Predict method for functional linear model

Computes predictions for regression between functional (and non functional) explanatory variables and scalar response.

predict.fregre.lm, Predict method for functional linear model of fregre.lm fits object using basis or principal component representation.
predict.fregre.plm, Predict method for semi-functional linear regression of fregre.plm fits object using using asymmetric kernel estimation.
predict.fregre.glm, Predict method for functional generalized linear model of fregre.glm fits object using basis or principal component representation.
predict.fregre.gsam, Predict method for functional generalized spectral additive model of fregre.gsam fits object using basis or principal component representation.
predict.fregre.gkam, Predict method for functional generalized kernel additive model of fregre.gkam fits object using backfitting algorithm.

These functions use the model fitting function lm, glm or gam properties.
If using functional data derived, is recommended to use a number of bases to represent beta lower than the number of bases used to represent the functional data.
The first item in the data list of newx argument is called "df" and is a data frame with the response and non functional explanatory variables, as lm, glm or gam. Functional variables (fdata and fd class) are introduced in the following items in the data list of newx argument.

Usage

# S3 method for class 'fregre.gkam'
predict(object, newx = NULL, type = "response", ...)

# S3 method for class 'fregre.glm'
predict(object, newx = NULL, type = "response", ...)

# S3 method for class 'fregre.gsam'
predict(object, newx = NULL, type = "response", ...)

# S3 method for class 'fregre.lm'
predict(
  object,
  newx = NULL,
  type = "response",
  se.fit = FALSE,
  scale = NULL,
  df = df,
  interval = "none",
  level = 0.95,
  weights = 1,
  pred.var = res.var/weights,
  ...
)

# S3 method for class 'fregre.plm'
predict(object, newx = NULL, ...)

Arguments

object: fregre.lm, fregre.plm, fregre.glm, fregre.gsam
or fregre.gkam object.
newx: An optional data list in which to look for variables with which to predict. If omitted, the fitted values are used. List of new explanatory data.
type: a character vector, Type of prediction: (response, terms for model terms or effects for model terms where the partial effects are summarized for each functional variable.
...: Further arguments passed to or from other methods.
se.fit: =TRUE (not default) standard error estimates are returned for each prediction.
scale: Scale parameter for std.err. calculation.
df: Degrees of freedom for scale.
interval: Type of interval calculation.
level: Tolerance/confidence level.
weights: variance weights for prediction. This can be a numeric vector or a one-sided model formula. In the latter case, it is interpreted as an expression evaluated in newdata
pred.var: the variance(s) for future observations to be assumed for prediction intervals. See link{predict.lm} for more details.

Value

Return the predicted values and optionally:

predict.lm,predict.glm,predict.gam: produces a vector of predictions or a matrix of predictions and bounds with column names fit, lwr, and upr if interval is set. If se.fit is TRUE, a list with the following components is returned: fit vector or matrix as above.
se.fit: standard error of predicted means.
residual.scale: residual standard deviations.
df: degrees of freedom for residual.

References

Febrero-Bande, M., Oviedo de la Fuente, M. (2012). Statistical Computing in Functional Data Analysis: The R Package fda.usc. Journal of Statistical Software, 51(4), 1-28. https://www.jstatsoft.org/v51/i04/

Author

Manuel Febrero-Bande, Manuel Oviedo de la Fuente manuel.oviedo@udc.es

Examples

if (FALSE) { # \dontrun{
data(tecator)
ind <- 1:129
x <- tecator$absorp.fdata
x.d2 <- fdata.deriv(x,nderiv=2)
tt <- x[["argvals"]]
dataf <- as.data.frame(tecator$y)
ldat <- ldata("df" = dataf[ind,], "x.d2" = x.d2[ind])
basis.x <- list("x.d2" = create.pc.basis(ldat$x.d2))
res <- fregre.gsam(Fat ~  s(x.d2,k=3),
                   data=ldat, family = gaussian(),
                   basis.x = basis.x)
newldat <- ldata("df" = dataf[-ind,], "x.d2" = x.d2[-ind])
pred <- predict(res, newldat)
plot(pred,tecator$y$Fat[-ind])
res.glm <- fregre.glm(Fat  ~  x.d2, data = ldat,
                  family = gaussian(),basis.x = basis.x)
pred.glm <- predict(res.glm, newldat)
newy <- tecator$y$Fat[-ind]
points(pred.glm,tecator$y$Fat[-ind],col=2)

# Time-consuming 
res.gkam <- fregre.gkam(Fat ~ x.d2, data = ldat)
pred.gkam <- predict(res.gkam, newldat)
points(pred.gkam,tecator$y$Fat[-ind],col = 4)

((1/length(newy)) * sum((drop(newy)-pred)^2)) / var(newy)
((1/length(newy)) * sum((newy-pred.glm)^2)) / var(newy)    
((1/length(newy)) * sum((newy-pred.gkam)^2)) / var(newy)    
} # }