  In this article, we test the hypothesis that Cepheids have infrared excesses
due to mass loss. We fit a model using the mass-loss rate and the stellar
radius as free parameters to optical observations from the OGLE-III survey and
infrared observations from the 2MASS and SAGE data sets. The sample of Cepheids
have predicted minimum mass-loss rates ranging from zero to $10^{-8}M_\odot$
$yr^{-1}$, where the rates depend on the chosen dust properties. We use the
predicted radii to compute the Period-Radius relation for LMC Cepheids, and to
estimate the uncertainty caused by the presence of infrared excess for
determining angular diameters with the infrared surface brightness technique.
Finally, we calculate the linear and non-linear Period-Luminosity (P-L)
relations for the LMC Cepheids at VIJHK + IRAC wavelengths and we find that the
P-L relations are consistent with being non-linear at infrared wavelengths,
contrary to previous results.
