msir: Model-based Sliced Inverse Regression (MSIR)

Description

A dimension reduction method based on Gaussian finite mixture models which provides an extension to sliced inverse regression (SIR). The basis of the subspace is estimated by modeling the inverse distribution within slice using Gaussian finite mixtures with number of components and covariance matrix parameterization selected by BIC or defined by the user.

Usage

msir(x, y, nslices = msir.nslices, slice.function = msir.slices, 
     modelNames = NULL, G = NULL, cov = c("mle", "regularized"), …)

Arguments

A \((n \times p)\) design matrix containing the predictors data values.

A \((n \times 1)\) vector of data values for the response variable. It can be a numeric vector (regression) but also a factor (classification). In the latter case, the levels of the factor define the slices used.

nslices

The number of slices used, unless y is a factor. By default the value returned by msir.nslices.

slice.function

The slice functions to be used, by default msir.slices, but the user can provide a different slicing function.

modelNames

A vector of character strings indicating the Gaussian mixture models to be fitted as described in mclustModelNames. If a vector of strings is given they are used for all the slices. If a list of vectors is provided then each vector refers to a single slice.

An integer vector specifying the numbers of mixture components used in fitting Gaussian mixture models. If a list of vectors is provided then each vector refers to a single slice.

cov

The predictors marginal covariance matrix. Possible choices are:

"mle": for the maximum likelihood estimate
"regularized": for a regularized estimate of the covariance matrix (see msir.regularizedSigma)
R matrix: a \((p \times p)\) user defined covariance matrix

…

other arguments passed to msir.compute.

Value

Returns an object of class 'msir' with attributes:

call

the function call.

the design matrix.

the response vector.

slice.info

output from slicing function.

mixmod

a list of finite mixture model objects as described in mclustModel.

loglik

the log-likelihood for the mixture models.

a vector of length equal to the total number of mixture components containing the fraction of observations in each fitted component within slices.

a matrix of component within slices predictors means.

sigma

the marginal predictors covariance matrix.

the msir kernel matrix.

evalues

the eigenvalues from the generalized eigen-decomposition of M.

evectors

the raw eigenvectors from the generalized eigen-decomposition of M ordered according to the eigenvalues.

basis

the normalized eigenvectors from the generalized eigen-decomposition of M ordered according to the eigenvalues.

std.basis

standardized basis vectors obtained by multiplying each coefficient of the eigenvectors by the standard deviation of the corresponding predictor. The resulting coefficients are scaled such that all predictors have unit standard deviation.

numdir

the maximal number of directions estimated.

dir

the estimated MSIR directions from mean-centered predictors.

References

Scrucca, L. (2011) Model-based SIR for dimension reduction. Computational Statistics & Data Analysis, 55(11), 3010-3026.

Examples

Run this code

# NOT RUN {
# 1-dimensional simple regression
n <- 200
p <- 5
b <- as.matrix(c(1,-1,rep(0,p-2)))
x <- matrix(rnorm(n*p), nrow = n, ncol = p)
y <- exp(0.5 * x%*%b) + 0.1*rnorm(n)
MSIR <- msir(x, y)
summary(MSIR)
plot(MSIR, type = "2Dplot")

# 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)
summary(MSIR)
plot(MSIR, type = "2Dplot")
plot(MSIR, type = "coefficients")

# 2-dimensional response curve
n <- 300
p <- 5
b1 <- c(1, 1, 1, rep(0, p-3))
b2 <- c(1,-1,-1, rep(0, p-3))
b <- cbind(b1,b2)
x <- matrix(rnorm(n*p), nrow = n, ncol = p)
y <- x %*% b1 + (x %*% b1)^3 + 4*(x %*% b2)^2 + rnorm(n)
MSIR <- msir(x, y)
summary(MSIR)
plot(MSIR, which = 1:2)
# }
# NOT RUN {
plot(MSIR, type = "spinplot")
# }
# NOT RUN {
plot(MSIR, which = 1, type = "2Dplot", span = 0.7)
plot(MSIR, which = 2, type = "2Dplot", span = 0.7)
# }