Description Usage Arguments Details Value References

Estimate the envelope subspace with specified dimension in logistic regression.

1 | ```
logit.envMU(X, Y, u)
``` |

`X` |
Predictors. An n by p matrix, p is the number of predictors. The predictors can be univariate or multivariate, discrete or continuous. |

`Y` |
Response. An n by 1 matrix. The univariate response must be binary. |

`u` |
Dimension of the envelope. An integer between 0 and p. |

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).

`Gammahat` |
The orthonormal basis of the envelope subspace. |

`Gamma0hat` |
The orthonormal basis of the complement of the envelope subspace. |

`muhat` |
The estimated intercept of the canonical parameter. |

`etahat` |
The estimated beta of the canonical parameter with respect to Gamma. |

`weighthat` |
The estimated weight defined as C"(theta) / E(C"(theta)) where C(theta) is the conditional log likelihood. |

`Vhat` |
The estimated V defined as V = theta + (Y - mu (theta) / W). |

`avar` |
The asympotic covariance of vec(beta). |

`objfun` |
The minimized objective function. |

Cook, R. D., Forzani, L. and Su, Z. (2016) A Note on Fast Envelope Estimation. Journal of Multivariate Analysis. 150, 42-54.

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