We perform a detailed analysis of Cepheids in NGC 4258, Magellanic Clouds and Milky Way in order to verify the reliability of the theoretical scenario based on a large set of nonlinear convective pulsation models. We derive Wesenheit functions from t
he synthetic BVI magnitudes of the pulsators and we show that the sign and the extent of the metallicity effect on the predicted Period-Wesenheit (P-W) relations change according to the adopted passbands. These P-W relations are applied to measured BVI magnitudes of NGC 4258, Magellanic and Galactic Cepheids available in the literature. We find that Magellanic and Galactic Cepheids agree with the metallicity dependence of the predicted P-W relations. Concerning the NGC 4258 Cepheids, the results strongly depend on the adopted metallicity gradient across the galactic disc. The most recent nebular oxygen abundances support a shallower gradient and provide a metallicity dependence that agrees well with current pulsation predictions. Moreover, the comparison of Cepheid distances based on VI magnitudes with distance estimates based on the revised TRGB method for external galaxies, on the HST trigonometric parallaxes for Galactic Cepheids, and on eclipsing binaries in the Magellanic Clouds seems to favor the metallicity correction predicted by pulsation models. The sign and the extent of the metallicity dependence of the Period-Wesenheit and of the Period-Luminosity relations change according to the adopted passbands. Therefore, distances based on different methods and/or bands should not be averaged. The use of extragalactic Cepheids to constrain the metallicity effect requires new accurate and extensive nebular oxygen measurements.
