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Measuring Divergence and Convergence in Sequence Analysis: A Spell-Based Extension of Longest Common Prefixes

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  • Liang, Yuqi
  • Meyerhoff-Liang, Jan

Abstract

Measuring sequence dissimilarity is central to sequence analysis, yet empirical applications remain dominated by optimal matching (OM), a widely used but contested approach. Longest common prefix (LCP) measures offer an alternative by capturing shared beginnings and endings, making them useful for studying divergence and convergence, important concepts in social science. However, existing LCP variants are position-wise: small shifts in transition timing can break the common prefix between trajectories that share the same spell sequence, making them appear to diverge early. This study develops a spell-based perspective on understanding sequence comparison. We introduce OMspellUnitFree (a modified spell-based OM) and propose LCPspell, a spell-based extension of LCP. Using simulations and an empirical demonstration, we show that whole-trajectory measures such as OM family capture broad trajectory profiles, whereas LCP-type measures identify where similarity breaks down or reappears. The paper provides practical guidance for choosing distance measures according to research questions and data characteristics.

Suggested Citation

  • Liang, Yuqi & Meyerhoff-Liang, Jan, 2026. "Measuring Divergence and Convergence in Sequence Analysis: A Spell-Based Extension of Longest Common Prefixes," SocArXiv 3pyhr_v1, Center for Open Science.
    • Handle: RePEc:osf:socarx:3pyhr_v1
    DOI: 10.31219/osf.io/3pyhr_v1
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