Although inequalities in health and socioeconomic status have an important influence on childhood educational performance, the interactions between these multiple factors relating to variation in educational outcomes at micro-level is unknown, and how to evaluate the many possible interactions of these factors is not well established. This paper aims to examine multi-dimensional deprivation factors and their impact on childhood educational outcomes at micro-level, focusing on geographic areas having widely different disparity patterns, in which each area is characterised by six deprivation domains (Income, Health, Geographical Access to Services, Housing, Physical Environment, and Community Safety). Traditional health statistical studies tend to use one global model to describe the whole population for macro-analysis. In this paper, we combine linked educational and deprivation data across small areas (median population of 1500), then use a local modelling technique, the Takagi-Sugeno fuzzy system, to predict area educational outcomes at ages 7 and 11. We define two new metrics, "Micro-impact of Domain" and "Contribution of Domain", to quantify the variations of local impacts of multidimensional factors on educational outcomes across small areas. The two metrics highlight differing priorities. Our study reveals complex multi-way interactions between the deprivation domains, which could not be provided by traditional health statistical methods based on single global model. We demonstrate that although Income has an expected central role, all domains contribute, and in some areas Health, Environment, Access to Services, Housing and Community Safety each could be the dominant factor. Thus the relative importance of health and socioeconomic factors varies considerably for different areas, depending on the levels of each of the other factors, and therefore each component of deprivation must be considered as part of a wider system. Childhood educational achievement could benefit from policies and intervention strategies that are tailored to the local geographic areas' profiles.