FDboost (version 1.0-0)

# funRsquared: Functional R-squared

## Description

Calculates the functional R-squared for a fitted FDboost-object

## Usage

funRsquared(object, overTime = TRUE, breaks = object\$yind, global = FALSE, ...)

## Arguments

object

fitted FDboost-object

overTime

per default the functional R-squared is calculated over time if overTime=FALSE, the R-squared is calculated per curve

breaks

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.

global

logical. defaults to FALSE, if TRUE the global R-squared like in a normal linear model is calculated

...

currently not used

## Value

Returns a vector with the calculated R-squared and some extra information in attributes.

## Details

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: $$R^2_i = 1 - \int (Y_i(t) - \hat{Y}_i(t))^2 dt / \int (Y_i(t) - \bar{Y}_i )^2 dt$$

## References

Ramsay, J., Silverman, B. (2006). Functional data analysis. Wiley Online Library. chapter 16.3