MRFA (version 0.6)

confidence.MRFA: Confidence Interval for Multiresolution Functional ANOVA (MRFA) Model

Description

The function computes the confidence intervals of predicted responses (only works for linear regression model).

Usage

confidence.MRFA(
  object,
  xnew,
  X,
  lambda = object$lambda,
  conf.level = 0.95,
  var.estimation = c("rss", "cv", "posthoc")[1],
  w.estimation = c("cv", "nugget")[1],
  K = 5,
  nugget = 1e-06,
  parallel = FALSE,
  verbose = FALSE
)

Value

lower bound

a vector with length n_new displaying lower bound of predicted responses at locations xnew.

upper bound

a vector with length n_new displaying upper bound of predicted responses at locations xnew.

conf.level

as above.

Arguments

object

a class MRFA object estimated by MRFA_fit.

xnew

a testing matrix with dimension n_new by d in which each row corresponds to a predictive location.

X

input for MRFA_fit.

lambda

a value. The default is min(object$lambda).

conf.level

a value specifying confidence level of the confidence interval. The default is 0.95.

var.estimation

a character string specifying the estimation method for variance. "rss" specifies residual sum of squares, "cv" specifies a cross-validation method with K fold, and "posthoc" specifies a post-hoc estimation method. The default is "rss".

w.estimation

a character string specifying the estimation method for weights w. "cv" specifies a cross-validation method with K fold, and "nugget" specifies a least square error method with nugget=nugget. The default is "cv".

K

a positive integer specifying the number of folds.

nugget

a value specifying the nugget value for w.estimation. The default is 1e-6. It only works when w.estimation="nugget".

parallel

logical. If TRUE, apply function in parallel using parallel backend provided by foreach.

verbose

logical. If TRUE, additional diagnostics are printed.

Author

Chih-Li Sung <[e-mail]>

Details

When The details about var.estimation and w.estimation can be seen in Sung et al. (2017+).

See Also

MRFA_fit for fitting of a multi-resolution functional ANOVA model; predict.MRFA for prediction of a multi-resolution functional ANOVA model.

Examples

if (FALSE) {

#####             Testing function: OTL circuit function                      #####
#####   Thanks to Sonja Surjanovic and Derek Bingham, Simon Fraser University #####
otlcircuit <- function(xx)
{
  Rb1  <- 50   + xx[1] * 100
  Rb2  <- 25   + xx[2] * 45
  Rf   <- 0.5  + xx[3] * 2.5
  Rc1  <- 1.2  + xx[4] * 1.3
  Rc2  <- 0.25 + xx[5] * 0.95
  beta <- 50   + xx[6] * 250

  Vb1 <- 12*Rb2 / (Rb1+Rb2)
  term1a <- (Vb1+0.74) * beta * (Rc2+9)
  term1b <- beta*(Rc2+9) + Rf
  term1 <- term1a / term1b

  term2a <- 11.35 * Rf
  term2b <- beta*(Rc2+9) + Rf
  term2 <- term2a / term2b

  term3a <- 0.74 * Rf * beta * (Rc2+9)
  term3b <- (beta*(Rc2+9)+Rf) * Rc1
  term3 <- term3a / term3b

  Vm <- term1 + term2 + term3
  return(Vm)
}



library(MRFA)
#####   training data and testing data   #############
set.seed(2)
n <- 100; n_new <- 10; d <- 6
X.train <- matrix(runif(d*n), ncol = d)
Y.train <- apply(X.train, 1, otlcircuit)
X.test <- matrix(runif(d*n_new), ncol = d)
Y.test <- apply(X.test, 1, otlcircuit)

#####   Fitting    #####
MRFA_model <- MRFA_fit(X.train, Y.train)

#####   Prediction   ######
Y.pred <- predict(MRFA_model, X.test, lambda = min(MRFA_model$lambda))$y_hat
print(sqrt(mean((Y.test - Y.pred)^2)))

### confidence interval ###
conf.interval <- confidence.MRFA(MRFA_model, X.test, X.train, lambda = min(MRFA_model$lambda))
print(conf.interval)
}