Package 'SGPR'

Coefficients from an SGP model

Description

A function that extracts the estimated coefficients from an SGP object.

Usage

## S3 method for class 'sgp'
coef(object, lambda, index = 1:length(object$lambda), drop = TRUE, ...)

Arguments

object	A object that was generated with sgp.
lambda	The value of lambda at which the coefficients are to be extracted.
index	The index that indicates the lambda at which the coefficients are to be extracted (alternative to specifying 'lambda').
drop	A Boolean value that specifies whether empty dimensions should be removed.
...	Other parameters of underlying basic functions.

Value

A vector or matrix with the estimated coefficients.

Examples

n <- 100
p <- 12
nr <- 4
g <- paste0("Group ",ceiling(1:p / nr))
X <- matrix(rnorm(n * p), n, p)
b <- c(-3:3)
y_lin <- X[, 1:length(b)] %*% b + 5 * rnorm(n)
y_log <- rbinom(n, 1, exp(y_lin) / (1 + exp(y_lin)))

lin_fit <- sgp(X, y_lin, g, type = "linear")
coef(lin_fit, index = 5:7)

log_fit <- sgp(X, y_log, g, type = "logit")
coef(log_fit, index = 5:7)

---

Coefficients from SGP models

Description

A function that extracts the estimated coefficients from an cross-validated SGP object.

Usage

## S3 method for class 'sgp.cv'
coef(object, lambda = object$lambda.min, index = object$min, ...)

Arguments

object	A object that was generated with sgp.cv.
lambda	The value of lambda at which the coefficients are to be extracted.
index	The index that indicates the lambda at which the coefficients are to be extracted (alternative to specifying 'lambda').
...	Other parameters of underlying basic functions.

Value

A vector or matrix with the estimated coefficients.

Examples

n <- 100
p <- 12
nr <- 4
g <- paste0("Group ",ceiling(1:p / nr))
X <- matrix(rnorm(n * p), n, p)
b <- c(-3:3)
y_lin <- X[, 1:length(b)] %*% b + 5 * rnorm(n)
y_log <- rbinom(n, 1, exp(y_lin) / (1 + exp(y_lin)))

lin_fit <- sgp.cv(X, y_lin, g, type = "linear")
coef(lin_fit)

log_fit <- sgp.cv(X, y_log, g, type = "logit")
coef(log_fit)

---

A function that calculates the loss/cost

Description

A function that calculates the loss/cost

Usage

get.loss(y, pred, type)

Arguments

y	The response vector.
pred	The predicted values for the response.
type	A string indicating the type of regression model (linear or binomial).

Value

The loss of the input vectors.

---

Plots the coefficient path of an SGP object

Description

Produces a coefficient profile plot of the coefficient paths for a fitted SGP object

Usage

## S3 method for class 'sgp'
plot(x, alpha = 1, legend.pos, label = FALSE, log.l = FALSE, norm = FALSE, ...)

Arguments

x	A object that was generated with sgp.
alpha	Tuning parameter for the alpha-blending.
legend.pos	Coordinates or keyword for positioning the legend.
label	A Boolean value that specifies whether the plot should be annotated.
log.l	A Boolean value that specifies whether the horizontal axis should be on the log scale.
norm	A Boolean value that specifies whether the norm of each group should be plotted.
...	Other parameters of underlying basic functions.

Value

A plot object with the coefficient path of an SGP.

Examples

n <- 100
p <- 12
nr <- 4
g <- paste0("Group ",ceiling(1:p / nr))
X <- matrix(rnorm(n * p), n, p)
b <- c(-3:3)
y_lin <- X[, 1:length(b)] %*% b + 5 * rnorm(n)
y_log <- rbinom(n, 1, exp(y_lin) / (1 + exp(y_lin)))

lin_fit <- sgp(X, y_lin, g, type = "linear")
plot(lin_fit, legend.pos = "topright", label = TRUE)
plot(lin_fit,  label = TRUE, norm = TRUE)

log_fit <- sgp(X, y_log, g, type = "logit")
plot(log_fit, legend.pos = "topright", label = TRUE)
plot(log_fit, label = TRUE, norm = TRUE)

---

Plots the cross-validation curve from a SGP object

Description

Plots the cross-validation curve as a function of the lambda values used.

Usage

## S3 method for class 'sgp.cv'
plot(x, log.l = TRUE, highlight = TRUE, col = "firebrick3", ...)

Arguments

x	A object that was generated with sgp.cv.
log.l	A Boolean value that specifies whether the horizontal axis should be on the log scale.
highlight	A Boolean value that specifies whether a vertical line should be added at the value where the cross-validation error is minimized.
col	Controls the color of the dots.
...	Other parameters of underlying basic functions.

Value

A plot object with the cross-validation curve of an SGP.

Examples

n <- 100
p <- 12
nr <- 4
g <- paste0("Group ",ceiling(1:p / nr))
X <- matrix(rnorm(n * p), n, p)
b <- c(-3:3)
y_lin <- X[, 1:length(b)] %*% b + 5 * rnorm(n)
y_log <- rbinom(n, 1, exp(y_lin) / (1 + exp(y_lin)))

lin_fit <- sgp.cv(X, y_lin, g, type = "linear")
plot(lin_fit, col = "blue")

log_fit <- sgp.cv(X, y_log, g, type = "logit")
plot(log_fit, col = "blue")

---

Predictions based on a SGP model

Description

A function that extracts information from a SGP object and performs predictions.

Usage

## S3 method for class 'sgp'
predict(
  object,
  X = NULL,
  extract = c("link", "response", "class", "coef", "vars", "groups", "nvars", "ngroups",
    "norm"),
  lambda,
  index = 1:length(object$lambda),
  ...
)

Arguments

object	A object that was generated with sgp.
X	The design matrix for making predictions.
extract	A string indicating the type of information to return.
lambda	The value of lambda at which predictions should be made.
index	The index that indicates the lambda at which predictions should be made (alternative to specifying 'lambda').
...	Other parameters of underlying basic functions.

Value

Different objects depending on the sting indicated by 'extract'.

Examples

n <- 100
p <- 12
nr <- 4
g <- paste0("Group ",ceiling(1:p / nr))
X <- matrix(rnorm(n * p), n, p)
b <- c(-3:3)
y_lin <- X[, 1:length(b)] %*% b + 5 * rnorm(n)
y_log <- rbinom(n, 1, exp(y_lin) / (1 + exp(y_lin)))

lin_fit <- sgp(X, y_lin, g, type = "linear")
predict(lin_fit, X = X, extract = "nvars")

log_fit <- sgp(X, y_log, g, type = "logit")
predict(log_fit, X = X, extract = "nvars")

---

Predictions based on a SGP models

Description

A function that extracts information from a cross-validated SGP object and performs predictions.

Usage

## S3 method for class 'sgp.cv'
predict(
  object,
  X,
  lambda = object$lambda.min,
  index = object$min,
  extract = c("link", "response", "class", "coefficients", "vars", "groups", "nvars",
    "ngroups", "norm"),
  ...
)

Arguments

object	A object that was generated with sgp.cv.
X	The design matrix for making predictions.
lambda	The value of lambda at which predictions should be made.
index	The index that indicates the lambda at which predictions should be made (alternative to specifying 'lambda').
extract	A string indicating the type of information to return.
...	Other parameters of underlying basic functions.

Value

Different objects depending on the sting indicated by 'extract'.

Examples

n <- 100
p <- 12
nr <- 4
g <- paste0("Group ",ceiling(1:p / nr))
X <- matrix(rnorm(n * p), n, p)
b <- c(-3:3)
y_lin <- X[, 1:length(b)] %*% b + 5 * rnorm(n)
y_log <- rbinom(n, 1, exp(y_lin) / (1 + exp(y_lin)))

lin_fit <- sgp.cv(X, y_lin, g, type = "linear")
predict(lin_fit, X = X, extract = "link")

log_fit <- sgp.cv(X, y_log, g, type = "logit")
predict(log_fit, X = X, extract = "class")

---

Process groupings for a sparse group penalty

Description

A function that checks the group information for possible errors and processes it.

Usage

process.group(group, group.weight)

Arguments

group	A vector that specifies the group membership of each variable in X.
group.weight	A vector specifying weights that are multiplied by the group penalty to account for different group sizes.

Value

A structure containing the prepared group structure and, as an attribute, its labels and group weights.

---

Set up a lambda sequence

Description

A function that sets up a lambda sequence for a sparse group penalty.

Usage

process.lambda(
  X,
  y,
  group,
  Z,
  type,
  alpha,
  lambda.min,
  log.lambda,
  nlambda,
  group.weight,
  ada_mult
)

Arguments

X	The design matrix without intercept with the variables to be selected.
y	The response vector.
group	A vector indicating the group membership of each variable in X.
Z	The design matrix of the variables to be included in the model without penalization.
type	A string indicating the type of regression model (linear or binomial).
alpha	Tuning parameter for the mixture of penalties at group and variable level. A value of 0 results in a selection at group level, a value of 1 results in a selection at variable level and everything in between is bi-level selection.
lambda.min	An integer multiplied by the maximum lambda to define the end of the lambda sequence.
log.lambda	A Boolean value that specifies whether the values of the lambda sequence should be on the log scale.
nlambda	An integer that specifies the length of the lambda sequence.
group.weight	A vector specifying weights that are multiplied by the group penalty to account for different group sizes.
ada_mult	An integer that defines the multiplier for adjusting the convergence threshold.

Value

A vector with values for lambda.

---

Process the arguments about the sparse group penalty

Description

A function that checks arguments about the penalty and translates them to integer (for the C++ code).

Usage

process.penalty(penalty, pvar, pgr, vargamma, grgamma, vartau, grtau, alpha)

Arguments

penalty	A string that specifies the sparse group penalty to be used.
pvar	A string that specifies the penalty used at the variable level.
pgr	A string that specifies the penalty used at the group level.
vargamma	An integer that defines the value of gamma for the penalty at the variable level.
grgamma	An integer that specifies the value of gamma for the penalty at the group level.
vartau	An integer that defines the value of tau for the penalty at the variable level.
grtau	An integer that specifies the value of tau for the penalty at the group level.
alpha	Tuning parameter for the mixture of penalties at group and variable level. A value of 0 results in a selection at group level, a value of 1 results in a selection at variable level and everything in between is bi-level selection.

Value

A list of two integers indicating the penalty for the C++ code.

---

Process X for a sparse group penalty

Description

A function that checks the design matrix X for possible errors and scales it.

Usage

process.X(X, group)

Arguments

X	The design matrix without intercept with the variables to be selected.
group	A vector that specifies the group membership of each variable in X.

Value

A list containing:

X

The standardized design matrix X.

vars

The variable names of the matrix.

center

The center of the variables before the transformation.

scale

The scale of the variables before the transformation.

---

Process y for a sparse group penalty

Description

A function that checks the response vector y for possible errors.

Usage

process.y(y, type)

Arguments

y	The response vector.
type	A string indicating the type of regression model (linear or binomial).

Value

The verified response vector y.

---

Process Z for a sparse group penalty

Description

A function that checks the design matrix Z for possible errors and scales it.

Usage

process.Z(Z)

Arguments

Z	The design matrix of the variables to be included in the model without penalization.

Value

A list containing:

Z

The standardized design matrix Z.

vars

The variable names of the matrix.

center

The center of the variables before the transformation.

scale

The scale of the variables before the transformation.

---

Fit a sparse group regularized regression path

Description

A function that determines the regularization paths for models with sparse group penalties at a grid of values for the regularization parameter lambda.

Usage

sgp(
  X,
  y,
  group = 1:ncol(X),
  penalty = c("sgl", "sgs", "sgm", "sge"),
  alpha = 1/3,
  type = c("linear", "logit"),
  Z = NULL,
  nlambda = 100,
  lambda.min = {
     if (nrow(X) > ncol(X)) 
         1e-04
     else 0.05
 },
  log.lambda = TRUE,
  lambdas,
  prec = 1e-04,
  ada_mult = 2,
  max.iter = 10000,
  standardize = TRUE,
  vargamma = ifelse(pvar == "scad" | penalty == "sgs", 4, 3),
  grgamma = ifelse(pgr == "scad" | penalty == "sgs", 4, 3),
  vartau = 1,
  grtau = 1,
  pvar = c("lasso", "scad", "mcp", "exp"),
  pgr = c("lasso", "scad", "mcp", "exp"),
  group.weight = rep(1, length(unique(group))),
  returnX = FALSE,
  ...
)

Arguments

X	The design matrix without intercept with the variables to be selected.
y	The response vector.
group	A vector indicating the group membership of each variable in X.
penalty	A string that specifies the sparse group penalty to be used.
alpha	Tuning parameter for the mixture of penalties at group and variable level. A value of 0 results in a selection at group level, a value of 1 results in a selection at variable level and everything in between is bi-level selection.
type	A string indicating the type of regression model (linear or binomial).
Z	The design matrix of the variables to be included in the model without penalization.
nlambda	An integer that specifies the length of the lambda sequence.
lambda.min	An integer multiplied by the maximum lambda to define the end of the lambda sequence.
log.lambda	A Boolean value that specifies whether the values of the lambda sequence should be on the log scale.
lambdas	A user supplied vector with values for lambda.
prec	The convergence threshold for the algorithm.
ada_mult	An integer that defines the multiplier for adjusting the convergence threshold.
max.iter	The convergence threshold for the algorithm.
standardize	An integer that defines the multiplier for adjusting the convergence threshold.
vargamma	An integer that defines the value of gamma for the penalty at the variable level.
grgamma	An integer that specifies the value of gamma for the penalty at the group level.
vartau	An integer that defines the value of tau for the penalty at the variable level.
grtau	An integer that specifies the value of tau for the penalty at the group level.
pvar	A string that specifies the penalty used at the variable level.
pgr	A string that specifies the penalty used at the group level.
group.weight	A vector specifying weights that are multiplied by the group penalty to account for different group sizes.
returnX	A Boolean value that specifies whether standardized design matrix should be returned.
...	Other parameters of underlying basic functions.

Details

Two options are available for choosing a penalty. With the argument penalty, the methods Sparse Group LASSO, Sparse Group SCAD, Sparse Group MCP and Sparse Group EP can be selected with the abbreviations sgl, sgs, sgm and sge. Alternatively, penalties can be combined additively with the arguments pvar and pgr, where pvar is the penalty applied at the variable level and pgr is the penalty applied at the group level. The options are lasso, scad, mcp and exp for Least Absolute Shrinkage and Selection Operator, Smoothly Clipped Absolute Deviation, Minimax Concave Penalty and Exponential Penalty.

Value

A list containing:

beta

A vector with estimated coefficients.

type

A string indicating the type of regression model (linear or binomial).

group

A vector indicating the group membership of the individual variables in X.

lambdas

The sequence of lambda values.

alpha

Tuning parameter for the mixture of penalties at group and variable level.

loss

A vector containing either the residual sum of squares (linear) or the negative log-likelihood (binomial).

prec

The convergence threshold used for each lambda.

n

Number of observations.

penalty

A string indicating the sparse group penalty used.

df

A vector of pseudo degrees of freedom for each lambda.

iter

A vector of the number of iterations for each lambda.

group.weight

A vector of weights multiplied by the group penalty.

y

The response vector.

X

The design matrix without intercept.

References

• Buch, G., Schulz, A., Schmidtmann, I., Strauch, K., and Wild, P. S. (2024) Sparse Group Penalties for bi-level variable selection. Biometrical Journal, 66, 2200334. doi:10.1002/bimj.202200334

• Simon, N., Friedman, J., Hastie, T., and Tibshirani, R. (2011) A Sparse-Group Lasso. Journal of computational and graphical statistics, 22(2), 231-245. doi:10.1080/10618600.2012.681250

• Breheny, P., and Huang J. (2009) Penalized methods for bi-level variable selection. Statistics and its interface, 2: 369-380. doi:10.4310/sii.2009.v2.n3.a10

Examples

# Generate data
 n <- 100
 p <- 200
 nr <- 10
 g <- ceiling(1:p / nr)
 X <- matrix(rnorm(n * p), n, p)
 b <- c(-3:3)
 y_lin <- X[, 1:length(b)] %*% b + 5 * rnorm(n)
 y_log <- rbinom(n, 1, exp(y_lin) / (1 + exp(y_lin)))

# Linear regression
 lin_fit <- sgp(X, y_lin, g, type = "linear", penalty = "sgl")
 plot(lin_fit)
 lin_fit <- sgp(X, y_lin, g, type = "linear", penalty = "sgs")
 plot(lin_fit)
 lin_fit <- sgp(X, y_lin, g, type = "linear", penalty = "sgm")
 plot(lin_fit)
 lin_fit <- sgp(X, y_lin, g, type = "linear", penalty = "sge")
 plot(lin_fit)

# Logistic regression
 log_fit <- sgp(X, y_log, g, type = "logit", penalty = "sgl")
 plot(log_fit)
 log_fit <- sgp(X, y_log, g, type = "logit", penalty = "sgs")
 plot(log_fit)
 log_fit <- sgp(X, y_log, g, type = "logit", penalty = "sgm")
 plot(log_fit)
 log_fit <- sgp(X, y_log, g, type = "logit", penalty = "sge")
 plot(log_fit)

---

Cross-validation for sparse group penalties

Description

A function that performs k-fold cross-validation for sparse group penalties for a lambda sequence.

Usage

sgp.cv(
  X,
  y,
  group = 1:ncol(X),
  Z = NULL,
  ...,
  nfolds = 10,
  seed,
  fold,
  type,
  returnY = FALSE,
  print.trace = FALSE
)

Arguments

X	The design matrix without intercept with the variables to be selected.
y	The response vector.
group	A vector indicating the group membership of each variable in X.
Z	The design matrix of the variables to be included in the model without penalization.
...	Other parameters of underlying basic functions.
nfolds	The number of folds for cross-validation.
seed	A seed provided by the user for the random number generator.
fold	A vector of folds specified by the user (default is a random assignment).
type	A string indicating the type of regression model (linear or binomial).
returnY	A Boolean value indicating whether the fitted values should be returned.
print.trace	A Boolean value that specifies whether the beginning of a fold should be printed.

Value

A list containing:

cve

The average cross-validation error for each value of lambda.

cvse

The estimated standard error for each value of cve.

lambdas

The sequence of lambda values.

fit

The sparse group penalty model fitted to the entire data.

fold

The fold assignments for each observation for the cross-validation procedure.

min

The index of lambda corresponding to the minimum cross-validation error.

lambda.min

The value of lambda with the minimum cross-validation error.

null.dev

The deviance for the empty model.

pe

The cross-validation prediction error for each value of lambda (for binomial only).

pred

The fitted values from the cross-validation folds.

Examples

# Generate data
 n <- 100
 p <- 200
 nr <- 10
 g <- ceiling(1:p / nr)
 X <- matrix(rnorm(n * p), n, p)
 b <- c(-3:3)
 y_lin <- X[, 1:length(b)] %*% b + 5 * rnorm(n)
 y_log <- rbinom(n, 1, exp(y_lin) / (1 + exp(y_lin)))

# Linear regression
 lin_fit <- sgp.cv(X, y_lin, g, type = "linear", penalty = "sgl")
 plot(lin_fit)
 predict(lin_fit, extract = "vars")
 lin_fit <- sgp.cv(X, y_lin, g, type = "linear", penalty = "sgs")
 plot(lin_fit)
 predict(lin_fit, extract = "vars")
 lin_fit <- sgp.cv(X, y_lin, g, type = "linear", penalty = "sgm")
 plot(lin_fit)
 predict(lin_fit, extract = "vars")
 lin_fit <- sgp.cv(X, y_lin, g, type = "linear", penalty = "sge")
 plot(lin_fit)
 predict(lin_fit, extract = "vars")

# Logistic regression
 log_fit <- sgp.cv(X, y_log, g, type = "logit", penalty = "sgl")
 plot(log_fit)
 predict(log_fit, extract = "vars")
 log_fit <- sgp.cv(X, y_log, g, type = "logit", penalty = "sgs")
 plot(log_fit)
 predict(log_fit, extract = "vars")
 log_fit <- sgp.cv(X, y_log, g, type = "logit", penalty = "sgm")
 plot(log_fit)
 predict(log_fit, extract = "vars")
 log_fit <- sgp.cv(X, y_log, g, type = "logit", penalty = "sge")
 plot(log_fit)
 predict(log_fit, extract = "vars")

---