Fitting a semi-parametric model based on two sources of information

This paper discusses fitting a semi-parametric model based on two sources of information, motivated by a rat sleep dataset. In a recent study, rats were exposed to two different lighting conditions. The first (baseline) condition was a standard 24-hour schedule of 12 hours lights on, 12 hours lights off; the second (test) condition exposed rats to a continuous 3 hours lights on, 3 hours lights off schedule. Rat sleep was believed to be affected mainly by the circadian rhythm under the baseline lighting condition and by both the circadian rhythm and light under the test lighting condition. This paper suggests fitting a non-parametric model for the dataset under the baseline lighting condition. For the dataset under the test lighting condition, a two-part model is suggested. The first part equals an unknown coefficient multiplied by the non-parametric function used for modelling the dataset under the baseline lighting condition, explaining the remnant of the circadian rhythm under the test lighting condition. The second part is a periodic non-parametric function which would explain the effect of the test lighting condition. This modelling procedure can be used to model other physiological parameters affected by both intrinsic and extrinsic factors.