Approach to analysing correlated contextual factors: An application for studies on violence

Background Numerous public health studies, especially in the area of violence, examine the effects of contextual or group-level factors on health outcomes. Often, these contextual factors exhibit strong pairwise correlations, which pose a challenge when these factors are included as covariates in a statistical model. Such models may be characterised by inflated standard errors and unstable parameter estimates that may fluctuate drastically from sample to sample, where the excessive estimation variability is reflected by inflated standard errors. Methods We propose a three-stage approach for analysing correlated contextual factors that proceeds as follows: (1) a principal components analysis (PCA) is performed on the original set of correlated variables, (2) the primary generated principal components are included in a multilevel multivariable model and (3) the estimated parameters for these components are transformed into estimates for each of the original contextual factors. Using school violence data, we examined the associations between school crime and correlated contextual school factors (ie, English proficiency, academic performance, pupil to teacher ratio, average class size and children on free and reduced meals). Results From models ignoring correlations, school crime was not reliably associated with any of the contextual school factors. When models were fit with principal components, school crime was found to be positively associated with a school's student to teacher ratio, average classroom size and academic performance but negatively associated with the proportion of children who were on free and reduced meals. Conclusion Our multistep approach is one way to address multicollinearity encountered in social epidemiological studies of violence.