  Near- to mid-infrared period-magnitude relations and also the
period-bolometric luminosity relation of OGLE-III Mira-like variables in the
LMC are derived. The relations have a kink, and the period at which the break
occurs is quantitatively obtained. There are many Mira-like variables whose
fluxes at the optical and the near-infrared wavebands are fainter than the ones
predicted by the period-magnitude relations. The deviation is due to the
circumstellar extinction, and the amount of the deviation is found to be
strongly correlated with near-infrared colors. The empirical formulae relating
the amount of the deviation and the near-infrared colors are derived. These
relations are useful to accurately calculate the distances to the dusty
Mira-like variables, because the dimmed fluxes due to the circumstellar
extinction can be estimated. In a manner analogous to the interstellar
extinction law, the ratios of deviations at any two different wavebands are
calculated. The ratios are found to change with the pulsation period,
indicating that the dust properties are subject to change as Mira-like
variables evolve.
