Goodness of fit of a cosinor from data that has multiple collections at different timepoints or from multiple cycles. The RSS is partitioned into pure error (SSPE) and lack of fit (SSLOF). An F-test compares the SSPE and SSLOF to detect appropriateness of model.
$$SSLOF = RSS - SSPE$$
$$SSPE = \sum_{i} \sum_{l} ( Y_{il} - \overline{Y}_{i} )^2$$
The fitted values for each time point are: $$\overline{Y}_{i} = \frac{ \sum_{l} Y_{il} }{ n_{i}}$$
cosinor_goodness_of_fit(object, level = 0.95, ...)requires cosinor model generated with card::cosinor to calculate statistics.
confidence level desired
additional parameters may be needed for extensibility
f-statistic as result of goodness of fit