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Measurements of (anti)proton, (anti)deuteron, and (anti)3He production in the rapidity range −1<y<0 as a function of the transverse momentum and event multiplicity in p-Pb collisions at a center-of-mass energy per nucleon-nucleon pair sNN−−−√=8.16 TeV are presented. The coalescence parameters B2 and B3, measured as a function of the transverse momentum per nucleon and of the mean charged-particle multiplicity density, confirm a smooth evolution from low to high multiplicity across different collision systems and energies. The ratios between (anti)deuteron and (anti)3He yields and those of (anti)protons are also reported as a function of the mean charged-particle multiplicity density. A comparison with the predictions of the statistical hadronization and coalescence models for different collision systems and center-of-mass energies favors the coalescence description for the deuteron-to-proton yield ratio with respect to the canonical statistical model.