Fit linear model on each feature after applying decorrelation projection to response and predictors.
Usage
lm_each_eclairs(
formula,
data,
X,
ecl,
subset,
weights,
na.action,
method = "qr",
model = TRUE,
x = FALSE,
y = FALSE,
qr = TRUE,
singular.ok = TRUE,
contrasts = NULL,
offset,
...
)Arguments
- formula
an object of class 'formula' (or one that can be coerced to that class): a symbolic description of the model to be fitted.
- data
a matrix or data.frame containing the variables in the model
- X
matrix or data.frame where each column stores a predictor to be evaluated by the regression model one at a time. The \(i^{th}\) model includes
X[,i]as a predictor.- ecl
estimate of covariance/correlation matrix from eclairs storing \(U\), \(d_1^2\), \(\lambda\) and \(\nu\)
- subset
same as for lm
- weights
same as for lm
- na.action
same as for lm
- method
same as for lm
- model
same as for lm
- x
same as for lm
- y
same as for lm
- qr
same as for lm
- singular.ok
same as for lm
- contrasts
same as for lm
- offset
same as for lm
- ...
other arguments passed to
lm()
Value
data.frame with columns beta, se, tsat, pvalue storing results for regression model fit for each feature
Examples
library(Rfast)
n <- 800 # number of samples
p <- 200 # number of features
# create correlation matrix
Sigma <- autocorr.mat(p, .9)
# draw data from correlation matrix Sigma
Y <- rmvnorm(n, rep(0, p), sigma = Sigma * 5.1, seed = 1)
# eclairs decomposition
ecl <- eclairs(Y)
# simulate covariates
data <- data.frame(matrnorm(p, 2, seed = 1))
colnames(data) <- paste0("v", 1:2)
# simulate response
y <- rnorm(p)
# Simulate 1000 features to test
X <- matrnorm(p, 1000, seed = 1)
colnames(X) <- paste0("set_", seq(ncol(X)))
# Use linear model to test each feature stored as columns in X
res <- lm_each_eclairs(y ~ v1 + v2, data, X, ecl)
head(res)
#> beta se tstat pvalue
#> set_1 2.887431e+13 1.563537e+14 0.1846730 0.853676462
#> set_2 -1.659811e+14 6.478078e+14 -0.2562197 0.798049901
#> set_3 -2.181485e-01 7.886980e-02 -2.7659318 0.006218786
#> set_4 -8.510124e-02 8.776742e-02 -0.9696222 0.333429845
#> set_5 1.186028e-02 7.372858e-02 0.1608641 0.872366104
#> set_6 -6.625690e-02 7.768578e-02 -0.8528833 0.394765035
# Analysis after non-linear transform
#------------------------------------
# Apply function to transforme data
f <- function(x) log(x^2 + 0.001)
# evaluate covariance of transformed data
ecl_transform <- cov_transform(ecl, f, 100)
# Use linear model to test each feature stored as columns in X
# in data transformed by f()
res2 <- lm_each_eclairs(f(y) ~ v1 + v2, data, X, ecl_transform)
head(res)
#> beta se tstat pvalue
#> set_1 2.887431e+13 1.563537e+14 0.1846730 0.853676462
#> set_2 -1.659811e+14 6.478078e+14 -0.2562197 0.798049901
#> set_3 -2.181485e-01 7.886980e-02 -2.7659318 0.006218786
#> set_4 -8.510124e-02 8.776742e-02 -0.9696222 0.333429845
#> set_5 1.186028e-02 7.372858e-02 0.1608641 0.872366104
#> set_6 -6.625690e-02 7.768578e-02 -0.8528833 0.394765035