Longitudinal Nomological Validity

They overlap but are not the same. Predictive validity asks whether scale scores at time 1 predict a specific outcome at time 2. Nomological validity is broader: it requires that the entire set of theoretically expected relationships — concurrent, predictive, and discriminant — hold across the nomological network and across waves. Predictive validity is one component of nomological validity, not a substitute for it.

Yes, at minimum metric invariance (equal factor loadings across waves) is required. Without it, latent variable scores at different waves are not on the same scale, so cross-lagged relationships among latent variables cannot be meaningfully interpreted as reflecting true construct dynamics rather than measurement artifacts.

The choice depends on theory. The traditional cross-lagged panel model estimates directional effects and autoregressive stability. The random-intercept cross-lagged panel model (RI-CLPM) separates stable between-person differences from within-person fluctuations, which is often theoretically more appropriate when you expect trait-level stability alongside occasion-specific change. Latent change score models are preferred when the theory concerns growth or change trajectories.

Two waves are the minimum, but they allow only limited evaluation of the nomological network (one cross-lagged estimate per pair of constructs). Three or more waves permit tests of whether relationships are consistent over multiple intervals, whether autoregressive stability is constant, and whether growth trajectories conform to predictions — all of which yield stronger validity evidence.

There is no universal threshold. Support is cumulative: theoretically predicted cross-lagged directions should be correct, approximate magnitudes should be consistent with prior theory or literature, discriminant constructs should remain separable at each wave, and the overall pattern should replicate across independent samples or wave intervals where feasible.