Variable selection method with multiple block-wise imputation (MBI)

Description

Fit a variable selection method with multiple block-wise imputation (MBI).

Usage

MBI(
  X,
  y,
  cov_index,
  sub_index,
  miss_source,
  complete,
  lambda = NULL,
  eps1 = 0.001,
  eps2 = 1e-07,
  eps3 = 1e-08,
  max.iter = 1000,
  lambda.min = ifelse(n > p, 0.001, 0.05),
  nlam = 100,
  beta0 = NULL,
  a = 3.7,
  gamma.ebic = 0.5,
  alpha1 = 0.5^(0:12),
  h1 = 2^(-(8:30)),
  ratio = 1
)

Arguments

Details

The function uses the penalized generalized method of moments with multiple block-wise imputation to handle block-wise missing data, commonly found in multi-source datasets.

Value

Author(s)

Fei Xue and Annie Qu

References

Xue, F., and Qu, A. (2021) Integrating Multisource Block-Wise Missing Data in Model Selection (2021), Journal of the American Statistical Association, Vol. 116(536), 1914-1927.

Examples

library(MASS)

# Number of subjects
n <- 30

# Number of total covariates
p <- 4

# Number of missing groups of subjects
ngroup <- 2

# Number of data sources
nsource <- 2

# Starting indexes of covariates in data sources
cov_index=c(1, 3)

# Starting indexes of subjects in missing groups
sub_index=c(1, 16)

# Indexes of missing data sources in missing groups, respectively ('NULL' represents no missing)
miss_source=list(NULL, 1)

# Indicator of whether there is a group of complete cases. If there is a group of complete cases,
# it should be the first group.
complete=TRUE

# Create a block-wise missing design matrix X and response vector y
set.seed(1)
sigma=diag(1-0.4,p,p)+matrix(0.4,p,p)
X <- mvrnorm(n,rep(0,p),sigma)
beta_true <- c(2.5, 0, 3, 0)
y <- rnorm(n) + X%*%beta_true

for (i in 1:ngroup) {
  if (!is.null(miss_source[[i]])) {
    if (i==ngroup) {
      if (miss_source[[i]]==nsource) {
        X[sub_index[i]:n, cov_index[miss_source[[i]]]:p] = NA
      } else {
        X[sub_index[i]:n, cov_index[miss_source[[i]]]:(cov_index[miss_source[[i]]+1]-1)] = NA
      }
    } else {
      if (miss_source[[i]]==nsource) {
        X[sub_index[i]:(sub_index[i+1]-1), cov_index[miss_source[[i]]]:p] = NA
      } else {
        X[sub_index[i]:(sub_index[i+1]-1), cov_index[miss_source[[i]]]:
        (cov_index[miss_source[[i]]+1]-1)] = NA
      }
    }
  }
}

# Now we can use the function with this simulated data
#start.time = proc.time()
result <- MBI(X=X, y=y, cov_index=cov_index, sub_index=sub_index, miss_source=miss_source,
complete=complete, nlam = 15, eps2 = 1e-3, h1=2^(-(8:20)))
#time = proc.time() - start.time

theta=result$beta
bic1=result$bic1
best=which.min(bic1[bic1!=0])
beta_est=theta[best,]

Imputation using generalized linear models for missing values

Description

The function performs imputation using generalized linear models for missing values in a dataset. It fits these models for each specified response variable separately, utilizing other specified variables, and returns the estimated coefficients and predicted values for each variable. The function handles different distribution families, such as Gaussian, Binomial, and Ordinal, for GLM estimation.

Usage

imputeglm.predict(X, ind_y, ind_x = -ind_y, miss, newdata, family = "gaussian")

Arguments

Value

A list containing the imputed values for each response variable.

Author(s)

Fei Xue and Annie Qu

Examples

library(MASS)

# Number of subjects
n <- 700

# Number of total covariates
p <- 40

# Number of missing groups of subjects
ngroup <- 4

# Number of data sources
nsource <- 4

# Starting indexes of covariates in data sources
cov_index=c(1, 13, 25, 37)

# Starting indexes of subjects in missing groups
sub_index=c(1, 31, 251, 471)

# Indexes of missing data sources in missing groups, respectively ('NULL' represents no missing)
miss_source=list(NULL, 3, 2, 1)

# Create a design matrix
set.seed(1)
sigma=diag(1-0.4,p,p)+matrix(0.4,p,p)
X <- mvrnorm(n,rep(0,p),sigma)

# Introduce some block-wise missing
for (i in 1:ngroup) {
  if (!is.null(miss_source[[i]])) {
    if (i==ngroup) {
      if (miss_source[[i]]==nsource) {
        X[sub_index[i]:n, cov_index[miss_source[[i]]]:p] = NA
      } else {
        X[sub_index[i]:n, cov_index[miss_source[[i]]]:(cov_index[miss_source[[i]]+1]-1)] = NA
      }
    } else {
      if (miss_source[[i]]==nsource) {
        X[sub_index[i]:(sub_index[i+1]-1), cov_index[miss_source[[i]]]:p] = NA
      } else {
        X[sub_index[i]:(sub_index[i+1]-1), cov_index[miss_source[[i]]]:
        (cov_index[miss_source[[i]]+1]-1)] = NA
      }
    }
  }
}

# Define missing data pattern
miss <- is.na(X)
# Choose response and predictor variables
ind_y <- 25:36
ind_x <- 13:24
# Data that need imputation
newdata <- X[31:250,]
# Use the function
result <- imputeglm.predict(X = X, ind_y = ind_y, ind_x = ind_x, miss = miss, newdata = newdata)