BrainCon (version 0.3.0)

population.est: Estimate population-level partial correlation coefficients

Description

Estimate population-level partial correlation coefficients in time series data. And also return coefficients for each individual. Input time series data for population as a 3-dimensional array or a list.

Usage

population.est(
  Z,
  lambda = NULL,
  type = c("slasso", "lasso"),
  alpha = 0.05,
  ind.ci = FALSE
)

Value

A popEst class object containing two components.

coef a \(p*p\) partial correlation coefficients matrix.

ind.est a \(m\)-length list, containing estimates for each individuals.

type regression type in estimation.

Arguments

Z

If each individual shares the same number of periods of time, Z can be a \(n*p*m\) dimensional array, where \(m\) is number of individuals. In general, Z should be a m-length list, and each element in the list is a \(n_i*p\) matrix, where \(n_i\) stands for the number of periods of time of the i-th individual.

lambda

a scalar or a m-length vector, representing the penalty parameters of order \(\sqrt{\log(p)/n_i}\) for each individual. If a scalar, the penalty parameters used in each individual are the same. If a m-length vector, the penalty parameters for each individual are specified in order. And if NULL, penalty parameters are specified by type. More details about the penalty parameters are in individual.est.

type

a character string representing the method of estimation. "slasso" means scaled lasso, and "lasso" means lasso. Default value is "slasso".

alpha

a numeric scalar, default value is 0.05. It is used when ind.ci is TRUE.

ind.ci

a logical indicating whether to compute \(1-\alpha\) confidence intervals of each subject, default value is FALSE.

References

Qiu Y. and Zhou X. (2021). Inference on multi-level partial correlations based on multi-subject time series data, Journal of the American Statistical Association, 00, 1-15.

Examples

## Quick example for the population-level estimates
data(popsimA)
# estimating partial correlation coefficients by scaled lasso
pc = population.est(popsimA)

## Inference on the first subject in population
Res_1 = individual.test(pc$ind.est[[1]])