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.
