Package 'glmgraph' reference manual

Title:	Graph-Constrained Regularization for Sparse Generalized Linear Models
Description:	We propose to use sparse regression model to achieve variable selection while accounting for graph-constraints among coefficients. Different linear combination of a sparsity penalty(L1) and a smoothness(MCP) penalty has been used, which induces both sparsity of the solution and certain smoothness on the linear coefficients.
Authors:	Li Chen, Jun Chen
Maintainer:	Li Chen <[email protected]>
License:	GPL-2
Version:	1.0.3
Built:	2026-09-17 08:51:01 UTC
Source:	https://github.com/cran/glmgraph

Fit a GLM with a combination of sparse and smooth regularization

Description

Fit a generalized linear model at grids of tuning parameter via penalized maximum likelihood. The regularization path is computed for a combination of sparse and smooth penalty at two grids of values for the regularization parameter lambda1(Lasso or MCP penalty) and lambda2(Laplacian penalty). Fits linear, logistic regression models.

Details

Package:	glmgraph
Type:	Package
Version:	1.0-0
Date:	2015-03-11
License:	GPL-2

The algorithm accepts a design matrix X, a vector of responses Y and a Laplacian matrix L. Produces the regularization path over the grid of tuning parameter lambda1 and lambda2. It consists of the following main functions
glmgraph
cv.glmgraph
plot.glmgraph
coef.glmgraph
predict.glmgraph

Author(s)

Li Chen <[email protected]>, Jun Chen <[email protected]>

References

Li Chen. Han Liu. Hongzhe Li. Jun Chen(2015) glmgraph: Graph-constrained Regularization for Sparse Generalized Linear Models.(Working paper)

Examples

 set.seed(1234)
 library(glmgraph)
 n <- 100
 p1 <- 10
 p2 <- 90
 p <- p1+p2
 X <- matrix(rnorm(n*p), n,p)
 magnitude <- 1
 ## Construct Adjacency and Laplacian matrices
 A <- matrix(rep(0,p*p),p,p)
 A[1:p1,1:p1] <- 1
 A[(p1+1):p,(p1+1):p] <- 1
 diag(A) <- 0
 diagL <- apply(A,1,sum)
 L <- -A
 diag(L) <- diagL
 btrue <- c(rep(magnitude,p1),rep(0,p2))
 intercept <- 0
 eta <- intercept+X%*%btrue
 Y <- eta+rnorm(n)
 obj <- glmgraph(X,Y,L,family="gaussian")
 plot(obj)
 betas <- coef(obj)
 betas <- coef(obj,lambda1=c(0.1,0.2))
 yhat <- predict(obj,X,type="response")
 cv.obj <- cv.glmgraph(X,Y,L)
 plot(cv.obj)
 beta.min <- coef(cv.obj)
 yhat.min <- predict(cv.obj,X)
 
set.seed(1234)
 library(glmgraph)
 n <- 100
 p1 <- 10
 p2 <- 90
 p <- p1+p2
 X <- matrix(rnorm(n*p), n,p)
 magnitude <- 1
 ## Construct Adjacency and Laplacian matrices
 A <- matrix(rep(0,p*p),p,p)
 A[1:p1,1:p1] <- 1
 A[(p1+1):p,(p1+1):p] <- 1
 diag(A) <- 0
 diagL <- apply(A,1,sum)
 L <- -A
 diag(L) <- diagL
 btrue <- c(rep(magnitude,p1),rep(0,p2))
 intercept <- 0
 eta <- intercept+X%*%btrue
 Y <- eta+rnorm(n)
 obj <- glmgraph(X,Y,L,family="gaussian")
 plot(obj)
 betas <- coef(obj)
 betas <- coef(obj,lambda1=c(0.1,0.2))
 yhat <- predict(obj,X,type="response")
 cv.obj <- cv.glmgraph(X,Y,L)
 plot(cv.obj)
 beta.min <- coef(cv.obj)
 yhat.min <- predict(cv.obj,X)

Retrieve coefficients from a fitted "cv.glmgraph" object.

Description

Retrieve coefficients from a fitted "cv.glmgraph" object based on the chosen regularization parameters from cross validation.

Usage

## S3 method for class 'cv.glmgraph'
coef(object,s,...)
## S3 method for class 'cv.glmgraph'
coef(object,s,...)

Arguments

object

Fitted "cv.glmgraph" model object.

s

Either "lambda1.min" or "lambda1.1se". If "lambda1.min" is used, coefficients of best cross validation criteria(minimum "mse" or "mae" if family is "gaussian"; maximum "auc" or minimum "deviance" if family is "binomial") are returned. Otherwise, coefficients based on one-standard error rule are returned. The default value is "lambda1.min".

...

Other parameters to coef

Author(s)

Li Chen <[email protected]> , Jun Chen <[email protected]>

References

Li Chen. Han Liu. Hongzhe Li. Jun Chen. (2015) glmgraph: Graph-constrained Regularization for Sparse Generalized Linear Models.(Working paper)

Examples

 set.seed(1234)
 library(glmgraph)
 n <- 100
 p1 <- 10
 p2 <- 90
 p <- p1+p2
 X <- matrix(rnorm(n*p), n,p)
 magnitude <- 1
 ## construct laplacian matrix from adjacency matrix
 A <- matrix(rep(0,p*p),p,p)
 A[1:p1,1:p1] <- 1
 A[(p1+1):p,(p1+1):p] <- 1
 diag(A) <- 0
 diagL <- apply(A,1,sum)
 L <- -A
 diag(L) <- diagL
 btrue <- c(rep(magnitude,p1),rep(0,p2))
 intercept <- 0
 eta <- intercept+X%*%btrue 
 ### gaussian
 Y <- eta+rnorm(n)
 cv.obj <- cv.glmgraph(X,Y,L)
 beta.min <- coef(cv.obj)
set.seed(1234)
 library(glmgraph)
 n <- 100
 p1 <- 10
 p2 <- 90
 p <- p1+p2
 X <- matrix(rnorm(n*p), n,p)
 magnitude <- 1
 ## construct laplacian matrix from adjacency matrix
 A <- matrix(rep(0,p*p),p,p)
 A[1:p1,1:p1] <- 1
 A[(p1+1):p,(p1+1):p] <- 1
 diag(A) <- 0
 diagL <- apply(A,1,sum)
 L <- -A
 diag(L) <- diagL
 btrue <- c(rep(magnitude,p1),rep(0,p2))
 intercept <- 0
 eta <- intercept+X%*%btrue 
 ### gaussian
 Y <- eta+rnorm(n)
 cv.obj <- cv.glmgraph(X,Y,L)
 beta.min <- coef(cv.obj)

Retrieve coefficients from a fitted "glmgraph" object.

Description

Retrieve coefficients from a fitted "glmgraph" object, depending on the user-specified regularization parameters.

Usage

## S3 method for class 'glmgraph'
coef(object,lambda1,lambda2,...)
## S3 method for class 'glmgraph'
coef(object,lambda1,lambda2,...)

Arguments

object

Fitted "glmgraph" model object.

lambda1

Values of the regularization parameter lambda1 at which retrieval of coefficients are requested. For values of lambda1 not in the sequence of fitted models, linear interpolation is used. However, lambda1 should be within the range of lambda1 used to fit glmgraph object.

lambda2

The user-specified regularization lambda2 should be exactly subset of the lambda2 used to fit glmgraph object. Linear interpolation is not used.

...

Other parameters to coef

Details

If lambda1 and lambda2 are missing, all coefficients of fitted glmgraph object will be returned. If only lambda1 is missing, then coefficients of specified lambda2 will be returned.

Value

The object returned depends on type.

Author(s)

Li Chen <[email protected]>, Jun Chen <[email protected]>

References

Li Chen. Han Liu. Hongzhe Li. Jun Chen. (2015) glmgraph: Graph-constrained Regularization for Sparse Generalized Linear Models.(Working paper)

Examples

 set.seed(1234)
 library(glmgraph)
 n <- 100
 p1 <- 10
 p2 <- 90
 p <- p1+p2
 X <- matrix(rnorm(n*p), n,p)
 magnitude <- 1
 ## construct laplacian matrix from adjacency matrix
 A <- matrix(rep(0,p*p),p,p)
 A[1:p1,1:p1] <- 1
 A[(p1+1):p,(p1+1):p] <- 1
 diag(A) <- 0
 btrue <- c(rep(magnitude,p1),rep(0,p2))
 intercept <- 0
 eta <- intercept+X%*%btrue
 diagL <- apply(A,1,sum)
 L <- -A
 diag(L) <- diagL
 ### gaussian
 Y <- eta+rnorm(n)
 obj <- glmgraph(X,Y,L)
 coefs <- coef(obj)
 coefs <- coef(obj,lambda2=0.01)
 coefs <- coef(obj,lambda1=c(0.11,0.12))
 coefs <- coef(obj,lambda1=c(0.11,0.12),lambda2=0.01)
set.seed(1234)
 library(glmgraph)
 n <- 100
 p1 <- 10
 p2 <- 90
 p <- p1+p2
 X <- matrix(rnorm(n*p), n,p)
 magnitude <- 1
 ## construct laplacian matrix from adjacency matrix
 A <- matrix(rep(0,p*p),p,p)
 A[1:p1,1:p1] <- 1
 A[(p1+1):p,(p1+1):p] <- 1
 diag(A) <- 0
 btrue <- c(rep(magnitude,p1),rep(0,p2))
 intercept <- 0
 eta <- intercept+X%*%btrue
 diagL <- apply(A,1,sum)
 L <- -A
 diag(L) <- diagL
 ### gaussian
 Y <- eta+rnorm(n)
 obj <- glmgraph(X,Y,L)
 coefs <- coef(obj)
 coefs <- coef(obj,lambda2=0.01)
 coefs <- coef(obj,lambda1=c(0.11,0.12))
 coefs <- coef(obj,lambda1=c(0.11,0.12),lambda2=0.01)

Cross-validation for glmgraph

Description

Performs k-fold cross validation for glmgraph

Usage

cv.glmgraph(X,Y,L,...,type.measure=c("mse","mae","deviance","auc"),nfolds=5,trace=TRUE)
cv.glmgraph(X,Y,L,...,type.measure=c("mse","mae","deviance","auc"),nfolds=5,trace=TRUE)

Arguments

X

X matrix as in glmgraph.

Y

Response Y as in glmgraph.

L

User-specified Laplacian matrix L as in glmgraph.

...

Additional arguments as in glmgraph.

type.measure

if family is "gaussian", the type.measure option is "mse"(mean squared error) or "mae"(mean absolute error); if family is "binomial", the type.measure option is "deviance" or "auc"(area under the curve). The default is "mse".

nfolds

The number of cross-validation folds. Default is 5.

trace

Print out the cross validation steps if trace is specified TRUE.

Details

The function runs glmgraph nfolds+1 times; the first to get the lambda1 and lambda2 sequence, and then the remainder to compute the fit with each of the folds omitted. The error is accumulated, and the average error and standard deviation over the folds is computed. Note also that the results of cv.glmgraph are random, since the folds are selected at random. Users can reduce this randomness by running cv.glmgraph many times, and averaging the error curves.

Value

An object "cv.glmgraph" containing:

obj

The fitted glmgraph object for the whole data.

cvmat

A data frame summarized cross validation results, which could be obtained by print function. It has lambda2,lambda1.min,cvmin,semin,lambda1.1se as columns. Each row represents that for this lambda2, lambda1 with best type.measure cvmin is chosen and reported as lambda1.min. If one standard error rule is applied, lambda1.1se and its corresponding best type.measure value semin is reported.

cvm

The mean cross-validated type.measure value. A list of vector contains type.measure. Each element of the list is a vector that is type.measure value for one lambda2 across all lambda1 sequence averaged across K-fold.

cvsd

The estimate of standard error of cvm.

cvmin

Best cross-validation type.measure value across all combination of lambda1 and lambda2. It is minimum "mse" or "mae" if family is "gaussian"; it is the maximum "auc" or minimum "deviance" if family is "binomial".

cv.1se

Simliar to cvmin except one standard error rule is applied.

lambda1.min

Coupled with lambda2.min is the optimal regularization parameter selection.

lambda2.min

Coupled with lambda1.min is the optimal regularization parameter selection.

lambda1.1se

Coupled with lambda2.1se is the optimal regularization parameter selection if one standard error rule is applied.

lambda2.1se

Coupled with lambda1.1se is the optimal regularization parameter selection if one standard error rule is applied.

beta.min

Estimated beta with best type.measure value with the regularization parameter of lambda1.min and lambda2.min.

beta.1se

Estimated beta with best type.measure value with the regularization parameter of lambda1.1se and lambda2.1se.

Author(s)

Li Chen <[email protected]> , Jun Chen <[email protected]>

References

Li Chen. Han Liu. Hongzhe Li. Jun Chen(2015) glmgraph: Graph-constrained Regularization for Sparse Generalized Linear Models.(Working paper)

Examples

 set.seed(1234)
 library(glmgraph)
 n <- 100
 p1 <- 10
 p2 <- 90
 p <- p1+p2
 X <- matrix(rnorm(n*p), n,p)
 magnitude <- 1
 ## construct laplacian matrix from adjacency matrix
 A <- matrix(rep(0,p*p),p,p)
 A[1:p1,1:p1] <- 1
 A[(p1+1):p,(p1+1):p] <- 1
 diag(A) <- 0
 diagL <- apply(A,1,sum)
 L <- -A
 diag(L) <- diagL
 btrue <- c(rep(magnitude,p1),rep(0,p2))
 intercept <- 0
 eta <- intercept+X%*%btrue
 ### gaussian
 Y <- eta+rnorm(n)
 cv.obj <- cv.glmgraph(X,Y,L,penalty="lasso",lambda2=c(0,1.28))
 beta.min <- coef(cv.obj)
 print(cv.obj)
 ### binomial
 Y <- rbinom(n,1,prob=1/(1+exp(-eta)))
 cv.obj <- cv.glmgraph(X,Y,L,family="binomial",lambda2=c(0,1.28),penalty="lasso",type.measure="auc")
 beta.min <- coef(cv.obj)
 print(cv.obj)
set.seed(1234)
 library(glmgraph)
 n <- 100
 p1 <- 10
 p2 <- 90
 p <- p1+p2
 X <- matrix(rnorm(n*p), n,p)
 magnitude <- 1
 ## construct laplacian matrix from adjacency matrix
 A <- matrix(rep(0,p*p),p,p)
 A[1:p1,1:p1] <- 1
 A[(p1+1):p,(p1+1):p] <- 1
 diag(A) <- 0
 diagL <- apply(A,1,sum)
 L <- -A
 diag(L) <- diagL
 btrue <- c(rep(magnitude,p1),rep(0,p2))
 intercept <- 0
 eta <- intercept+X%*%btrue
 ### gaussian
 Y <- eta+rnorm(n)
 cv.obj <- cv.glmgraph(X,Y,L,penalty="lasso",lambda2=c(0,1.28))
 beta.min <- coef(cv.obj)
 print(cv.obj)
 ### binomial
 Y <- rbinom(n,1,prob=1/(1+exp(-eta)))
 cv.obj <- cv.glmgraph(X,Y,L,family="binomial",lambda2=c(0,1.28),penalty="lasso",type.measure="auc")
 beta.min <- coef(cv.obj)
 print(cv.obj)

Fit a GLM with a combination of sparse and smooth regularization

Description

Usage

glmgraph(X, Y, L, family=c("gaussian","binomial"), penalty=c("MCP","lasso") ,
mcpapproach=c("mmcd", "adaptive", "original"),gamma=8,
lambda1,nlambda1=100,lambda2=c(0, 0.01 * 2^(0:7)),eps=1e-3,max.iter=2000,
dfmax=round(ncol(X)/2),penalty.factor=rep(1,ncol(X)),standardize=TRUE,warn=FALSE,...)
glmgraph(X, Y, L, family=c("gaussian","binomial"), penalty=c("MCP","lasso") ,
mcpapproach=c("mmcd", "adaptive", "original"),gamma=8,
lambda1,nlambda1=100,lambda2=c(0, 0.01 * 2^(0:7)),eps=1e-3,max.iter=2000,
dfmax=round(ncol(X)/2),penalty.factor=rep(1,ncol(X)),standardize=TRUE,warn=FALSE,...)

Arguments

X

Input matrix; each row is an observation vector.

Y

Response vector. Quantitative for family="gaussian" or binary(0/1) for family="binomial".

family

Either "gaussian", "binomial", depending on the response.

L

User-specified Laplacian matrix.

penalty

The sparse penalty to be applied to the model. Either "MCP" (the default), or "lasso".

mcpapproach

For family="binomial", three optional algorithms are provided when penalty is set to MCP: "mmcd"(Majorization minimization by coordinate descent); "adaptive"(Adaptive rescaling) and "original"(without any adjustment). For family="gaussian", the option could only be "original".

gamma

The tuning parameter of the MCP penalty.The default value is 8.

nlambda1

The number of lambda1 values. Default is 100.

lambda1

A user-specified sequence of lambda1 values. Typical usage is to have the program compute its own lambda1 sequence based on nlambda1 and lambda1.min.ratio. Supplying a value of lambda1 overrides this. By default, a sequence of values of length nlambda1 is computed, equally spaced on the log scale.

lambda2

A user-specified sequence of lambda2 values. The default value are 0 and 0.01*2^(0:7). The selection of lambda2 depends on the data and should be adapted in some cases. A good suggestion is to try a few lambda2 and plot the results.

eps

Convergence threshold for coordinate descent. Each inner coordinate-descent loop continues until the relative change in the objective function is less than eps1. Default is 1e-3.

max.iter

Maximum number of passes over the data for all lambda1 values. Default is 2000.

dfmax

Limit the maximum number of variables in the model. Useful for very large p. Default value equals to half of p.

penalty.factor

A multiplicative factor for the penalty applied to each coefficient. If supplied, penalty.factor must be a numeric vector of length equal to the number of columns of X. The purpose of penalty.factor is to apply differential penalization if some coefficients are thought to be more likely than others to be in the model. In particular, penalty.factor can be 0, in which case the coefficient is always in the model without shrinkage.

standardize

Logical flag for x variable standardization, prior to fitting the model sequence. The coefficients are always returned on the original scale. Default is standardize=TRUE. If variables are in the same units already, you might not wish to standardize.

warn

Return warning messages for failures to converge and model selection issues. Default is FALSE.

...

Other parameters to glmgraph

Value

An object "glmgraph" containing:

betas

A list of fitted coefficients. The number of rows for each matrix is equal to the number of coefficients, and the number of columns is smaller or equal to nlambda1.

lambda1s

A list of vector. Each vector is a sequence of used lambda1 for each used lambda2.

lambda2

A sequence of lambda2 actually used.

loglik

A list of log likelihood for each value of lambda1 and lambda2.

df

A list of the number of nonzero values for each value of lambda1 and lambda2.

Author(s)

Li Chen <[email protected]>, Jun Chen <[email protected]>

References

Li Chen. Han Liu. Hongzhe Li. Jun Chen. (2015) Graph-constrained Regularization for Sparse Generalized Linear Models.(Working paper)

Examples

	
 set.seed(1234)
 library(glmgraph)
 n <- 100
 p1 <- 10
 p2 <- 90
 p <- p1+p2
 X <- matrix(rnorm(n*p), n,p)
 magnitude <- 1
 A <- matrix(rep(0,p*p),p,p)
 A[1:p1,1:p1] <- 1
 A[(p1+1):p,(p1+1):p] <- 1
 diag(A) <- 0
 btrue <- c(rep(magnitude,p1),rep(0,p2))
 intercept <- 0
 eta <- intercept+X%*%btrue
 ### construct laplacian matrix from adjacency matrix
 diagL <- apply(A,1,sum)
 L <- -A
 diag(L) <- diagL
 ### gaussian
 Y <- eta+rnorm(n)
 obj <- glmgraph(X,Y,L,family="gaussian")
 plot(obj)
 ### binomial
 Y <- rbinom(n,1,prob=1/(1+exp(-eta)))
 obj <- glmgraph(X,Y,L,family="binomial")
 plot(obj) 
 
set.seed(1234)
 library(glmgraph)
 n <- 100
 p1 <- 10
 p2 <- 90
 p <- p1+p2
 X <- matrix(rnorm(n*p), n,p)
 magnitude <- 1
 A <- matrix(rep(0,p*p),p,p)
 A[1:p1,1:p1] <- 1
 A[(p1+1):p,(p1+1):p] <- 1
 diag(A) <- 0
 btrue <- c(rep(magnitude,p1),rep(0,p2))
 intercept <- 0
 eta <- intercept+X%*%btrue
 ### construct laplacian matrix from adjacency matrix
 diagL <- apply(A,1,sum)
 L <- -A
 diag(L) <- diagL
 ### gaussian
 Y <- eta+rnorm(n)
 obj <- glmgraph(X,Y,L,family="gaussian")
 plot(obj)
 ### binomial
 Y <- rbinom(n,1,prob=1/(1+exp(-eta)))
 obj <- glmgraph(X,Y,L,family="binomial")
 plot(obj)

Plot the cross-validation curve produced by cv.glmgraph

Description

Plots the cross-validation curve for the "cv.glmgraph" object, along with standard error bars.

Usage

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

Arguments

x

A "cv.glmgraph" object.

...

Other graphical parameters to plot

Author(s)

Li Chen <[email protected]> , Jun Chen <[email protected]>

References

Li Chen. Han Liu. Hongzhe Li. Jun Chen. (2015) glmgraph: Graph-constrained Regularization for Sparse Generalized Linear Models.(Working paper)

Examples

 set.seed(1234)
 library(glmgraph)
 n <- 100
 p1 <- 10
 p2 <- 90
 p <- p1+p2
 X <- matrix(rnorm(n*p), n,p)
 magnitude <- 1
 A <- matrix(rep(0,p*p),p,p)
 A[1:p1,1:p1] <- 1
 A[(p1+1):p,(p1+1):p] <- 1
 diag(A) <- 0
 btrue <- c(rep(magnitude,p1),rep(0,p2))
 intercept <- 0
 eta <- intercept+X%*%btrue
 ### construct laplacian matrix from adjacency matrix
 diagL <- apply(A,1,sum)
 L <- -A
 diag(L) <- diagL
 ### gaussian
 Y <- eta+rnorm(n)
 cv.obj <- cv.glmgraph(X,Y,L)
 plot(cv.obj)
set.seed(1234)
 library(glmgraph)
 n <- 100
 p1 <- 10
 p2 <- 90
 p <- p1+p2
 X <- matrix(rnorm(n*p), n,p)
 magnitude <- 1
 A <- matrix(rep(0,p*p),p,p)
 A[1:p1,1:p1] <- 1
 A[(p1+1):p,(p1+1):p] <- 1
 diag(A) <- 0
 btrue <- c(rep(magnitude,p1),rep(0,p2))
 intercept <- 0
 eta <- intercept+X%*%btrue
 ### construct laplacian matrix from adjacency matrix
 diagL <- apply(A,1,sum)
 L <- -A
 diag(L) <- diagL
 ### gaussian
 Y <- eta+rnorm(n)
 cv.obj <- cv.glmgraph(X,Y,L)
 plot(cv.obj)

Plot coefficients from a "glmgraph" object

Description

Plot solution path for a fitted "glmgraph" object.

Usage

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

Arguments

x

Fitted "glmgraph" model.

...

Other graphical parameters to plot

Author(s)

Li Chen <[email protected]> , Jun Chen <[email protected]>

References

Li Chen. Han Liu. Hongzhe Li. Jun Chen. (2015) glmgraph: Graph-constrained Regularization for Sparse Generalized Linear Models.(Working paper)

Examples

 set.seed(1234)
 library(glmgraph)
 n <- 100
 p1 <- 10
 p2 <- 90
 p <- p1+p2
 X <- matrix(rnorm(n*p), n,p)
 magnitude <- 1
 ### construct laplacian matrix from adjacency matrix
 A <- matrix(rep(0,p*p),p,p)
 A[1:p1,1:p1] <- 1
 A[(p1+1):p,(p1+1):p] <- 1
 diag(A) <- 0
 btrue <- c(rep(magnitude,p1),rep(0,p2))
 intercept <- 0
 eta <- intercept+X%*%btrue
 diagL <- apply(A,1,sum)
 L <- -A
 diag(L) <- diagL
 ### gaussian
 Y <- eta+rnorm(n)
 obj <- glmgraph(X,Y,L)
 plot(obj)
 ### binomial
 Y <- rbinom(n,1,prob=1/(1+exp(-eta)))
 obj <- glmgraph(X,Y,L,family="binomial")
 plot(obj) 

set.seed(1234)
 library(glmgraph)
 n <- 100
 p1 <- 10
 p2 <- 90
 p <- p1+p2
 X <- matrix(rnorm(n*p), n,p)
 magnitude <- 1
 ### construct laplacian matrix from adjacency matrix
 A <- matrix(rep(0,p*p),p,p)
 A[1:p1,1:p1] <- 1
 A[(p1+1):p,(p1+1):p] <- 1
 diag(A) <- 0
 btrue <- c(rep(magnitude,p1),rep(0,p2))
 intercept <- 0
 eta <- intercept+X%*%btrue
 diagL <- apply(A,1,sum)
 L <- -A
 diag(L) <- diagL
 ### gaussian
 Y <- eta+rnorm(n)
 obj <- glmgraph(X,Y,L)
 plot(obj)
 ### binomial
 Y <- rbinom(n,1,prob=1/(1+exp(-eta)))
 obj <- glmgraph(X,Y,L,family="binomial")
 plot(obj)

make prediction from a fitted "cv.glmgraph" object.

Description

This function makes predictions from a cross-validated glmgraph model, using the stored "cv.glmgraph" object, and the optimal value chosen for lambda1 and lambda2.

Usage

## S3 method for class 'cv.glmgraph'
predict(object,X,s=c("lambda1.min","lambda1.1se"),
type=c("response", "coefficients","class", "nzeros","link"),...)
## S3 method for class 'cv.glmgraph'
predict(object,X,s=c("lambda1.min","lambda1.1se"),
type=c("response", "coefficients","class", "nzeros","link"),...)

Arguments

object

Fitted "cv.glmgraph" model object.

X

Matrix at which predictions are to be made.

s

Either "lambda1.min" or "lambda1.1se".If "lambda1.min" is used, prediction based on coefficient of best cross validation criteria(minimum "mse" or "mae" if family is "gaussian"; maximum "auc" or minimum "deviance" if family is "binomial") are returned. Otherwise, predictficients based on one-standard error rule are returned. The default value is "lambda1.min".

type

Type of prediction: "link" returns the linear predictors; "response" gives the fitted values; "class" returns the binomial outcome with the highest probability; "coefficients" returns the coefficients; "nzeros" returns a list containing the indices and names of the nonzero variables at each combination of lambda1 and lambda2.

...

Other parameters to predict

Author(s)

Li Chen <[email protected]> , Jun Chen <[email protected]>

References

Li Chen. Han Liu. Hongzhe Li. Jun Chen. (2015) Graph-constrained Regularization for Sparse Generalized Linear Models.(Working paper)

Examples

 set.seed(1234)
 library(glmgraph)
 n <- 100
 p1 <- 10
 p2 <- 90
 p <- p1+p2
 X <- matrix(rnorm(n*p), n,p)
 magnitude <- 1
 ### construct laplacian matrix from adjacency matrix
 A <- matrix(rep(0,p*p),p,p)
 A[1:p1,1:p1] <- 1
 A[(p1+1):p,(p1+1):p] <- 1
 diag(A) <- 0
 btrue <- c(rep(magnitude,p1),rep(0,p2))
 intercept <- 0
 eta <- intercept+X%*%btrue
 diagL <- apply(A,1,sum)
 L <- -A
 diag(L) <- diagL
 ### gaussian
 Y <- eta+rnorm(n)
 cv.obj <- cv.glmgraph(X,Y,L)
 beta.min <- predict(cv.obj,X,type="coefficients")
set.seed(1234)
 library(glmgraph)
 n <- 100
 p1 <- 10
 p2 <- 90
 p <- p1+p2
 X <- matrix(rnorm(n*p), n,p)
 magnitude <- 1
 ### construct laplacian matrix from adjacency matrix
 A <- matrix(rep(0,p*p),p,p)
 A[1:p1,1:p1] <- 1
 A[(p1+1):p,(p1+1):p] <- 1
 diag(A) <- 0
 btrue <- c(rep(magnitude,p1),rep(0,p2))
 intercept <- 0
 eta <- intercept+X%*%btrue
 diagL <- apply(A,1,sum)
 L <- -A
 diag(L) <- diagL
 ### gaussian
 Y <- eta+rnorm(n)
 cv.obj <- cv.glmgraph(X,Y,L)
 beta.min <- predict(cv.obj,X,type="coefficients")

Model predictions based on a fitted "glmgraph" object.

Description

Similar to other predict methods, this function returns predictions from a fitted "glmgraph" object.

Usage

## S3 method for class 'glmgraph'
predict(object, X, type=c("response", "coefficients",
"class", "nzeros","link"), lambda1, lambda2,...)
## S3 method for class 'glmgraph'
predict(object, X, type=c("response", "coefficients",
"class", "nzeros","link"), lambda1, lambda2,...)

Arguments

object

Fitted "glmgraph" model object.

X

Matrix of values at which predictions are to be made.

lambda1

Values of the regularization parameter lambda1 at which predictions are requested. For values of lambda1 not in the sequence of fitted models, linear interpolation is used.

lambda2

Values of the regularization parameter lambda1 at which predictions are requested. Specified lambda2 should be the subet of lambda2 used to fit glmgraph object.

type

...

Other parameters to predict

Author(s)

Li Chen <[email protected]> , Jun Chen <[email protected]>

References

Li Chen. Han Liu. Hongzhe Li. Jun Chen. (2015) glmgraph: Graph-constrained Regularization for Sparse Generalized Linear Models.(Working paper)

Examples

 set.seed(1234)
 library(glmgraph)
 n <- 100
 p1 <- 10
 p2 <- 90
 p <- p1+p2
 X <- matrix(rnorm(n*p), n,p)
 magnitude <- 1
 ## construct laplacian matrix from adjacency matrix
 A <- matrix(rep(0,p*p),p,p)
 A[1:p1,1:p1] <- 1
 A[(p1+1):p,(p1+1):p] <- 1
 diag(A) <- 0
 btrue <- c(rep(magnitude,p1),rep(0,p2))
 intercept <- 0
 eta <- intercept+X%*%btrue
 diagL <- apply(A,1,sum)
 L <- -A
 diag(L) <- diagL
 ### gaussian
 Y <- eta+rnorm(n)
 obj <- glmgraph(X,Y,L)
 res <- predict(obj, X, type="link", lambda1=0.05,lambda2=0.01)
 res <- predict(obj, X, type="response", lambda1=0.05,lambda2=0.01)
 res <- predict(obj,X,type="nzeros",lambda1=0.05,lambda2=0.01)
 ### binomial
 Y <- rbinom(n,1,prob=1/(1+exp(-eta)))
 obj <- glmgraph(X,Y,L,family="binomial")
 res <- predict(obj,X,type="class",lambda1=c(0.05,0.06),lambda2=c(0.02,0.16,0.32))
set.seed(1234)
 library(glmgraph)
 n <- 100
 p1 <- 10
 p2 <- 90
 p <- p1+p2
 X <- matrix(rnorm(n*p), n,p)
 magnitude <- 1
 ## construct laplacian matrix from adjacency matrix
 A <- matrix(rep(0,p*p),p,p)
 A[1:p1,1:p1] <- 1
 A[(p1+1):p,(p1+1):p] <- 1
 diag(A) <- 0
 btrue <- c(rep(magnitude,p1),rep(0,p2))
 intercept <- 0
 eta <- intercept+X%*%btrue
 diagL <- apply(A,1,sum)
 L <- -A
 diag(L) <- diagL
 ### gaussian
 Y <- eta+rnorm(n)
 obj <- glmgraph(X,Y,L)
 res <- predict(obj, X, type="link", lambda1=0.05,lambda2=0.01)
 res <- predict(obj, X, type="response", lambda1=0.05,lambda2=0.01)
 res <- predict(obj,X,type="nzeros",lambda1=0.05,lambda2=0.01)
 ### binomial
 Y <- rbinom(n,1,prob=1/(1+exp(-eta)))
 obj <- glmgraph(X,Y,L,family="binomial")
 res <- predict(obj,X,type="class",lambda1=c(0.05,0.06),lambda2=c(0.02,0.16,0.32))

print a glmgraph object

Description

Print a summary of the cv.glmgraph solution path information during cross validation

Usage

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

Arguments

x

fitted cv.glmgraph object

...

Other parameters to print

Details

The call prints the cvmat object from a fitted cv.glmgraph object. The call also prints the chosen regularization parameters lambda1 and lambda2 along with best cv.type(minimum "mse" or "mae" if family is "gaussian"; maximum "auc" or minimum "deviance" if family is "binomial") after cross validation.

Author(s)

Li Chen <[email protected]> , Jun Chen <[email protected]>

References

Li Chen. Han Liu. Hongzhe Li. Jun Chen. (2015) glmgraph: Graph-constrained Regularization for Sparse Generalized Linear Models.(Working paper)

Examples

 set.seed(1234)
 library(glmgraph)
 n <- 100
 p1 <- 10
 p2 <- 90
 p <- p1+p2
 X <- matrix(rnorm(n*p), n,p)
 magnitude <- 1
 A <- matrix(rep(0,p*p),p,p)
 A[1:p1,1:p1] <- 1
 A[(p1+1):p,(p1+1):p] <- 1
 diag(A) <- 0
 btrue <- c(rep(magnitude,p1),rep(0,p2))
 intercept <- 0
 eta <- intercept+X%*%btrue
 ### construct laplacian matrix from adjacency matrix
 diagL <- apply(A,1,sum)
 L <- -A
 diag(L) <- diagL
 ### gaussian
 Y <- eta+rnorm(n)
 cv.obj <- cv.glmgraph(X,Y,L)
 print(cv.obj)
set.seed(1234)
 library(glmgraph)
 n <- 100
 p1 <- 10
 p2 <- 90
 p <- p1+p2
 X <- matrix(rnorm(n*p), n,p)
 magnitude <- 1
 A <- matrix(rep(0,p*p),p,p)
 A[1:p1,1:p1] <- 1
 A[(p1+1):p,(p1+1):p] <- 1
 diag(A) <- 0
 btrue <- c(rep(magnitude,p1),rep(0,p2))
 intercept <- 0
 eta <- intercept+X%*%btrue
 ### construct laplacian matrix from adjacency matrix
 diagL <- apply(A,1,sum)
 L <- -A
 diag(L) <- diagL
 ### gaussian
 Y <- eta+rnorm(n)
 cv.obj <- cv.glmgraph(X,Y,L)
 print(cv.obj)

Package 'glmgraph'

Help Index

Fit a GLM with a combination of sparse and smooth regularization

Description

Details

Author(s)

References

Examples

Retrieve coefficients from a fitted "cv.glmgraph" object.

Description

Usage

Arguments

Author(s)

References

See Also

Examples

Retrieve coefficients from a fitted "glmgraph" object.

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

Cross-validation for glmgraph

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

Fit a GLM with a combination of sparse and smooth regularization

Description

Usage

Arguments

Value

Author(s)

References

See Also

Examples

Plot the cross-validation curve produced by cv.glmgraph

Description

Usage

Arguments

Author(s)

References

See Also

Examples

Plot coefficients from a "glmgraph" object

Description

Usage

Arguments

Author(s)

References

See Also

Examples

make prediction from a fitted "cv.glmgraph" object.

Description

Usage

Arguments

Author(s)

References

See Also

Examples

Model predictions based on a fitted "glmgraph" object.

Description

Usage

Arguments

Author(s)

References

See Also

Examples

print a glmgraph object

Description

Usage