The detailed forms of the LMC Cepheid PL and PLC relations
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Possible deviations from linearity of the Large Magellanic Cloud Cepheid period–luminosity (PL) and period–luminosity–colour (PLC) relations are investigated. Two data sets are studied, respectively from the Optical Gravitational Lensing Experiment (OGLE) and MACHO projects. A non-parametric test, based on linear regression residuals, suggests that neither PL relation is linear. If colour dependence is allowed for, then the MACHO PL relation is found to deviate more significantly from the linear, while the OGLE PL relation is consistent with linearity. These findings are confirmed by fitting ‘Generalized Additive Models’ (non-parametric regression functions) to the two data sets. Colour dependence is shown to be non-linear in both data sets, distinctly so in the case of the MACHO Cepheids. It is also shown that there is interaction between the period and the colour functions in the MACHO data.