eppls | R Documentation |
Fit the Envelope-based Partial Partial Least Squares model for multivariate linear regression with dimension u.
eppls(X1, X2, Y, u, asy = TRUE, init = NULL)
X1 |
An n by p1 matrix of continuous predictors, where p1 is the number of continuous predictors with p1 < n. |
X2 |
An n by p2 matrix of categorical predictors, where p2 is the number of categorical predictors with p2 < n. |
Y |
An n by r matrix of multivariate responses, where r is the number of responses. |
u |
A given dimension of the Envelope-based Partial Partial Least Squares. It should be an interger between 0 and p1. |
asy |
Flag for computing the asymptotic variance of the envelope estimator. The default is |
init |
The user-specified value of Gamma for the envelope subspace. An r by u matrix. The default is the one generated by function envMU. |
This function the Envelope-based Partial Partial Least Squares model for multivariate linear regression with dimension u,
Y = μ + Γη X + \varepsilon, Σ=ΓΩΓ' + Γ_{0}Ω_{0}Γ'_{0}
using the maximum likelihood estimation. When the dimension of the envelope is between 1 and p1-1, the starting value and blockwise coordinate descent algorithm in Cook et al. (2016) is implemented. When the dimension is p1, then the envelope model degenerates to the standard multivariate linear regression. When the dimension is 0, it means that X and Y are uncorrelated, and the fitting is different.
The output is a list that contains the following components:
muY |
The estimator of mean of |
mu1 |
The estimator of mean of |
mu2 |
The estimator of mean of |
beta1 |
A p1 by r matrix for the estimator of regression coefficients for continuous predictors. |
beta2 |
A p2 by r matrix for the estimator of regression coefficients for categorical predictors. |
Gamma |
An p1 by d matrix for the orthogonal basis of the Envelope-based Partial Partial Least Squares. |
Gamma0 |
An p1 by (p1-d) matrix for the orthogonal basis of the complement of the Envelope-based Partial Partial Least Squares. |
gamma |
A p2 by p1 matrix for the estimator of regression coefficients based on the regression of |
eta |
A d by p1 matrix for the coordinates of |
Omega |
A d by d matrix for the coordinates of |
Omega0 |
A (p1-d) by (p1-d) matrix for the coordinates of |
SigmaX1 |
The estimator of error covariance matrix |
SigmaYcX |
The estimator of error covariance matrix |
loglik |
The maximized log likelihood function. |
n |
The number of observations in the data. |
covMatrix1 |
The asymptotic covariance of vec(beta1). The covariance matrix returned are asymptotic. For the actual standard errors, multiply by 1 / n. |
covMatrix2 |
The asymptotic covariance of vec(beta2). The covariance matrix returned are asymptotic. For the actual standard errors, multiply by 1 / n. |
asySE1 |
The asymptotic standard error matrix for elements in |
asySE2 |
The asymptotic standard error matrix for elements in |
Park, Y., Su, Z. and Chung, D. (2022+) Envelope-based Partial Partial Least Squares with Application to Cytokine-based Biomarker Analysis for COVID-19.
data(amitriptyline) Y <- amitriptyline[ , 1:2] X1 <- amitriptyline[ , 4:7] X2 <- amitriptyline[ , 3] u <- u.eppls(X1, X2, Y) u m <- eppls(X1, X2, Y, 2) m
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