Package 'transreg' reference manual

Title:	Penalised Regression with Multiple Sets of Prior Effects ('Transfer Learning')
Description:	Improves the predictive performance of ridge and lasso regression exploiting one or more sources of prior information on the importance and direction of effects (Rauschenberger and others 2023, <doi:10.1093/bioinformatics/btad680>). For running the vignette (optional), install 'fwelnet' from 'GitHub' <https://github.com/kjytay/fwelnet>.
Authors:	Armin Rauschenberger [aut, cre]
Maintainer:	Armin Rauschenberger <[email protected]>
License:	GPL-3
Version:	1.0.3
Built:	2024-10-28 05:08:52 UTC
Source:	https://github.com/rauschenberger/transreg

Penalised regression with multiple sets of prior effects

Description

The R package 'transreg' implements penalised regression with multiple sets of prior effects.

Details

Use function [transreg()] for model fitting. Type 'library(transreg)' and then '?transreg' or 'help("transreg")' to open its help file.

See the vignette for further examples. Type 'vignette("transreg")' or 'browseVignettes("transreg")' to open the vignette.

Author(s)

Maintainer: Armin Rauschenberger [email protected] (ORCID)

References

Armin Rauschenberger, Zied Landoulsi, Mark A. van de Wiel, and Enrico Glaab (2023). "Penalised regression with multiple sets of prior effects". Bioinformatics 39(12):btad680. doi:10.1093/bioinformatics/btad680. (Click here to access PDF.)

Examples

?transreg
?predict.transreg
?coef.transreg

?transreg
?predict.transreg
?coef.transreg

Calculate residuals

Description

Calculates residuals from observed outcome and predicted values (Gaussian family) or predicted probabilities (binomial family). Called by '.exp.multiple' and '.iso.multiple'.

Usage

.residuals(y, y_hat, family)
.residuals(y, y_hat, family)

Arguments

`y`	response: vector of length $n$ (see family)
`y_hat`	predicted values or probabilities (see family): vector of length $n$ , or matrix with $n$ rows (samples) and $k$ columns (methods)
`family`	character "gaussian" ( $y$ : real numbers, $y\_hat$ : real numbers) or "binomial" ( $y$ : 0s and 1s, $y\_hat$ : unit interval)

Examples

n <- 100
p <- 5
X <- matrix(stats::rnorm(n*p),nrow=n,ncol=p)
#y <- stats::rbinom(n,size=1,prob=0.5)
y <- stats::rnorm(n)
glm <- glm(y~X,family="gaussian")
res <- residuals.glm(glm)
y_hat <- predict(glm,type="response")
all.equal(res,y-y_hat)

n <- 100
p <- 5
X <- matrix(stats::rnorm(n*p),nrow=n,ncol=p)
#y <- stats::rbinom(n,size=1,prob=0.5)
y <- stats::rnorm(n)
glm <- glm(y~X,family="gaussian")
res <- residuals.glm(glm)
y_hat <- predict(glm,type="response")
all.equal(res,y-y_hat)

Sign discovery

Description

Assigns signs to prior weights to obtain prior coefficients

Usage

.signdisc(y, X, prior, family, foldid = NULL, nfolds = 10, track = FALSE)
.signdisc(y, X, prior, family, foldid = NULL, nfolds = 10, track = 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);
`foldid`	fold identifiers: vector of length $n$ with entries from 1 to 'nfolds'
`nfolds`	number of folds: positive integer
`track`	show intermediate output (messages and plots): logical

Internal functions

Description

Internal functions called by [transreg()], depending on choice between exponential and isotonic calibration.

Usage

.exp.multiple(
  y,
  X,
  prior,
  family,
  switch = FALSE,
  select = TRUE,
  track = FALSE
)

.iso.multiple(
  y,
  X,
  prior,
  family,
  switch = FALSE,
  select = TRUE,
  track = FALSE
)

.iso.fast.single(y, X, prior, family)

.iso.slow.single(y, X, prior, family)
.exp.multiple(
  y,
  X,
  prior,
  family,
  switch = FALSE,
  select = TRUE,
  track = FALSE
)

.iso.multiple(
  y,
  X,
  prior,
  family,
  switch = FALSE,
  select = TRUE,
  track = FALSE
)

.iso.fast.single(y, X, prior, family)

.iso.slow.single(y, X, prior, family)

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);
`switch`	choose between positive and negative weights for each source: logical
`select`	select from sources: logical
`track`	show intermediate output (messages and plots): logical

Functions

.exp.multiple(): called by 'transreg' if 'scale="exp"'
.iso.multiple(): called by 'transreg' if 'scale="iso"'
.iso.fast.single(): called by 'transreg' if 'scale="iso"' (via '.iso.multiple')
.iso.slow.single(): replaced by '.iso.fast.single'

Extract Coefficients

Description

Extracts coefficients from an object of class [transreg].

Usage

## S3 method for class 'transreg'
coef(object, stack = NULL, ...)
## S3 method for class 'transreg'
coef(object, stack = NULL, ...)

Arguments

`object`	object of class 'transreg'
`stack`	character "sta" (standard stacking) or "sim" (simultaneous stacking)
`...`	(not applicable)

Value

Returns estimated coefficients. The output is a list with two slots: slot 'alpha' with the estimated intercept (scalar), and slot 'beta' with the estimated slopes (vector).

References

Examples

#--- simulation ---
set.seed(1)
n <- 100; p <- 500
X <- matrix(rnorm(n=n*p),nrow=n,ncol=p)
beta <- rnorm(p)
prior <- beta + rnorm(p)
y <- X %*% beta

#--- glmnet (without prior effects) ---
object <- glmnet::cv.glmnet(y=y,x=X,alpha=0)
beta_hat <- coef(object,s="lambda.min")[-1]
mean((beta-beta_hat)^2)

#--- transreg (with prior effects) ---
object <- transreg(y=y,X=X,prior=prior,alpha=0)
beta_hat <- coef(object)$beta
mean((beta-beta_hat)^2) # decrease in MSE?

#--- simulation ---
set.seed(1)
n <- 100; p <- 500
X <- matrix(rnorm(n=n*p),nrow=n,ncol=p)
beta <- rnorm(p)
prior <- beta + rnorm(p)
y <- X %*% beta

#--- glmnet (without prior effects) ---
object <- glmnet::cv.glmnet(y=y,x=X,alpha=0)
beta_hat <- coef(object,s="lambda.min")[-1]
mean((beta-beta_hat)^2)

#--- transreg (with prior effects) ---
object <- transreg(y=y,X=X,prior=prior,alpha=0)
beta_hat <- coef(object)$beta
mean((beta-beta_hat)^2) # decrease in MSE?

Cross-validation (reproducibility)

Description

Function for reproducing hold-out method (simulation) and $k$ -fold cross-validation (application). See vignette.

Usage

compare(
  target,
  source = NULL,
  prior = NULL,
  z = NULL,
  family,
  alpha,
  scale = "iso",
  sign = FALSE,
  switch = FALSE,
  select = TRUE,
  foldid.ext = NULL,
  nfolds.ext = 10,
  foldid.int = NULL,
  nfolds.int = 10,
  type.measure = "deviance",
  alpha.prior = NULL,
  naive = TRUE,
  seed = NULL,
  cores = 1,
  xrnet = FALSE
)
compare(
  target,
  source = NULL,
  prior = NULL,
  z = NULL,
  family,
  alpha,
  scale = "iso",
  sign = FALSE,
  switch = FALSE,
  select = TRUE,
  foldid.ext = NULL,
  nfolds.ext = 10,
  foldid.int = NULL,
  nfolds.int = 10,
  type.measure = "deviance",
  alpha.prior = NULL,
  naive = TRUE,
  seed = NULL,
  cores = 1,
  xrnet = FALSE
)

Arguments

`target`	list with slot x (feature matrix with n rows and p columns) and slot y (target vector of length n)
`source`	list of k lists, each with slot x (feature matrix with m_i rows and p columns) and slot y (target vector of length m_i)
`prior`	prior coefficients: matrix with $p$ rows (features) and $k$ columns (sources of co-data)
`z`	prior weights
`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
`scale`	character "exp" for exponential calibration or "iso" for isotonic calibration
`sign`	sign discovery procedure: logical (experimental argument)
`switch`	choose between positive and negative weights for each source: logical
`select`	select from sources: logical
`foldid.ext`	external fold identifiers
`nfolds.ext`	number of external folds
`foldid.int`	internal fold identifiers
`nfolds.int`	number of internal folds
`type.measure`	character
`alpha.prior`	alpha for source regression
`naive`	compare with naive transfer learning: logical
`seed`	random seed
`cores`	number of cores for parallel computing (requires R package 'doMC')
`xrnet`	compare with xrnet: logical

Internal functions

Description

Internal functions called by [coef.transreg()], [predict.transreg()] and [weights.transreg()], depending on choice between standard stacking and simultaneous stacking.

Usage

.predict.sta(object, newx, ...)

.predict.sim(object, newx, ...)

.coef.sta(object, ...)

.coef.sim(object, ...)

.weights.sta(object, ...)

.weights.sim(object, ...)

.which.stack(object, stack)
.predict.sta(object, newx, ...)

.predict.sim(object, newx, ...)

.coef.sta(object, ...)

.coef.sim(object, ...)

.weights.sta(object, ...)

.weights.sim(object, ...)

.which.stack(object, stack)

Arguments

`object`	object of class 'transreg'
`newx`	features: matrix with $n$ rows (samples) and $p$ columns (variables)
`...`	(not applicable)
`stack`	character "sta" (standard stacking) or "sim" (simultaneous stacking)

Functions

.predict.sta(): called by 'predict.transreg' if 'stack="sta"'
.predict.sim(): called by 'predict.transreg' if 'stack="sim"'
.coef.sta(): called by 'coef.transreg' if 'stack="sta"'
.coef.sim(): called by 'coef.transreg' if 'stack="sim"'
.weights.sta(): called by 'weights.transreg' if 'stack="sta"'
.weights.sim(): called by 'weights.transreg' if 'stack="sim"'
.which.stack(): called by 'coef.transreg', 'predict.transreg' and 'weights.transreg'

Fitted values

Description

Extracts fitted values

Usage

## S3 method for class 'transreg'
fitted(object, stack = NULL, ...)
## S3 method for class 'transreg'
fitted(object, stack = NULL, ...)

Arguments

`object`	object of class 'transreg'
`stack`	character "sta" (standard stacking) or "sim" (simultaneous stacking)
`...`	(not applicable)

Value

Returns fitted values. The output is a numerical vector with one entry for sample.

References

Examples

#--- simulation ---
set.seed(1)
n0 <- 100; n1 <- 10000; n <- n0 + n1; p <- 500
X <- matrix(rnorm(n=n*p),nrow=n,ncol=p)
beta <- rnorm(p)
prior <- beta + rnorm(p)
y <- X %*% beta

#--- train-test split ---
foldid <- rep(c(0,1),times=c(n0,n1))
y0 <- y[foldid==0]
X0 <- X[foldid==0,]
y1 <- y[foldid==1]
X1 <- X[foldid==1,]

object <- transreg(y=y0,X=X0,prior=prior)

#--- fitted values ---
y0_hat <- fitted(object)
mean((y0-y0_hat)^2)

#--- predicted values ---
y1_hat <- predict(object,newx=X1)
mean((y1-y1_hat)^2) # increase in MSE?

#--- simulation ---
set.seed(1)
n0 <- 100; n1 <- 10000; n <- n0 + n1; p <- 500
X <- matrix(rnorm(n=n*p),nrow=n,ncol=p)
beta <- rnorm(p)
prior <- beta + rnorm(p)
y <- X %*% beta

#--- train-test split ---
foldid <- rep(c(0,1),times=c(n0,n1))
y0 <- y[foldid==0]
X0 <- X[foldid==0,]
y1 <- y[foldid==1]
X1 <- X[foldid==1,]

object <- transreg(y=y0,X=X0,prior=prior)

#--- fitted values ---
y0_hat <- fitted(object)
mean((y0-y0_hat)^2)

#--- predicted values ---
y1_hat <- predict(object,newx=X1)
mean((y1-y1_hat)^2) # increase in MSE?

* top-left: Calibrated prior effects ( $y$ -axis) against original prior effects ( $x$ -axis). Each line is for one source of prior effects, with the colour given by [grDevices::palette()] (black: 1, red: 2, green: 3, blue: 4, ...).

* top-right: Estimated coefficients with transfer learning ( $y$ -axis) against estimated coefficients without transfer learning ( $x$ -axis). Each point represents one feature.

* bottom-left: Estimated weights for sources of prior effects (labels 1 to $k$ ), and either estimated weights for 'lambda.min' and 'lambda.1se' models (standard stacking) or estimated weights for features (simultaneous stacking).

* bottom-right: Absolute deviance residuals ( $y$ -axis) against fitted values ( $x$ -axis). Each point represents one sample.

References

Examples

#--- simulation ---
set.seed(1)
n <- 100; p <- 500
X <- matrix(rnorm(n=n*p),nrow=n,ncol=p)
beta <- rnorm(p) #*rbinom(n=n,size=1,prob=0.2)
prior1 <- beta + rnorm(p)
prior2 <- beta + rnorm(p)
prior3 <- rnorm(p)
prior4 <- rnorm(p)
y <- X %*% beta

prior <- cbind(prior1,prior2,prior3,prior4)
object <- transreg(y=y,X=X,prior=prior,alpha=0,stack=c("sta","sim"))

plot(object,stack="sta")

#--- simulation ---
set.seed(1)
n <- 100; p <- 500
X <- matrix(rnorm(n=n*p),nrow=n,ncol=p)
beta <- rnorm(p) #*rbinom(n=n,size=1,prob=0.2)
prior1 <- beta + rnorm(p)
prior2 <- beta + rnorm(p)
prior3 <- rnorm(p)
prior4 <- rnorm(p)
y <- X %*% beta

prior <- cbind(prior1,prior2,prior3,prior4)
object <- transreg(y=y,X=X,prior=prior,alpha=0,stack=c("sta","sim"))

plot(object,stack="sta")

Make Predictions

Description

Predicts outcome

Usage

## S3 method for class 'transreg'
predict(object, newx, stack = NULL, ...)
## S3 method for class 'transreg'
predict(object, newx, stack = NULL, ...)

Arguments

`object`	object of class 'transreg'
`newx`	features: matrix with $n$ rows (samples) and $p$ columns (variables)
`stack`	character "sta" (standard stacking) or "sim" (simultaneous stacking)
`...`	(not applicable)

Value

Returns predicted values or predicted probabilities. The output is a column vector with one entry for each sample.

References

Examples

#--- simulation ---
set.seed(1)
n0 <- 100; n1 <- 10000; n <- n0 + n1; p <- 500
X <- matrix(rnorm(n=n*p),nrow=n,ncol=p)
beta <- rnorm(p)
prior <- beta + rnorm(p)
y <- X %*% beta

#--- train-test split ---
foldid <- rep(c(0,1),times=c(n0,n1))
y0 <- y[foldid==0]
X0 <- X[foldid==0,]
y1 <- y[foldid==1]
X1 <- X[foldid==1,]

#--- glmnet (without prior effects) ---
object <- glmnet::cv.glmnet(y=y0,x=X0)
y_hat <- predict(object,newx=X1,s="lambda.min")
mean((y1-y_hat)^2)

#--- transreg (with prior effects) ---
object <- transreg(y=y0,X=X0,prior=prior)
y_hat <- predict(object,newx=X1)
mean((y1-y_hat)^2) # decrease in MSE?

#--- simulation ---
set.seed(1)
n0 <- 100; n1 <- 10000; n <- n0 + n1; p <- 500
X <- matrix(rnorm(n=n*p),nrow=n,ncol=p)
beta <- rnorm(p)
prior <- beta + rnorm(p)
y <- X %*% beta

#--- train-test split ---
foldid <- rep(c(0,1),times=c(n0,n1))
y0 <- y[foldid==0]
X0 <- X[foldid==0,]
y1 <- y[foldid==1]
X1 <- X[foldid==1,]

#--- glmnet (without prior effects) ---
object <- glmnet::cv.glmnet(y=y0,x=X0)
y_hat <- predict(object,newx=X1,s="lambda.min")
mean((y1-y_hat)^2)

#--- transreg (with prior effects) ---
object <- transreg(y=y0,X=X0,prior=prior)
y_hat <- predict(object,newx=X1)
mean((y1-y_hat)^2) # decrease in MSE?

Print transreg-object

Description

Show summary of transreg-object

Usage

## S3 method for class 'transreg'
print(x, ...)
## S3 method for class 'transreg'
print(x, ...)

Arguments

`x`	object of class transreg
`...`	(not applicable)

Value

Returns family of distributions, elastic net mixing parameter ( $alpha$ ), number of samples ( $n$ ), number of features ( $p$ ), number of sources of co-data ( $k$ ), chosen calibration method (exponential or isotonic), and chosen stacking method (standard or simultaneous).

Examples

#--- simulation ---
set.seed(1)
n <- 100; p <- 500
X <- matrix(rnorm(n=n*p),nrow=n,ncol=p)
beta <- rnorm(p)
prior <- beta + rnorm(p)
y <- X %*% beta

#--- print.transreg  ---
object <- transreg(y=y,X=X,prior=prior)
object

#--- simulation ---
set.seed(1)
n <- 100; p <- 500
X <- matrix(rnorm(n=n*p),nrow=n,ncol=p)
beta <- rnorm(p)
prior <- beta + rnorm(p)
y <- X %*% beta

#--- print.transreg  ---
object <- transreg(y=y,X=X,prior=prior)
object

Simulation (reproducibility)

Description

Function for reproducing 'internal' simulation study. See vignette.

Usage

simulate(
  p = 1000,
  n.target = 100,
  n.source = 150,
  k = 2,
  family = "gaussian",
  prop = 0.01,
  rho.beta = 0.95,
  rho.x = 0.95,
  w = 0.5,
  trans = rep(TRUE, times = k),
  exp = rep(1, times = k)
)
simulate(
  p = 1000,
  n.target = 100,
  n.source = 150,
  k = 2,
  family = "gaussian",
  prop = 0.01,
  rho.beta = 0.95,
  rho.x = 0.95,
  w = 0.5,
  trans = rep(TRUE, times = k),
  exp = rep(1, times = k)
)

Arguments

`p`	number of features
`n.target`	sample size for target data set
`n.source`	sample size(s) for source data set(s), scalar or vector of length k
`k`	number of source data sets
`family`	"Gaussian", "binomial" or "poisson"
`prop`	approximate proportion of features with effects
`rho.beta`	correlation between effects (across different data sets)
`rho.x`	base for decreasing correlation structure for correlation between features
`w`	weight between signal and noise
`trans`	logical vector of length $k$ : transferable (TRUE) or non-transferable (FALSE) source
`exp`	non-negative vector of length $k$ for transforming beta to sign(beta)*abs(beta)^exp

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
)
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

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)

#--- 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)

Extract Weights

Description

Extracts weights from an object of class [transreg].

Usage

## S3 method for class 'transreg'
weights(object, stack = NULL, ...)
## S3 method for class 'transreg'
weights(object, stack = NULL, ...)

Arguments

`object`	object of class 'transreg'
`stack`	character "sta" (standard stacking) or "sim" (simultaneous stacking)
`...`	(not applicable)

Value

Returns weights. The output is a numerical vector with one entry for each source of co-data.

References

Examples

#--- simulation ---
set.seed(1)
n <- 100; p <- 500
X <- matrix(rnorm(n=n*p),nrow=n,ncol=p)
beta <- rnorm(p)
prior <- cbind(beta+rnorm(p),beta+rnorm(p),rnorm(p),rnorm(p))
y <- X %*% beta

#--- example ---
object <- transreg(y=y,X=X,prior=prior)
weights(object)

#--- simulation ---
set.seed(1)
n <- 100; p <- 500
X <- matrix(rnorm(n=n*p),nrow=n,ncol=p)
beta <- rnorm(p)
prior <- cbind(beta+rnorm(p),beta+rnorm(p),rnorm(p),rnorm(p))
y <- X %*% beta

#--- example ---
object <- transreg(y=y,X=X,prior=prior)
weights(object)

`x`	object of type transreg
`stack`	character "sta" (standard stacking) or "sim" (simultaneous stacking)
`...`	(not applicable)

Package 'transreg'

Help Index

Penalised regression with multiple sets of prior effects

Description

Details

Author(s)

References

See Also

Examples

Calculate residuals

Description

Usage

Arguments

Examples

Sign discovery

Description

Usage

Arguments

Internal functions

Description

Usage

Arguments

Functions

See Also

Extract Coefficients

Description

Usage

Arguments

Value

References

See Also

Examples

Cross-validation (reproducibility)

Description

Usage

Arguments

See Also

Internal functions

Description

Usage

Arguments

Functions

See Also

Fitted values

Description

Usage

Arguments

Value

References

See Also

Examples

Plot transreg-object

Description

Usage

Arguments

Value

References

See Also

Examples

Make Predictions

Description

Usage

Arguments

Value

References

See Also

Examples

Print transreg-object

Description

Usage

Arguments

Value

Examples

Simulation (reproducibility)

Description

Usage

Arguments

See Also

Penalised regression with multiple sets of prior effects

Description