Small area estimation (SAE) plays a crucial role in the social sciences due to the growing need for reliable and accurate estimates for small domains. In the study of well-being, for example, policy makers need detailed information about the geographical distribution of a range of social indicators. We investigate data dimensionality reduction using factor analysis models and implement SAE on the factor scores under the empirical best linear unbiased prediction approach. We contrast this approach with the standard approach of providing a dashboard of indicators or a weighted average of indicators at the local level. We demonstrate the approach in a simulation study and a real data application based on the European Union Statistics for Income and Living Conditions for the municipalities of Tuscany.