The degree of shrinkage, or equivalently, the number of non-zero effects selected by EBglmnet are
controlled by the hyperparameters in the prior distribution, which can be obtained
via Cross Validation (CV). This function performs k-fold CV for hyperparameter selection, and
outputs the model fit results using the optimal parameters. Therefore, this function runs
EBglmnet for (k x n_parameters + 1) times. By default, EBlasso-NE tests 20
\(\lambda\)s , EBEN tests an additional 10 \(\alpha\)s (thus a total of 200 pair of
hyperparameters), and EBlasso-NEG tests up to 25 pairs of (a,b).
cv.EBglmnet(x, y, family=c("gaussian","binomial"),
prior= c("lassoNEG","lasso","elastic net"), nfolds=5,
foldId, verbose = 0)
matrix of CV result with columns of:
column 1: hyperparameter1
column 2: hyperparameter2
column 3: prediction metrics/Criteria
column 4: standard error in the k-fold CV.
Prediction metrics is the mean square error (MSE) for Gaussian model and mean log likelihood (logL) for the binomial model.
the hyperparameters that yield the smallest MSE or the largest logL.
model fit using the optimal parameters computed by CV. See EBglmnet for values in this item.
the Wald Score for the posterior distribution. See (Huang A., Martin E., et al., 2014b) for using Wald Score to identify significant effect set.
model intercept. This parameter is not shrunk (assumes uniform prior).
the residual variance if the Gaussian family is assumed in the GLM
the log Likelihood if the Binomial family is assumed in the GLM
the hyperparameter(s) used to fit the model
the GLM family specified in this function call
the prior used in this function call
the call that produced this object
number of observations
number of folds in CV
input matrix of dimension n x p; each row is an
observation vector, and each column is a candidate variable. When epistasis is considered, users do not need
to create a giant matrix including both main and interaction terms. Instead, x should always be
the matrix corresponding to the p main effects, and cv.EBglmnet will generate the interaction terms
dynamically during running time.
response variable. Continuous for family="gaussian", and binary for
family="binomial". For binary response variable, y can be a Boolean or numeric vector, or factor type
array.
model type taking values of "gaussian" (default) or "binomial".
prior distribution to be used. Taking values of "lassoNEG"(default), "lasso", and "elastic net". All priors will produce a sparse outcome of the regression coefficients; see Details for choosing priors.
number of n-fold CV. nfolds typically >=3. Although nfolds
can be as large as the sample size (leave-one-out CV), it will be computationally intensive for large datasets. Default value is nfolds=5.
an optional vector of values between 1 and nfolds
identifying which fold each observation is assigned to. If not supplied, each of the n samples will be
assigned to the nfolds randomly.
parameter that controls the level of message output from EBglment. It takes values from 0 to 5; larger verbose displays more messages. 0 is recommended for CV to avoid excessive outputs. Default value for verbose is minimum message output.
Anhui Huang and Dianting Liu
Dept of Electrical and Computer Engineering, Univ of Miami, Coral Gables, FL
The three priors in EBglmnet all contain hyperparameters that control how heavy the tail probabilities are. Different values of the hyperparameters will yield different number of non-zero effects retained in the model.
Appropriate selection of their values is required to obtain optimal results, and CV is the most
oftenly used method. For Gaussian model, CV determines the optimal hyperparameter values that yield
the minimum square error. In Binomial model, CV calculates the mean logLikelihood in each of
the left out fold, and chooses the values that yield the maximum mean logLikelihood value of the k-folds.
See EBglmnet for the details of hyperparameters in each prior distribution.
Cai, X., Huang, A., and Xu, S. (2011). Fast empirical Bayesian LASSO for multiple quantitative trait locus mapping. BMC Bioinformatics 12, 211.
Huang A, Xu S, Cai X. (2013). Empirical Bayesian LASSO-logistic regression for multiple binary trait locus mapping. BMC genetics 14(1):5.
Huang, A., Xu, S., and Cai, X. (2014a). Empirical Bayesian elastic net for multiple quantitative trait locus mapping. Heredity 10.1038/hdy.2014.79
uang, A., E. Martin, et al. (2014b). Detecting genetic interactions in pathway-based genome-wide association studies. Genet Epidemiol 38(4): 300-309.
rm(list = ls())
library(EBglmnet)
#Use R built-in data set state.x77
y= state.x77[,"Life Exp"]
xNames = c("Population","Income","Illiteracy", "Murder","HS Grad","Frost","Area")
x = state.x77[,xNames]
#
#Gaussian Model
#lassoNEG prior as default
out = cv.EBglmnet(x,y)
out$fit
#lasso prior
out = cv.EBglmnet(x,y,prior= "lasso")
out$fit
#elastic net prior
out = cv.EBglmnet(x,y,prior= "elastic net")
out$fit
#
#Binomial Model
#create a binary response variable
yy = y>mean(y);
out = cv.EBglmnet(x,yy,family="binomial")
out$fit
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