We study missing-link inference in partially observed networks by systematically comparing dyadic link prediction (LP) with hyperlink prediction (HP) and an estimation-based ERGM comparator. LP serves as the primary baseline, using classical heuristics computed on the observed graph. HP extends this framework by scoring candidate higher-order structures (cliques) via lifted dyadic scores and via the CHEbyshev Spectral HyperlInk pREdictor (CHESHIRE). All methods are evaluated under a common masking protocol that removes dyadic evidence induced by held-out hyperlinks to ensure comparability. Across public email and covert-network datasets, LP remains strong for dyadic recovery, while HP -- particularly CHESHIRE -- provides gains when the inferential target is higher-order group structure. ERGMs offer an interpretable dependence-based complement through conditional tie probabilities. The contribution is a comparative, reproducible evaluation clarifying when LP, HP, and ERGM estimation are most appropriate under network missingness.