd size, and home advantage in the English soccer Premiership.

In a recent paper in this journal, Boyko and colleagues (2007) identified differences in attendance and referee bias as factors influencing home advantage at soccer matches in the English Premiership. A replication of their study using more recent data found no evidence to sustain either of their claims.

Local neighbourhood and mental health: evidence from the UK.

This paper examines the association between neighbourhood and levels and changes in common mental disorders. Using data from a large scale nationally representative survey of individuals and households (the British Household Panel Survey), it locates individuals in their local neighbourhoods. These are defined as the nearest 500-800 persons centered around each individual in the survey. These 'bespoke' neighbourhoods are characterised according to five dimensions--disadvantage, mobility, age, ethnicity and urbanness--derived from factor analysis of the census characteristics of the residents of neighbourhoods in 1991. These dimensions measure characteristics of place that have been argued to be associated with mental ill health. The paper estimates multilevel models of the level and 5-year changes of common mental disorders (measured by the twelve item version of the General Health Questionnaire). Three and two level models are estimated, all of which allow for individual and household characteristics that may act as confounders of any neighbourhood effect. The results show the extent of association between neighbourhood and both levels and changes in mental health is limited. Less than one percent of the variance across individuals is at the neighbourhood level. The neighbourhood characteristics are not generally statistically associated with levels or changes in mental ill health. There is some evidence of interaction between neighbourhood characteristics and gender and ethnicity, but while statistically significant these interactions are small in size compared to the main effects of individual and household characteristics. What appears to be important for levels of common mental disorders are the observed characteristics of individuals and their households, not of place.