Description Usage Arguments Details Value Author(s) References See Also Examples
Main function of the package. It creates objects of one of classes core
, lad
, or pfc
to estimate a sufficient dimension reduction subspace using covariance reducing models (CORE), likelihood acquired directions (LAD), or principal fitted components (PFC).
1 2 3 |
X |
Design matrix with |
y |
The response vector of length |
fy |
Basis function to be obtained using |
Sigmas |
A list object of sample covariance matrices corresponding to the different populations. It is used exclusively with |
ns |
A vector of number of observations of the samples corresponding to the different populations. |
numdir |
The number of directions to be used in estimating the reduction subspace. When calling |
nslices |
Number of slices for a continuous response. It is used exclusively with |
model |
One of the following: |
numdir.test |
Boolean. If |
... |
Additional arguments for specific models and/or Grassmannoptim. |
Likelihood-based methods to sufficient dimension reduction are model-based inverse regression approaches using the conditional distribution of the p-vector of predictors X given the response Y=y. Three methods are implemented in this package: covariance reduction (CORE), principal fitted components (PFC), and likelihood acquired directions (LAD). All three assume that X|(Y=y) \sim N(μ_y, Δ_y).
For CORE, given a set of h covariance matrices, the goal is to find a sufficient reduction that accounts for the heterogeneity among the population covariance matrices. See the documentation of "core"
for details.
For PFC, μ_y=μ + Γ β f_y, with various structures of Δ. The simplest is the isotropic ("iso"
) with Δ=δ^2 I_p. The anisotropic ("aniso"
) PFC model assumes that Δ=\mathrm{diag}(δ_1^2, ..., δ_p^2), where the conditional predictors are independent and on different measurement scales. The unstructured ("unstr"
) PFC model allows a general structure for Δ. Extended structures are considered. See the help file of pfc
for more detail.
LAD assumes that the response Y is discrete. A continuous response is sliced into finite categories to meet this condition. It estimates the central subspace \mathcal{S}_{Y|X} by modeling both μ_y and Δ_y. See lad
for more detail.
An object of one of the classes core
, lad
, or pfc
. The output depends on the model used. See pfc
, lad
, and core
for further detail.
Kofi Placid Adragni <kofi@umbc.edu>
Adragni, KP and Cook, RD (2009): Sufficient dimension reduction and prediction in regression. Phil. Trans. R. Soc. A 367, 4385-4405.
Cook, RD (2007): Fisher Lecture - Dimension Reduction in Regression (with discussion). Statistical Science, 22, 1–26.
Cook, R. D. and Forzani, L. (2008a). Covariance reducing models: An alternative to spectral modelling of covariance matrices. Biometrika 95, 799-812.
Cook, R. D. and Forzani, L. (2008b). Principal fitted components for dimension reduction in regression. Statistical Science 23, 485–501.
Cook, R. D. and Forzani, L. (2009). Likelihood-based sufficient dimension reduction. Journal of the American Statistical Association, Vol. 104, 485, pp 197–208.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 | data(bigmac)
fit1 <- ldr(X=bigmac[,-1], y=bigmac[,1], fy=bf(y=bigmac[,1], case="pdisc",
degree=0, nslices=5), numdir=3, structure="unstr", model="pfc")
summary(fit1)
plot(fit1)
fit2 <- ldr(X=bigmac[,-1], y=bigmac[,1], fy=bf(y=bigmac[,1], case="poly",
degree=2), numdir=2, structure="aniso", model="pfc")
summary(fit2)
plot(fit2)
fit3 <- ldr(X=as.matrix(bigmac[,-1]), y=bigmac[,1], model="lad", nslices=5)
summary(fit3)
plot(fit3)
|
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