Description Usage Arguments Details Value Author(s) References Examples
This function performs inference on the model coefficient β.
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Y |
a data list of length n. Each list element is a T\times p matrix, the data matrix of T observations from p features. |
X |
a n\times q data matrix, the covariate matrix of n subjects with q-1 predictors. The first column is all ones. |
gamma |
a p-dimensional vector, the projecting direction γ. Default is |
beta |
a q-dimensional vector, the model coefficient β. Default is |
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 0.95. |
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 β coefficient, as well as the corresponding standard error, test statistic, p-value, and the lower and upper bound of the confidence interval. |
beta.boot |
the estimate of the β coefficient in each iteration. |
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>
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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)
#############################################
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