mcb {mcb}

Model Confidence Bound

Description

When choosing proper variable selection methods, it is important to consider the uncertainty of a certain method. The MCB for variable selection identifies two nested models (upper and lower confidence bound models) containing the true model at a given confidence level. A good variable selection method is the one of which the MCB under a certain confidence level has the shortest width. When visualizing the variability of model selection and comparing different model selection procedures, Model uncertainty curve is a good graphical tool. A good variable selection method is the one of whose MUC will tend to arch towards the upper left corner. This function aims to obtain the MCB and draw the MUC of certain single model selection method under a coverage rate equal or little higher than user-given confidential level.

Usage

mcb(x, y, B=200, lambda=NA, method='Lasso', level=0.95, seed=122)

Arguments

x

input matrix; each column is an observation vector of certain independent variable, and will be given a name automatically in the order of x1, x2, x3…

y

y is a matrix of one column which presents the response vector B number of bootstrap replicates to perform, default value is 200.

B

number of bootstrap replicates to perform; Default value is 200.

lambda

A user supplied lambda value. It is the penalty tuning parameter for the variable selection method tested. The default value is the optimization outcome automatically computed in consideration of the specific case.

method

Default value is ‘Lasso; user can choose from 'aLasso', 'Lasso', 'SCAD', 'MCP', 'stepwise', 'LAD', 'SQRT'

level

a positive value between 0 and 1, like the concept of confidence level for point estimation; Default value is 0.95

seed

seed for bootstrap procedures; Default value is 122;

Value

The mcb method returns an object of class “mcb” The generic accessor functions mcb, mucplot and mcbframe extract various useful features of the value returned by mcb. An object of class “mcb” is a list containing at least the following components:

mcb

a list containing the bootstrap coverage rate (which is the closest to the user-given confidence level) and the corresponding model confidence bound of the user-chosen variable selection method in the form of lower confidence bound and upper confidence bound.

mucplot

plot of the model uncertainty curve for this specific user-chosen variable selectionmethod.

mcbframe

a dataframe containing all the information about MCBs for the specific variable selectionmethod under all bootstrap coverage rates including width(w), lower confidence bound(lcb) and upper confidence bound(ucb) for each bootstrap coverage rate(bcr)

References

Li,Y., Luo,Y., Ferrari,D., Hu,X. and Qin,Y. (2019) Model Confidence Bounds for Variable Selection. Biometrics, 75:392-403.

Examples

data(Diabetes) # load data
x <- Diabetes[,c('S1', 'S2', 'S3', 'S4', 'S5')]
y <- Diabetes[,c('Y')]
x <- data.matrix(x)
y <- data.matrix(y)
result <- mcb(x=x, y=y)
# plot of the model uncertainty curve
result$mucplot
# a list containing the bootstrap coverage rate and mcb
result$mcb
# a dataframe containing all the information about MCBs
result$mcbframe