Setting Cost in Optimal Matching to Uncover Contemporaneous Socio-Temporal Patterns

Abstract

This article addresses the question of the effects of cost setting on the kind of temporal patterns optimal matching (OM) can uncover when applied to social science data. It is argued that the balance between indel (insertion and deletion) and substitution costs determines what kind of socio-temporal pattern can be brought to light. Insertion and deletion operations favor identically coded states irrespective of their locations whereas substitutions focus on contemporaneous similarities. The lower the ratio of substitution to indel costs, the closer OM is to the Hamming distance where only substitutions are used. The higher this ratio, the closer OM is to the Levenshtein II distance, which amounts to finding the longest common subsequence. When the timing of sequences is crucial, substitutions should be favored over indels and their costs should be carefully fixed. Ideally, substitution costs should vary with time to better take into account the timing of the sequences studied. As indels warp time, hence the timing of sequences, it is suggested to use only substitution operations with time-dependent costs inversely proportional to transition frequencies whenever the timing of sequences is central. This OM variant, coined dynamic Hamming matching, is applied to the question of the scheduling of paid work where timing is critical (1985 and 1999 French time use surveys, N = 7,908) along with three classical OM variants (Hamming and Levenshtein I and II). As expected, the two Hamming dissimilarity measures fare better to identify patterns of workday schedules, as measured by entropy, than the two Levenshtein ones.