Type:	Package
Version:	0.2.0
Title:	Distributed Linear Regression Models with Response Missing Variables
Depends:	R (≥ 4.1.0)
Description:	As a distributed imputation strategy, the Distributed full information Multiple Imputation method is developed to impute missing response variables in distributed linear regression. The philosophy of the package is described in 'Guo' (2025) <doi:10.1038/s41598-025-93333-6>.
License:	Apache License (== 2.0)
RoxygenNote:	7.3.2
Encoding:	UTF-8
Imports:	stats
Packaged:	2025-06-23 08:59:58 UTC; lenovo
Date/Publication:	2025-06-24 05:10:02 UTC
Config/testthat/edition:	3
NeedsCompilation:	no
Author:	Guangbao Guo [aut, cre], Limin Song [aut]
Maintainer:	Guangbao Guo <ggb11111111@163.com>
Repository:	CRAN

Averaged Generalized Method of Moments Imputation (AVGM)

Description

This function performs multiple imputations on missing values in the response variable Y, using AVGMMI logic with support for grouped data. It is fully self-contained.

Usage

AVGM(data, M, midx = 1)

Arguments

Value

A list containing:

Examples

set.seed(123)
data <- data.frame(
  y = c(rnorm(50), rep(NA, 10)),
  x1 = rnorm(60),
  x2 = rnorm(60)
)
result <- AVGM(data, M = 10)
head(result$Yhat)

CSLMI: Consensus-based Stochastic Linear Multiple Imputation (Simplified Version)

Description

Performs multiple imputation and parameter estimation using a consensus-based approach. It assumes: - The response variable is in the first column - All other columns are predictors - Missing values are automatically detected - The whole dataset is treated as one block

Usage

CSLMI(data, M)

Arguments

Value

A list containing:

Examples

set.seed(123)
data <- data.frame(
  y = c(rnorm(50), rep(NA, 10)),
  x1 = rnorm(60),
  x2 = rnorm(60)
)
result <- CSLMI(data = data, M = 10)
head(result$Yhat)
print(result$betahat)
print(result$comm)

Impute Missing Values in Response Variable Y Using Distributed AVGMMI Method (With Grouping)

Description

This function implements the Distributed Averaged Generalized Method of Moments Imputation (DAVGMMI) to fill in missing values in the response variable Y based on observed covariates X. Assumes a single group structure and does not require group size input ('n').

Usage

DAVGMMI(data, R, M)

Arguments

Value

A list containing:

Examples

set.seed(123)
data <- data.frame(
  y = c(rnorm(50), rep(NA, 10)),
  x1 = rnorm(60),
  x2 = rnorm(60)
)
result <- DAVGMMI(data, R = 50, M = 10)
head(result$Yhat)

Distributed and Consensus-Based Stochastic Linear Multiple Imputation (DCSLMI)

Description

Performs multiple imputation for missing response variables in linear regression models. This method iteratively updates parameter estimates using ordinary least squares (OLS) and generates M complete datasets by imputing missing values with different parameter draws.

Usage

DCSLMI(data, R = 1000, M = 20)

Arguments

Value

A list containing:

Yhat

A matrix of size n x M, where each column is a completed response vector.

betahat

A matrix of size (p+1) x M, where each column contains the estimated regression coefficients.

missing_count

The number of missing values in the original response variable.

Examples

# Simulate data with missing responses
set.seed(123)
data <- data.frame(
  y = c(rnorm(50), rep(NA, 10)),
  x1 = rnorm(60),
  x2 = rnorm(60)
)

# Perform multiple imputation
result <- DCSLMI(data, R = 500, M = 10)

# View imputed response values
head(result$Yhat)

# View coefficient estimates
apply(result$betahat, 1, mean)  # average estimates
apply(result$betahat, 1, sd)    # uncertainty across imputations

EM Algorithm for Linear Regression with Missing Data

Description

EM Algorithm for Linear Regression with Missing Data

Usage

EMRE(data, d = 1, tol = 1e-06, nb = 100, niter = 1)

Arguments

Value

List containing:

Examples

# Generate data with 20% missing Y values
set.seed(123)
data <- data.frame(Y=c(rnorm(80),rep(NA,20)), X1=rnorm(100), X2=rnorm(100))

# Run EM algorithm
result <- EMRE(data, d=1, tol=1e-5, nb=50)
print(result$betahat) # View coefficients

Exponentially Weighted Recursive Least Squares with Missing Value Imputation

Description

Exponentially Weighted Recursive Least Squares with Missing Value Imputation

Usage

ERLS(data, rho = 0.01, lambda = 0.95, nb = 100, niter = 1)

Arguments

Value

List containing:

Examples

set.seed(123)
data <- data.frame(
  y = c(rnorm(50), rep(NA, 10)),
  x1 = rnorm(60),
  x2 = rnorm(60)
)
result <- ERLS(data, rho = 0.01, lambda = 0.95, nb = 100, niter = 1)
head(result$Yhat)

FimIMI: Multiple Runs of Improved Multiple Imputation (IMI)

Description

This function performs multiple runs of the Improved Multiple Imputation (IMI) estimation and collects the results. It is designed to facilitate batch processing and repeated runs of IMI.

Usage

FimIMI(d, R, n, M, batch = 0)

Arguments

Details

This function assumes that the data structure d is properly defined and contains the necessary information. The function repeatedly calls the IMI function and collects the regression coefficients and indicator variables.

Value

A list containing:

Examples

# Example data
set.seed(123)
n <- c(300, 300, 400)  # Sample sizes for each group
p <- 5  # Number of independent variables
d <- list(p = p, Y = rnorm(sum(n)), X0 = matrix(rnorm(sum(n) * p), ncol = p))

# Call FimIMI function
result <- FimIMI(d = d, R = 10, n = n, M = 20, batch = 1)

# View results
print(result$Beta)  # Regression coefficients for each run

Generate Missing Data function

Description

This function generates missing data in a specified column of a data frame according to a given missing ratio.

Usage

GMD(data, ratio)

Arguments

Value

Examples

set.seed(123) # for reproducibility
data <- data.frame(x = 1:10, y = rnorm(10))
modified_data <- GMD(data, ratio = 0.5)
summary(modified_data)

Improved Multiple Imputation (IMI) Estimation

Description

This function performs Improved Multiple Imputation (IMI) estimation for grouped data with missing values. It iteratively imputes missing values using the LS function and estimates regression coefficients using the PPLS function. The final regression coefficients are averaged across multiple imputations.

Usage

IMI(d, M, midx, n)

Arguments

Details

The function assumes the data is grouped and contains missing values in specified columns (midx). It uses the LS function to impute missing values and the PPLS function to estimate regression coefficients. The process is repeated M times, and the final regression coefficients are averaged.

Value

A list containing the following elements:

Examples

# Example data

set.seed(123)
n <- c(300, 300, 400)  # Sample sizes for each group
p <- 5  # Number of independent variables
Y <- rnorm(sum(n))  # Dependent variable
X0 <- matrix(rnorm(sum(n) * p), ncol = p)  # Independent variables matrix
d <- list(p = p, Y = Y, X0 = X0)  # Data list
d$all <- cbind(Y, X0)
# Indices of missing variables (assuming some variables are missing)
midx <- c(2, 3)  # For example, the second and third variables are missing
# Call IMI function
result <- IMI(d, M = 5, midx = midx, n = n)
# View results
print(result$betahat)  # Average regression coefficients

Least Squares Estimation for Grouped Data with Ridge Regularization

Description

This function implements the least squares estimation for grouped data, supporting ridge regression regularization. It can handle missing data and returns regression coefficients and the sum of squared residuals for each group.

Usage

LS(d, yidx, Xidx, n, lam = 0.005)

Arguments

Value

A list containing the following elements:

Examples

# Example data
set.seed(123)
n <- 1000
p <- 5
d <- list(all = cbind(rnorm(n), matrix(rnorm(n*p), ncol=p)))

# Call the LS function
result <- LS(d, yidx = 1, Xidx = 2:(p + 1), n = c(1, 300, 600, 1000))

# View the results
print(result$beta)  # Regression coefficients
print(result$SSE)   # Sum of squared residuals

Predictive Mean Matching with Multiple Imputation

Description

Implements PMM algorithm for handling missing data in linear regression models. Uses chained equations approach to generate multiple imputed datasets and pools results using Rubin's rules.

Usage

PMMI(data, k = 5, m = 5)

Arguments

Value

List containing:

Examples

# Create dataset with 30% missing values
data <- data.frame(Y=c(rnorm(70),rep(NA,30)), X1=rnorm(100))
results <- PMMI(data, k=5, m=5)

Penalized Partial Least Squares (PPLS) Estimation

Description

This function performs Penalized Partial Least Squares (PPLS) estimation for grouped data. It supports ridge regression regularization and handles missing data by excluding incomplete cases. The function returns regression coefficients, residual sum of squares, and other diagnostic information.

Usage

PPLS(d, yidx, Xidx, n, lam = 0.005)

Arguments

Details

This function assumes that the data is grouped and that the sample sizes for each group are provided. It excludes cases with missing values in the dependent or independent variables. The function uses Cholesky decomposition to solve the regularized least squares problem.

Value

A list containing the following elements:

Examples

# Example data
set.seed(123)
n_total <- 1000
p <- 5
n_groups <- c(300, 300, 400)
d <- list(all = cbind(rnorm(n_total), matrix(rnorm(n_total*p), ncol=p)),p = p)

# Call PPLS function
result <- PPLS(d, yidx=1, Xidx=2:(p+1), n=n_groups)

# View results
print(result$beta)  # Regression coefficients
print(result$SSE)   # Residual sum of squares

fiMI: Predict Missing Response Variables using Multiple Imputation

Description

This function predicts missing response variables in a linear regression dataset using multiple imputation. It leverages the FimIMI function to perform multiple runs of improved multiple imputation and averages the regression coefficients to predict the missing response values.

Usage

fiMI(data, R, n, M)

Arguments

Details

This function assumes that the first column of data is the response variable and the remaining columns are the independent variables. The function uses the FimIMI function to perform multiple runs of improved multiple imputation and averages the regression coefficients to predict the missing response values.

Value

A list containing:

Examples

# Example data
set.seed(123)
n <- 1000  # Number of rows
p <- 5  # Number of independent variables
data <- data.frame(Y = rnorm(n), X1 = rnorm(n), X2 = rnorm(n))
data[sample(n, 100), 1] <- NA  # Introduce missing response values

# Call fiMI function
result <- fiMI(data, R = 10, n = n, M = 20)

# View results
print(result$Yhat)  # Predicted response values