cate: The main function for confounder adjusted testing
In cate: High Dimensional Factor Analysis and Confounder Adjusted Testing and Estimation

Description Usage Arguments Details Value Functions References See Also Examples

The main function for confounder adjusted testing

cate(
  formula,
  X.data = NULL,
  Y,
  r,
  fa.method = c("ml", "pc", "esa"),
  adj.method = c("rr", "nc", "lqs", "naive"),
  psi = psi.huber,
  nc = NULL,
  nc.var.correction = TRUE,
  calibrate = TRUE
)

cate.fit(
  X.primary,
  X.nuis = NULL,
  Y,
  r,
  fa.method = c("ml", "pc", "esa"),
  adj.method = c("rr", "nc", "lqs", "naive"),
  psi = psi.huber,
  nc = NULL,
  nc.var.correction = TRUE,
  calibrate = TRUE
)

`formula`	a formula indicating the known covariates including both primary variables and nuisance variables, which are seperated by `\|`. The variables before `\|` are primary variables and the variables after `\|` are nuisance variables. It's OK if there is no nuisance variables, then `\|` is not needed and `formula` becomes a typical formula with all the covariates considered primary. When there is confusion about where the intercept should be put, `cate` will include it in X.nuis.
`X.data`	the data frame used for `formula`
`Y`	outcome, n*p matrix
`r`	number of latent factors, can be estimated using the function `est.confounder.num`
`fa.method`	factor analysis method
`adj.method`	adjustment method
`psi`	derivative of the loss function in robust regression
`nc`	position of the negative controls, if d0 > 1, this should be a matrix with 2 columns
`nc.var.correction`	correct asymptotic variance based on our formula
`calibrate`	if TRUE, use the Median and the Mean Absolute Deviation(MAD) to calibrate the test statistics
`X.primary`	primary variables, n*d0 matrix or data frame
`X.nuis`	nuisance covarites, n*d1 matrix

Ideally nc can either be a vector of numbers between 1 and p, if d0 = 1 or the negative controls are the same for every treatment variable, or a 2-column matrix specifying which positions of beta are known to be zero. But this is yet implemented.

a list of objects

alpha: estimated alpha, r*d1 matrix
alpha.p.value: asymptotic p-value for the global chi squared test of alpha, a vector of length d1
beta: estimated beta, p*d1 matrix
beta.cov.row: estimated row covariance of beta, a length p vector
beta.cov.col: estimated column covariance of beta, a d1*d1 matrix
beta.t: asymptotic z statistics for beta
beta.p.value: asymptotic p-values for beta, based on beta.t
Y.tilde: the transformed outcome matrix, an n*p matrix
Gamma: estimated factor loadings, p*r matrix
Z: estimated latent factors
Sigma: estimated noise variance matrix, a length p vector

cate.fit: Basic computing function called by cate

J. Wang, Q. Zhao, T. Hastie, and A. B. Owen (2017). Confounder adjustment in multiple testing. Annals of Statistics, 45(5), 1863–1894.

wrapper for wrapper functions of some existing methods.

## simulate a dataset with 100 observations, 1000 variables and 5 confounders
data <- gen.sim.data(n = 100, p = 1000, r = 5)
X.data <- data.frame(X1 = data$X1)

## linear regression without any adjustment
output.naive <- cate(~ X1 | 1, X.data, Y = data$Y, r = 0, adj.method = "naive")
## confounder adjusted linear regression
output <- cate(~ X1 | 1, X.data, Y = data$Y, r = 5)
## plot the histograms of unadjusted and adjusted regression statistics
par(mfrow = c(1, 2))
hist(output.naive$beta.t)
hist(output$beta.t)

## simulate a dataset with 100 observations, 1000 variables and 5 confounders
data <- gen.sim.data(n = 100, p = 1000, r = 5)
## linear regression without any adjustment
output.naive <- cate.fit(X.primary = data$X1, X.nuis = NULL, Y = data$Y,
                         r = 0, adj.method = "naive")
## confounder adjusted linear regression
output <- cate.fit(X.primary = data$X1, X.nuis = NULL, Y = data$Y, r = 5)
## plot the histograms of unadjusted and adjusted regression statistics
par(mfrow = c(1, 2))
hist(output.naive$beta.t)
hist(output$beta.t)