transreg {transreg}

Penalised regression with multiple sets of prior effects

Description

Implements penalised regression with multiple sets of prior effects

Usage

transreg(
  y,
  X,
  prior,
  family = "gaussian",
  alpha = 1,
  foldid = NULL,
  nfolds = 10,
  scale = "iso",
  stack = "sim",
  sign = FALSE,
  switch = FALSE,
  select = TRUE,
  track = FALSE,
  parallel = FALSE
)

Arguments

y

target: vector of length n (see family)

X

features: matrix with n rows (samples) and p columns (features)

prior

prior coefficients: matrix with p rows (features) and k columns (sources of co-data)

family

character "gaussian" (y: real numbers), "binomial" (y: 0s and 1s), or "poisson" (y: non-negative integers);

alpha

elastic net mixing parameter (0=ridge, 1=lasso): number between 0 and 1

foldid

fold identifiers: vector of length n with entries from 1 to nfolds

nfolds

number of folds: positive integer

scale

character "exp" for exponential calibration or "iso" for isotonic calibration

stack

character "sta" (standard stacking) or "sim" (simultaneous stacking)

sign

sign discovery procedure: logical (experimental argument)

switch

choose between positive and negative weights for each source: logical

select

select from sources: logical

track

show intermediate output (messages and plots): logical

parallel

logical (see cv.glmnet)

Details

• n: sample size

• p: number of features

• k: number of sources

Value

Returns an object of class transreg. Rather than accessing its slots (see list below), it is recommended to use methods like coef.transreg() and predict.transreg().

• slot base: Object of class glmnet. Regression of outcome on features (without prior effects), with 1 + p estimated coefficients (intercept + features).

• slot meta.sta: NULL or object of class glmnet. Regression of outcome on cross-validated linear predictors from prior effects and estimated effects, with 1 + k + 2 estimated coefficients (intercept + sources of co-data + lambda_min and lambda_1se).

• slot meta.sim: NULL or object of class glmnet. Regression of outcome on meta-features (cross-validated linear predictors from prior effects) and original features, with 1 + k + p estimated coefficients (intercept + sources of co-data + features).

• slot prior.calib: Calibrated prior effects. Matrix with p rows and k columns.

• slot data: Original data. List with slots y, X and prior (see arguments).

• slot info: Information on call. Data frame with entries n, p, k, family, alpha, scale and stack (see details and arguments).

References

Armin Rauschenberger, Zied Landoulsi, Mark A. van de Wiel, and Enrico Glaab (2023). "Penalised regression with multiple sets of prior effects". Bioinformatics (In press). doi:10.1093/bioinformatics/btad680 [e-mail]

See Also

Methods for objects of class transreg include coef and predict.

Examples

#--- simulation ---
n <- 100; p <- 500
X <- matrix(rnorm(n=n*p),nrow=n,ncol=p)
beta <- rnorm(p)*rbinom(n=p,size=1,prob=0.2)
prior1 <- beta + rnorm(p)
prior2 <- beta + rnorm(p)
y_lin <- X %*% beta
y_log <- 1*(y_lin > 0)

#--- single vs multiple priors ---
one <- transreg(y=y_lin,X=X,prior=prior1)
two <- transreg(y=y_lin,X=X,prior=cbind(prior1,prior2))
weights(one)
weights(two)


#--- linear vs logistic regression ---
lin <- transreg(y=y_lin,X=X,prior=prior1,family="gaussian")
log <- transreg(y=y_log,X=X,prior=prior1,family="binomial")
hist(predict(lin,newx=X)) # predicted values
hist(predict(log,newx=X)) # predicted probabilities

#--- ridge vs lasso penalisation ---
ridge <- transreg(y=y_lin,X=X,prior=prior1,alpha=0)
lasso <- transreg(y=y_lin,X=X,prior=prior1,alpha=1)
# initial coefficients (without prior)
plot(x=coef(ridge$base)[-1]) # dense
plot(x=coef(lasso$base)[-1]) # sparse
# final coefficients (with prior)
plot(x=coef(ridge)$beta) # dense
plot(x=coef(lasso)$beta) # not sparse

#--- exponential vs isotonic calibration ---
exp <- transreg(y=y_lin,X=X,prior=prior1,scale="exp")
iso <- transreg(y=y_lin,X=X,prior=prior1,scale="iso")
plot(x=prior1,y=exp$prior.calib)
plot(x=prior1,y=iso$prior.calib)

#--- standard vs simultaneous stacking ---
prior <- c(prior1[1:250],rep(0,250))
sta <- transreg(y=y_lin,X=X,prior=prior,stack="sta")
sim <- transreg(y=y_lin,X=X,prior=prior,stack="sim")
plot(x=coef(sta$base)[-1],y=coef(sta)$beta)
plot(x=coef(sim$base)[-1],y=coef(sim)$beta)