Calculates the functional R-squared for a fitted FDboost-object
funRsquared(object, overTime = TRUE, breaks = object$yind, global = FALSE, ...)Returns a vector with the calculated R-squared and some extra information in attributes.
fitted FDboost-object
per default the functional R-squared is calculated over time
if overTime=FALSE, the R-squared is calculated per curve
an optional vector or number giving the time-points at which the model is evaluated. Can be specified as number of equidistant time-points or as vector of time-points. Defaults to the index of the response in the model.
logical. defaults to FALSE,
if TRUE the global R-squared like in a normal linear model is calculated
currently not used
breaks should be set to some grid, if there are many
missing values or time-points with very few observations in the dataset.
Otherwise at these points of t the variance will be almost 0
(or even 0 if there is only one observation at a time-point),
and then the prediction by the local means \(\mu(t)\) is locally very good.
The observations are interpolated linearly if necessary.
Formula to calculate R-squared over time, overTime=TRUE:
\(R^2(t) = 1 - \sum_{i}( Y_i(t) - \hat{Y}_i(t))^2 / \sum_{i}( Y_i(t) - \bar{Y}(t) )^2 \)
Formula to calculate R-squared over subjects, overTime=FALSE:
\(R^2_i = 1 - \int (Y_i(t) - \hat{Y}_i(t))^2 dt / \int (Y_i(t) - \bar{Y}_i )^2 dt \)
Ramsay, J., Silverman, B. (2006). Functional data analysis. Wiley Online Library. chapter 16.3