Are Higher qpAdm P-Values Better?

Yes. For two qpAdm models with the same target, the same right groups, and the same settings, the model with the higher p-value is the better statistical fit.

qpAdm calculates a covariance-weighted discrepancy between the observed and model-fitted f4-statistics. The p-value indicates how unusual that discrepancy is under the model. A higher p-value means the discrepancy is less unusual and therefore indicates a better statistical fit.

This does not mean that the model with the highest p-value for a target is automatically the best one, because qpAdm results depend on the selected right groups. Uninformative right-groups can lack the power to detect a bad model, while poorly chosen or overly restrictive ones might make a plausible model appear to fit badly. Hence, comparisons of p-values are most meaningful when models for the same target are compared using the same right groups and settings. Models with different numbers of sources are also comparable because p-values account for different degrees of freedom. Z-scores can be used to assess whether an additional source is justified.

Everything mentioned here assumes that the models are feasible, and have weights that are large relative to their standard errors (have Z-scores above 3 ideally).