Package 'cornet'

Arguments

Description

Verifies whether an argument matches formal requirements.

Usage

.check(
  x,
  type,
  dim = NULL,
  miss = FALSE,
  min = NULL,
  max = NULL,
  values = NULL,
  inf = FALSE,
  null = FALSE
)

Arguments

x	argument
type	character "string", "scalar", "vector", "matrix"
dim	vector/matrix dimensionality: integer scalar/vector
miss	accept missing values: logical
min	lower limit: numeric
max	upper limit: numeric
values	only accept specific values: vector
inf	accept infinite (Inf or -Inf) values: logical
null	accept NULL: logical

Examples

cornet:::.check(0.5,type="scalar",min=0,max=1)

---

Equality

Description

Verifies whether two or more arguments are identical.

Usage

.equal(..., na.rm = FALSE)

Arguments

...	scalars, vectors, or matrices of equal dimensions
na.rm	remove missing values: logical

Examples

cornet:::.equal(1,1,1)

---

Data simulation

Description

Simulates data for unit tests

Usage

.simulate(n, p, cor = 0, prob = 0.1, sd = 1, exp = 1, frac = 1)

Arguments

n	sample size: positive integer
p	covariate space: positive integer
cor	correlation coefficient : numeric between $0$ and $1$
prob	effect proportion: numeric between $0$ and $1$
sd	standard deviation: positive numeric
exp	exponent: positive numeric
frac	class proportion: numeric between $0$ and $1$

Details

For simulating correlated features (cor$>0$), this function requires the R package MASS (see mvrnorm).

Value

Returns invisible list with elements y and X.

Examples

data <- cornet:::.simulate(n=10,p=20)
names(data)

---

Single-split test

Description

Compares models for a continuous response with a cut-off value.

Usage

.test(y, cutoff, X, alpha = 1, type.measure = "deviance")

Arguments

y	continuous outcome: vector of length $n$
cutoff	cut-off point for dichotomising outcome into classes: meaningful value between min(y) and max(y)
X	features: numeric matrix with $n$ rows (samples) and $p$ columns (variables)
alpha	elastic net mixing parameter: numeric between $0$ (ridge) and $1$ (lasso)
type.measure	loss function for binary classification: character "deviance", "mse", "mae", or "class" (see cv.glmnet)

Details

Splits samples into $80$ percent for training and $20$ percent for testing, calculates squared deviance residuals of logistic and combined regression, conducts the paired one-sided Wilcoxon signed rank test, and returns the $p$-value. For the multi-split test, use the median $p$-value from $50$ single-split tests (van de Wiel 2009).

Examples

n <- 100; p <- 200
y <- rnorm(n)
X <- matrix(rnorm(n*p),nrow=n,ncol=p)
cornet:::.test(y=y,cutoff=0,X=X)

---

Extract estimated coefficients

Description

Extracts estimated coefficients from linear and logistic regression, under the penalty parameter that minimises the cross-validated loss.

Usage

## S3 method for class 'cornet'
coef(object, ...)

Arguments

object	cornet object
...	further arguments (not applicable)

Value

This function returns a matrix with $n$ rows and two columns, where $n$ is the sample size. It includes the estimated coefficients from linear regression (1st column: "beta") and logistic regression (2nd column: "gamma").

Examples

n <- 100; p <- 200
y <- rnorm(n)
X <- matrix(rnorm(n*p),nrow=n,ncol=p)
net <- cornet(y=y,cutoff=0,X=X)
coef(net)

---

Combined regression

Description

Implements lasso and ridge regression for dichotomised outcomes. Such outcomes are not naturally but artificially binary. They indicate whether an underlying measurement is greater than a threshold.

Usage

cornet(
  y,
  cutoff,
  X,
  alpha = 1,
  npi = 101,
  pi = NULL,
  nsigma = 99,
  sigma = NULL,
  nfolds = 10,
  foldid = NULL,
  type.measure = "deviance",
  ...
)

Arguments

y	continuous outcome: vector of length $n$
cutoff	cut-off point for dichotomising outcome into classes: meaningful value between min(y) and max(y)
X	features: numeric matrix with $n$ rows (samples) and $p$ columns (variables)
alpha	elastic net mixing parameter: numeric between $0$ (ridge) and $1$ (lasso)
npi	number of pi values (weighting)
pi	pi sequence: vector of increasing values in the unit interval; or NULL (default sequence)
nsigma	number of sigma values (scaling)
sigma	sigma sequence: vector of increasing positive values; or NULL (default sequence)
nfolds	number of folds: integer between $3$ and $n$
foldid	fold identifiers: vector with entries between $1$ and nfolds; or NULL (balance)
type.measure	loss function for binary classification: character "deviance", "mse", "mae", or "class" (see cv.glmnet)
...	further arguments passed to glmnet

Details

The argument family is unavailable, because this function fits a gaussian model for the numeric response, and a binomial model for the binary response.

Linear regression uses the loss function "deviance" (or "mse"), but the loss is incomparable between linear and logistic regression.

The loss function "auc" is unavailable for internal cross-validation. If at all, use "auc" for external cross-validation only.

Value

Returns an object of class cornet, a list with multiple slots:

• gaussian: fitted linear model, class glmnet

• binomial: fitted logistic model, class glmnet

• sigma: scaling parameters sigma, vector of length nsigma

• pi: weighting parameters pi, vector of length npi

• cvm: evaluation loss, matrix with nsigma rows and npi columns

• sigma.min: optimal scaling parameter, positive scalar

• pi.min: optimal weighting parameter, scalar in unit interval

• cutoff: threshold for dichotomisation

References

Armin Rauschenberger and Enrico Glaab (2023). "Predicting artificial binary outcomes from high-dimensional data in biomedicine". Journal of Applied Statistics. In press. doi:10.1080/02664763.2023.2233057

See Also

Methods for objects of class cornet include coef and predict.

Examples

n <- 100; p <- 200
y <- rnorm(n)
X <- matrix(rnorm(n*p),nrow=n,ncol=p)
net <- cornet(y=y,cutoff=0,X=X)
net

---

Performance measurement

Description

Compares models for a continuous response with a cut-off value.

Usage

cv.cornet(
  y,
  cutoff,
  X,
  alpha = 1,
  nfolds.ext = 5,
  nfolds.int = 10,
  foldid.ext = NULL,
  foldid.int = NULL,
  type.measure = "deviance",
  rf = FALSE,
  xgboost = FALSE,
  ...
)

Arguments

y	continuous outcome: vector of length $n$
cutoff	cut-off point for dichotomising outcome into classes: meaningful value between min(y) and max(y)
X	features: numeric matrix with $n$ rows (samples) and $p$ columns (variables)
alpha	elastic net mixing parameter: numeric between $0$ (ridge) and $1$ (lasso)
nfolds.ext	number of external folds
nfolds.int	internal fold identifiers: vector of length $n$ with entries between $1$ and nfolds.int; or NULL
foldid.ext	external fold identifiers: vector of length $n$ with entries between $1$ and nfolds.ext; or NULL
foldid.int	number of internal folds
type.measure	loss function for binary classification: character "deviance", "mse", "mae", or "class" (see cv.glmnet)
rf	comparison with random forest: logical
xgboost	comparison with extreme gradient boosting: logical
...	further arguments passed to cornet or glmnet

Details

Computes the cross-validated loss of logistic and combined regression.

Examples

## Not run: n <- 100; p <- 200
y <- rnorm(n)
X <- matrix(rnorm(n*p),nrow=n,ncol=p)
start <- Sys.time()
loss <- cv.cornet(y=y,cutoff=0,X=X)
end <- Sys.time()
end - start

loss
## End(Not run)

---

Plot loss matrix

Description

Plots the loss for different combinations of scaling (sigma) and weighting (pi) parameters.

Usage

## S3 method for class 'cornet'
plot(x, ...)

Arguments

x	cornet object
...	further arguments (not applicable)

Value

This function plots the evaluation loss (cvm). Whereas the matrix has sigma in the rows, and pi in the columns, the plot has sigma on the $x$-axis, and pi on the $y$-axis. For all combinations of sigma and pi, the colour indicates the loss. If the R package RColorBrewer is installed, blue represents low. Otherwise, red represents low. White always represents high.

Examples

n <- 100; p <- 200
y <- rnorm(n)
X <- matrix(rnorm(n*p),nrow=n,ncol=p)
net <- cornet(y=y,cutoff=0,X=X)
plot(net)

---

Predict binary outcome

Description

Predicts the binary outcome with linear, logistic, and combined regression.

Usage

## S3 method for class 'cornet'
predict(object, newx, type = "probability", ...)

Arguments

object	cornet object
newx	covariates: numeric matrix with $n$ rows (samples) and $p$ columns (variables)
type	"probability", "odds", "log-odds"
...	further arguments (not applicable)

Details

For linear regression, this function tentatively transforms the predicted values to predicted probabilities, using a Gaussian distribution with a fixed mean (threshold) and a fixed variance (estimated variance of the numeric outcome).

Examples

n <- 100; p <- 200
y <- rnorm(n)
X <- matrix(rnorm(n*p),nrow=n,ncol=p)
net <- cornet(y=y,cutoff=0,X=X)
predict(net,newx=X)

---

Combined regression

Description

Prints summary of cornet object.

Usage

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

Arguments

x	cornet object
...	further arguments (not applicable)

Value

Returns sample size $n$, number of covariates $p$, information on dichotomisation, tuned scaling parameter (sigma), tuned weighting parameter (pi), and corresponding loss.

Examples

n <- 100; p <- 200
y <- rnorm(n)
X <- matrix(rnorm(n*p),nrow=n,ncol=p)
net <- cornet(y=y,cutoff=0,X=X)
print(net)

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