glmvsd {glmvsd}

Variable Selection Deviation (VSD)

Description

The package calculates the variable selection deviation (VSD) to measure the uncertainty of the selection in terms of inclusion of predictors in the model.

Usage

glmvsd(x, y, n_train = ceiling(n/2), no_rep = 100,
                 n_train_bound = n_train - 2, n_bound = n - 2,
                 model_check, psi = 1, family = c("gaussian",
                 "binomial"), method = c("union", "customize"),
                 candidate_models, weight_type = c("BIC", "AIC",
                 "ARM"), prior = TRUE, reduce_bias = FALSE)

Arguments

x

Matrix of predictors.

y

Response variable.

n_train

Size of training set when the weight function is ARM or ARM with prior. The default value is n_train=ceiling(n/2).

no_rep

Number of replications when the weight function is ARM and ARM with prior. The default value is no_rep=100.

n_train_bound

When computing the weights using "ARM", the candidate models with the size larger than n_train_bound will be dropped. The default value is n_train-2.

n_bound

When computing the weights using "AIC" or "BIC", the candidate models with the size larger than n_train_bound will be dropped. The default value is n-2.

model_check

The index of the model to be assessed by calculating the VSD measures.

psi

A positive number to control the improvement of the prior weight. The default value is 1.

family

Choose the family for GLM models. So far only gaussian, binomial and tweedie are implemented. The default is gaussian.

method

User chooses one of the union and customize. If method=="union", then the program automatically provides the candidate models as a union of solution paths of Lasso, SCAD, and MCP; If method="customize", the user must provide their own set of candidate models in the input argument candidate_models as a matrix, each row of which is a 0/1 index vector representing whether each variable is included/excluded in the model.

candidate_models

Only available when method="customize". It is a matrix of candidate models, each row of which is a 0/1 index vector representing whether each variable is included/excluded in the model.

weight_type

Options for computing weights for VSD measure. User chooses one of the ARM, AIC and BIC. The default is BIC.

prior

Whether use prior in the weight function. The default is TRUE.

reduce_bias

If the binomial model is used, occasionally the algorithm might has convergence issue when the problem of so-called complete separation or quasi-complete separation happens. Users can set reduce_bias=TRUE to solve the issue. The algorithm will use an adjusted-score approach when ftting the binomial model for computing the weights. This method is developed in Firth, D. (1993). Bias reduction of maximum likelihood estimates. Biometrika 80, 27-38.

Details

See Reference section.

Value

A "glmvsd" object is retured. The components are:

candidate_models_cleaned

Cleaned candidate models: the duplicated candidate models are cleaned; When computing VSD weights using AIC and BIC, the models with more than n-2 variables are removed (n is the number of observaitons); When computing VSD weights using ARM, the models with more than n_train-2 variables are removed (n_train is the number of training observations).

VSD

Variable selection deviation (VSD) value.

VSD_minus

The lower VSD value of model_check, representing the number of predictors in the model (model_check) not quite justified at the present sample size.

VSD_plus

The upper VSD value of model_check model, representing the number of predictors missed by the model (model_check).

Precision

A vector of precision values computed using each candidate model.

Recall

A vector of recall values computed using each candidate model.

Fmeasure

F-measure for the given model under check.

Gmeasure

G-measure for the given model under check.

sd.F

Estimated standard deviation of F-measure for the given model under check.

sd.G

Estimated standard deviation of G-measure for the given model under check.

weight

The weight for each candidate model.

References

Nan, Y. and Yang, Y. (2013), "Variable Selection Diagnostics Measures for High-dimensional Regression," Journal of Computational and Graphical Statistics, 23:3, 636-656.
BugReport: https://github.com/emeryyi/glmvsd

Examples

# REGRESSION CASE

# generate simulation data
n <- 50
p <- 8
beta <- c(3,1.5,0,0,2,0,0,0)
sigma <- matrix(0,p,p)
for(i in 1:p){
   for(j in 1:p) sigma[i,j] <- 0.5^abs(i-j)
}
x <- mvrnorm(n, rep(0,p), sigma)
e <- rnorm(n)
y <- x %*% beta + e

# user provide a model to be checked
model_check <- c(0,1,1,1,0,0,0,1)

# compute VSD for model_check using ARM with prior
v_ARM <- glmvsd(x, y, n_train = ceiling(n/2), 
no_rep=50, model_check = model_check, psi=1, 
family = "gaussian", method = "union", 
weight_type = "ARM", prior = TRUE)

# compute VSD for model_check using AIC
v_AIC <- glmvsd(x, y, 
model_check = model_check,
family = "gaussian", method = "union", 
weight_type = "AIC", prior = TRUE)

# compute VSD for model_check using BIC
v_BIC <- glmvsd(x, y, 
model_check = model_check,
family = "gaussian", method = "union", 
weight_type = "BIC", prior = TRUE)

# user supplied candidate models
candidate_models = rbind(c(0,0,0,0,0,0,0,1), 
c(0,1,0,0,0,0,0,1), c(0,1,1,1,0,0,0,1), 
c(0,1,1,0,0,0,0,1), c(1,1,0,1,1,0,0,0), 
c(1,1,0,0,1,0,0,0))

v1_BIC <- glmvsd(x, y, 
model_check = model_check, psi=1, 
family = "gaussian",
method = "customize", 
candidate_models = candidate_models, 
weight_type = "BIC", prior = TRUE)

# CLASSIFICATION CASE

# generate simulation data
n = 300 
p = 8
b <- c(1,1,1,-3*sqrt(2)/2) 
x=matrix(rnorm(n*p, mean=0, sd=1), n, p) 
feta=x[, 1:4]%*%b 
fprob=exp(feta)/(1+exp(feta))
y=rbinom(n, 1, fprob)

# user provide a model to be checked
model_check <- c(0,1,1,1,0,0,0,1)

# compute VSD for model_check using BIC with prior
b_BIC <- glmvsd(x, y, n_train = ceiling(n/2),
family = "binomial",
no_rep=50, model_check = model_check, psi=1, 
method = "union", weight_type = "BIC", 
prior = TRUE)

candidate_models = 
rbind(c(0,0,0,0,0,0,0,1), 
c(0,1,0,0,0,0,0,1), 
c(1,1,1,1,0,0,0,0), 
c(0,1,1,0,0,0,0,1), 
c(1,1,0,1,1,0,0,0), 
c(1,1,0,0,1,0,0,0), 
c(0,0,0,0,0,0,0,0),
c(1,1,1,1,1,0,0,0))

# compute VSD for model_check using AIC
# user supplied candidate models
b_AIC <- glmvsd(x, y, 
family = "binomial",
model_check = model_check, psi=1, 
method = "customize", 
candidate_models = candidate_models, 
weight_type = "AIC")