A bayesian shared component spatial modeling approach for identifying the geographic pattern of local associations: a case study of young offenders and violent crimes in Greater Toronto Area.

Background setting: Traditional spatial or non-spatial regression techniques require individual variables to be defined as dependent and independent variables, often assuming a unidirectional and (global) linear relationship between the variables under study. This research studies the Bayesian shared component spatial (BSCS) modeling as an alternative approach to identifying local associations between two or more variables and their spatial patterns. Methods: The variables to be studied, young offenders (YO) and violent crimes (VC), are treated as (multiple) outcomes in the BSCS model. Separate non-BSCS models that treat YO as the outcome variable and VC as the independent variable have also been developed. Results are compared in terms of model fit, risk estimates, and identification of hotspot areas. Results: Compared to the traditional non-BSCS models, the BSCS models fitted the data better and identified a strong spatial association between YO and VC. Using the BSCS technique allowed both the YO and VC to be modeled as outcome variables, assuming common data-generating processes that are influenced by a set of socioeconomic covariates. The BSCS technique offered smooth and easy mapping of the identified association, with the maps displaying the common (shared) and separate (individual) hotspots of YO and VC. Conclusions: The proposed method can transform existing association analyses from methods requiring inputs as dependent and independent variables to outcome variables only and shift the reliance on regression coefficients to probability risk maps for characterizing (local) associations between the outcomes. Supplementary Information: The online version contains supplementary material available at 10.1186/s40163-024-00235-5.