confidence.MRFA {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
)

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.

Details

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

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.

Author(s)

Chih-Li Sung <[e-mail]>

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

## Not run: 

#####             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)

## End(Not run)