logit.env | R Documentation |
Fit the envelope model in logistic regression with dimension u.
logit.env(X, Y, u, asy = TRUE, init = NULL)
X |
Predictors. An n by p matrix, p is the number of predictors and n is number of observations. The predictors must be continuous variables. |
Y |
Response. An n by 1 matrix. The univariate response must be binary. |
u |
Dimension of the envelope. An integer between 0 and p. |
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 in logistic regression. An p by u matrix. The default is the one generated by function logit.envMU. |
This function fits the envelope model in logistic regression,
Y = exp(\mu + \beta' X) / (1 + exp(\mu + \beta' X)), \Sigma_{X}=\Gamma\Omega\Gamma'+\Gamma_{0}\Omega_{0}\Gamma'_{0}
using the maximum likelihood estimation. When the dimension of the envelope is between 1 and p-1, the starting value and blockwise coordinate descent algorithm in Cook et al. (2016) is implemented. This model works the best when X is multivariate normal.
The output is a list that contains the following components:
beta |
The envelope estimator of the canonical parameter. |
SigmaX |
The envelope estimator of the covariance matrix of X. |
Gamma |
An orthonormal basis of the envelope subspace. |
Gamma0 |
An orthonormal basis of the complement of the envelope subspace. |
eta |
The estimated beta of the canonical parameter with respect to Gamma. |
Omega |
The coordinates of SigmaX with respect to Gamma. |
Omega0 |
The coordinates of SigmaX with respect to Gamma0. |
mu |
The estimated intercept of the canonical parameter. |
loglik |
The maximized log likelihood function. |
covMatrix |
The asymptotic covariance of vec(beta). The covariance matrix returned are asymptotic. For the actual standard errors, multiply by 1 / n. |
asySE |
The asymptotic standard error for elements in beta under the envelope model. The standard errors returned are asymptotic, for actual standard errors, multiply by 1 / sqrt(n). |
ratio |
The asymptotic standard error ratio of the standard multivariate linear regression estimator over the envelope estimator, for each element in beta. |
n |
The number of observations in the data. |
Cook, R. D., Zhang, X. (2015). Foundations for Envelope Models and Methods. Journal of the American Statistical Association 110, 599 - 611.
Cook, R. D., Forzani, L. and Su, Z. (2016) A Note on Fast Envelope Estimation. Journal of Multivariate Analysis. 150, 42-54.
data(horseshoecrab)
X1 <- as.numeric(horseshoecrab[ , 1] == 2)
X2 <- as.numeric(horseshoecrab[ , 1] == 3)
X3 <- as.numeric(horseshoecrab[ , 1] == 4)
X4 <- as.numeric(horseshoecrab[ , 2] == 2)
X5 <- as.numeric(horseshoecrab[ , 2] == 3)
X6 <- horseshoecrab[ , 3]
X7 <- horseshoecrab[ , 5]
X <- cbind(X1, X2, X3, X4, X5, X6, X7)
Y <- as.numeric(ifelse(horseshoecrab[ , 4] > 0, 1, 0))
## Not run: u <- u.logit.env(X, Y)
## Not run: u
## Not run: m <- logit.env(X, Y, 1)
## Not run: m$beta
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.