We derive the near- to mid-infrared period-magnitude relations and the period-bolometric luminosity relation of OGLE-III Mira-like variables in the Large Magellanic Cloud. 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 near-infrared wavebands are fainter than those predicted by the period-magnitude relations. The deviation is a result of the circumstellar extinction, and the amount of deviation is found to be strongly correlated with near-infrared colours. We derive the empirical formulae relating the amount of deviation and the near-infrared colours. These relations are useful to accurately calculate the distances to the dusty Mira-like variables, because the dimmed fluxes resulting from 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.
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