msir.bic {msir}

BIC-type criterion for dimensionality

Description

BIC-type criterion for selecting the dimensionality of a dimension reduction subspace.

Usage

msir.bic(object, type = 1, plot = FALSE)

bicDimRed(M, x, nslices, type = 1, tol = sqrt(.Machine$double.eps))

Arguments

object

a 'msir' object

plot

if TRUE a plot of the criterion is shown.

M

the kernel matrix. See details below.

x

the predictors data matrix. See details below.

type

See details below.

nslices

the number of slices. See details below.

tol

a tolerance value

Details

This BIC-type criterion for the determination of the structural dimension selects d as the maximizer of

G(d) = l(d) - Penalty(p,d,n)

where l(d) is the log-likelihood for dimensions up to d, p is the number of predictors, and n is the sample size. The term Penalty(p,d,n) is the type of penalty to be used:

• type = 1: Penalty(p,d,n) = -(p-d) \log(n)

• type = 2: Penalty(p,d,n) = 0.5 C d (2p-d+1), where C = (0.5 \log(n) + 0.1 n^(1/3))/2 nslices/n

• type = 3: Penalty(p,d,n) = 0.5 C d (2p-d+1), where C = \log(n) nslices/n

• type = 4 Penalty(p,d,n) = 1/2 d \log(n)

Value

Returns a list with components:

evalues

eigenvalues

l

log-likelihood

crit

BIC-type criterion

d

selected dimensionality

The msir.bic also assign the above information to the corresponding 'msir' object.

Author(s)

Luca Scrucca [e-mail]

References

Zhu, Miao and Peng (2006) "Sliced Inverse Regression for CDR Space Estimation", JASA.
Zhu, Zhu (2007) "On kernel method for SAVE", Journal of Multivariate Analysis.

See Also

msir

Examples

# 1-dimensional symmetric response curve
n <- 200
p <- 5
b <- as.matrix(c(1,-1,rep(0,p-2)))
x <- matrix(rnorm(n*p), nrow = n, ncol = p)
y <- (0.5 * x%*%b)^2 + 0.1*rnorm(n)
MSIR <- msir(x, y)
msir.bic(MSIR, plot = TRUE)
summary(MSIR)
msir.bic(MSIR, type = 3, plot = TRUE)
summary(MSIR)