funMSE() R function from [FDboost]

Functional MSE

Calculates the functional MSE for a fitted FDboost-object


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

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

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

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:

$MSE_i = \int (Y_i(t) - \hat{Y}_i(t))^2 dt \approx G^{-1} \sum_g (Y_i(t_g) - \hat{Y}_i(t_g))^2$

breaks cannot be changed in the case the bsignal()

is used over the same domain as the response! In that case you would have to rename the index of the response or that of the covariates.

Useful links