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 |

`X2` |
An |

`Y` |
An |

`u` |
A given dimension of the Envelope-based Partial Partial Least Squares. It should be an interger between |

`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 |

This function the Envelope-based Partial Partial Least Squares model for multivariate linear regression with dimension `u`

,

```
Y = \mu + \Gamma\eta X + \varepsilon, \Sigma=\Gamma\Omega\Gamma' + \Gamma_{0}\Omega_{0}\Gamma'_{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 |

`beta2` |
A |

`Gamma` |
An |

`Gamma0` |
An |

`gamma` |
A |

`eta` |
A |

`Omega` |
A |

`Omega0` |
A |

`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
```

Embedding an R snippet on your website

Add the following code to your website.

For more information on customizing the embed code, read Embedding Snippets.