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JessLGraves authored Feb 28, 2025
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__Sigmoidally transformed extended cosine models__

<img src="https://github.com/JessLGraves/RAR/blob/master/param_ex1.png" width="400">
<img src="https://github.com/JessLGraves/RAR/blob/master/images/param_ex1.png" width="400">
<sub> <b> Figure 1. </b> 60-second epoch RAR data with fitted antilogistic cosine model (red). Top right: residuals estimated from the fitted anti-logistic model. </sub>
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See <a href = "https://onlinelibrary.wiley.com/doi/epdf/10.1002/sim.2466">Marler et al. 2006</a> for a summary of the model structure and parameters estimated from the models.

__Residual Circadian Spectrum Analysis__

<img src="https://github.com/JessLGraves/RAR/blob/master/RAR_Spectrum_bands.png" width="500">
<img src="https://github.com/JessLGraves/RAR/blob/master/images/RAR_Spectrum_bands.png" width="500">
<sub> <b> Figure 2. </b> Top left: 60-second epoch RAR data with fitted antilogistic cosine model (red). Top right: residuals estimated from the fitted anti-logistic model. Bottom left: estimated log power spectrum of the residuals from the top right panel with a smoothing cubic spline (blue). Bottom right: example of frequency band selection (a, b) to estimate frequency band score.</sub><br>
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Spectral analysis is performed on the residuals of derived from the anti-logistic extended cosine model. From there, a user-specified band (a, c) for which the area under the smoothed spectrum is estimated.
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__Localized Measures__

<img src="https://github.com/JessLGraves/RAR/blob/master/graves_sensors_figure.png" width="500">
<img src="https://github.com/JessLGraves/RAR/blob/master/images/graves_sensors_figure.png" width="500">
<sub> <b> Figure 3. </b> Example of mean and SD of activity estiamted using RAR_Local function. Mean and standard deviation of daily log activity counts stratified by the Pittsburgh Fatigability Scale (PFS) at 4-h time bin intervals. Solid line represents greater perceived physical fatigability (PFS ≥ 15); dotted line represents lesser perceived physical fatigability (PFS < 15). <i>Taken from <a href = "https://www.mdpi.com/1424-8220/21/5/1718">Graves et al. 2021, Sensors</a></i> </sub>

## Basics of using RAR
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