FDboost (version 1.0-0)

# funMSE: Functional MSE

## Description

Calculates the functional MSE for a fitted FDboost-object

## Usage

funMSE(
object,
overTime = TRUE,
breaks = object\$yind,
global = FALSE,
relative = FALSE,
root = 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

relative

logical. defaults to FALSE. If TRUE the MSE is standardized by the global variance of the response $$n^{-1} \int \sum_i (Y_i(t) - \bar{Y})^2 dt \approx G^{-1} n^{-1} \sum_g \sum_i (Y_i(t_g) - \bar{Y})^2$$

root

take the square root of the MSE

...

currently not used

## Value

Returns a vector with the calculated MSE and some extra information in attributes.

## Details

Formula to calculate MSE over time, overTime=TRUE: $$MSE(t) = n^{-1} \sum_i (Y_i(t) - \hat{Y}_i(t))^2$$

Formula to calculate MSE over subjects, overTime=FALSE: $$MSE_i = \int (Y_i(t) - \hat{Y}_i(t))^2 dt \approx G^{-1} \sum_g (Y_i(t_g) - \hat{Y}_i(t_g))^2$$