cap_beta {cap} | R Documentation |
Inference of model coefficients
Description
This function performs inference on the model coefficient \beta
.
Usage
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)
Arguments
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 |
Details
Considering y_{it}
are p
-dimensional independent and identically distributed random samples from a multivariate normal distribution with mean zero and covariance matrix \Sigma_{i}
. We assume there exits a p
-dimensional vector \gamma
such that z_{it}:=\gamma'y_{it}
satisfies the multiplicative heteroscedasticity:
\log(\mathrm{Var}(z_{it}))=\log(\gamma'\Sigma_{i}\gamma)=\beta_{0}+x_{i}'\beta_{1},
where x_{i}
contains explanatory variables of subject i
, and \beta_{0}
and \beta_{1}
are model coefficients.
The \beta
coefficient is estimated by maximizing the likelihood function. The asymptotic variance is obtained based on maximum likelihood estimator theory.
Value
When method = "asmp"
, the output is a q \times 6
data frame containing the estimate of \beta
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 \beta
coefficient, the test statistic, and the p
-value.
When boot = TRUE
,
Inference |
point estimate of the |
beta.boot |
the estimate of the |
Author(s)
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>
References
Zhao et al. (2018) Covariate Assisted Principal Regression for Covariance Matrix Outcomes <doi:10.1101/425033>
Examples
#############################################
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)
#############################################