Estimate the envelope subspace with specified dimension in logistic regression.
logit.envMU(X, Y, u)Predictors. An n by p matrix, p is the number of predictors. The predictors can be univariate or multivariate, discrete or continuous.
Response. An n by 1 matrix. The univariate response must be binary.
Dimension of the envelope. An integer between 0 and p.
The orthonormal basis of the envelope subspace.
The orthonormal basis of the complement of the envelope subspace.
The estimated intercept of the canonical parameter.
The estimated beta of the canonical parameter with respect to Gamma.
The estimated weight defined as C"(theta) / E(C"(theta)) where C(theta) is the conditional log likelihood.
The estimated V defined as V = theta + (Y - mu (theta) / W).
The asympotic covariance of vec(beta).
The minimized objective function.
This function estimate the envelope subspace in logistic regression using an non-Grassmann optimization algorithm. The starting value and optimization algorithm is described in Cook et al. (2016).
Cook, R. D., Forzani, L. and Su, Z. (2016) A Note on Fast Envelope Estimation. Journal of Multivariate Analysis. 150, 42-54.