The mixture problem in flake analysis: Allocating flake samples to segments of reduction using CLSR methods

Flake assemblages often are mixtures from knapping episodes that vary by reduction mode or stage. Stahle and Dunn (1982) developed a constrained least-squares regression (CLSR) method to allocate hypothetically mixed chert assemblages to successive biface-reduction stages, a partial solution to the mixing problem. ConReg is a recently developed alternative, validated against Stahle and Dunn’s and our own experimental controls from replication of obsidian biface preforms. Using both controls, we apply ConReg to the “unmixing” of flake assemblages from North American Great Basin obsidian quarries. Controls produce different solutions; their separate comparison to independent analytical results of stage composition favor ConReg used with our controls. What appeared to be relatively similar early “stage” assemblages are resolved to finer proportional allocation across wider ranges of the reduction continuum, in the process showing considerable variation between samples that otherwise might escape detection. The mixture problem is a challenge to all approaches to flake analysis, not just mass analysis, but one that ConReg can help us surmount.