cap_beta {cap} | R Documentation |

This function performs inference on the model coefficient *β*.

cap_beta(Y, X, gamma = NULL, beta = NULL, method = c("asmp", "LLR"), boot = FALSE, sims = 1000, boot.ci.type = c("bca", "perc"), conf.level = 0.95, verbose = TRUE)

`Y` |
a data list of length |

`X` |
a |

`gamma` |
a |

`beta` |
a |

`method` |
a character of inference method. If |

`boot` |
a logic variable, whether bootstrap inference is performed. |

`sims` |
a numeric value, the number of bootstrap iterations will be performed. |

`boot.ci.type` |
a character of the way of calculating bootstrap confidence interval. If |

`conf.level` |
a numeric value, the designated significance level. Default is |

`verbose` |
a logic variable, whether the bootstrap procedure is printed. Default is |

Considering *y_{it}* are *p*-dimensional independent and identically distributed random samples from a multivariate normal distribution with mean zero and covariance matrix *Σ_{i}*. We assume there exits a *p*-dimensional vector *γ* such that *z_{it}:=γ'y_{it}* satisfies the multiplicative heteroscedasticity:

*\log(\mathrm{Var}(z_{it}))=\log(γ'Σ_{i}γ)=β_{0}+x_{i}'β_{1},*

where *x_{i}* contains explanatory variables of subject *i*, and *β_{0}* and *β_{1}* are model coefficients.

The *β* coefficient is estimated by maximizing the likelihood function. The asymptotic variance is obtained based on maximum likelihood estimator theory.

When `method = "asmp"`

, the output is a *q \times 6* data frame containing the estimate of *β* coefficient, the asymptotic standard error, the test statistic, the *p*-value, and the lower and upper bound of the confidence interval.

When `method = "LLR"`

, the output is a *q \times 3* data frame containing the estimate of *β* coefficient, the test statistic, and the *p*-value.

When `boot = TRUE`

,

`Inference` |
point estimate of the |

`beta.boot` |
the estimate of the |

Yi Zhao, Johns Hopkins University, <zhaoyi1026@gmail.com>

Bingkai Wang, Johns Hopkins University, <bwang51@jhmi.edu>

Stewart Mostofsky, Johns Hopkins University, <mostofsky@kennedykrieger.org>

Brian Caffo, Johns Hopkins University, <bcaffo@gmail.com>

Xi Luo, Brown University, <xi.rossi.luo@gmail.com>

Zhao et al. (2018) *Covariate Assisted Principal Regression for Covariance Matrix Outcomes* <doi:10.1101/425033>

############################################# data(env.example) X<-get("X",env.example) Y<-get("Y",env.example) Phi<-get("Phi",env.example) # asymptotic variance re1<-cap_beta(Y,X,gamma=Phi[,2],method=c("asmp"),boot=FALSE) # likelihood ratio test re2<-cap_beta(Y,X,gamma=Phi[,2],method=c("LLR"),boot=FALSE) # bootstrap confidence interval re3<-cap_beta(Y,X,gamma=Phi[,2],boot=TRUE,sims=500,verbose=FALSE) #############################################

[Package *cap* version 1.0 Index]