We present new near-infrared Cepheid Period-Wesenheit relations in the LMC using time-series observations from the Large Magellanic Cloud Near-Infrared Synoptic Survey .
We also derive optical + near-infrared P-W relations using V and I magnitudes from OGLE-III .
We employ our new JHK _ { s } data to determine an independent distance to the LMC of \mu _ { LMC } = 18.47 \pm 0.07 { \textit { ( statistical ) } } mag , using an absolute calibration of the Galactic relations based on several distance determination methods and accounting for the intrinsic scatter of each technique .
We also derive new near-infrared Period-Luminosity and Wesenheit relations for Cepheids in M31 using observations from the PHAT survey .
We use the absolute calibrations of the Galactic and LMC W _ { J,H } relations to determine the distance modulus of M31 , \mu _ { M 31 } = 24.46 \pm 0.20 mag .
We apply a simultaneous fit to Cepheids in several Local Group galaxies covering a range of metallicities ( 7.7 < 12 + \log [ O / H ] < 8.6 dex ) to determine a global slope of - 3.244 \pm 0.016 mag/dex for the W _ { J,K _ { s } } relation and obtain robust distance estimates .
Our distances are in good agreement with recent TRGB based distance estimates and we do not find any evidence for a metallicity dependence in the near-infrared P-W relations .