This paper examines the impacts on suicide and self harm rates of latent area constructs (deprivation, fragmentation and rurality), obtained via multivariate analysis of a larger set of census and non-census indicators. A case study involves male and female suicides and self-harm hospitalisations in 3242 small areas (known as wards) in East and South East England, including London. A Poisson regression model is applied to these data allowing for nonlinear effects of constructs and for interaction between them, as well as for Poisson extra-heterogeneity. In particular, the gain in model fit from predicting suicide and self-harm risk using the three constructs is assessed in terms of how far they account for spatially structured variation and for unstructured heterogeneity. Evidence for nonlinear effects and interaction between constructs is obtained, and implications for health resource allocation by regression evaluated.