When Specification Constructs the Object: Empirical Identification of Crime Generators and Crime Attractors

Methodological refinements are generally assumed to improve empirical measurement while preserving the theoretical object to which inference refers. We examine whether this assumption holds for the empirical identification of crime generators and crime attractors. Using convenience stores in Mexico City as a case study, we reproduce the sequence of specification refinements proposed in recent environmental criminology research and compare the resulting classifications across specifications, rather than evaluating which specification performs best. Successive specifications produce systematically different classifications of the same establishments: across the refinement sequence, the sets of establishments identified as high-order attractors are largely non-overlapping, and this divergence arises before any statistical model is estimated. Changes in classification therefore reflect more than statistical sensitivity or improved measurement; they arise because different specifications construct analytically different empirical objects. Before specification affects statistical estimation, it determines the empirical object to which inference refers. Although demonstrated through crime generator and crime attractor classifications, the implication extends to place-based criminology more broadly: the accumulation of empirical knowledge depends not only on improved estimation but on the comparability of the empirical objects being analyzed.