This study develops a model-based index creation approach called the Generalized Shared Component Model (GSCM) by drawing on the large field of factor models. The proposed fully Bayesian approach accommodates heteroscedastic model error, multiple shared factors and flexible spatial priors. Moreover, our model, unlike previous index approaches, provides indices with uncertainty. Focusing on Australian risk factor data, the proposed GSCM is used to develop the Area Indices of Behaviors Impacting Cancer product - representing the first area level cancer risk factor index in Australia. This advancement aids in identifying communities with elevated cancer risk, facilitating targeted health interventions.

翻译：本研究借鉴因子模型领域的丰富成果，提出一种基于模型的指数构建方法——广义共享成分模型（GSCM）。该全贝叶斯方法能够处理异方差模型误差、多个共享因子以及灵活的空间先验分布。与以往的指数方法不同，我们的模型提供的指数包含不确定性估计。以澳大利亚风险因素数据为研究对象，运用所提出的GSCM方法开发了"行为影响癌症区域指数"产品——这是澳大利亚首个区域层面的癌症风险因素指数。这一进展有助于识别癌症风险较高的社区，从而促进针对性健康干预措施的实施。