Type: Package
Title: Sparse High-Dimensional Linear Mixed Modeling with a Partitioned Empirical Bayes ECM Algorithm
Version: 0.1.0
Date: 2026-02-27
Description: Implements a partitioned Empirical Bayes Expectation Conditional Maximization (ECM) algorithm for sparse high-dimensional linear mixed modeling as described in Zgodic, Bai, Zhang, and McLain (2025) <doi:10.1007/s11222-025-10649-z>. The package provides efficient estimation and inference for mixed models with high-dimensional fixed effects.
License: GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
URL: https://github.com/anjazgodic/lmmprobe
BugReports: https://github.com/anjazgodic/lmmprobe/issues
Encoding: UTF-8
RoxygenNote: 7.3.3
Depends: R (≥ 3.5.0)
Imports: Rcpp (≥ 1.0.8.3), lme4 (≥ 1.1-29), future.apply (≥ 1.10.0)
LinkingTo: Rcpp, RcppArmadillo
Suggests: testthat (≥ 3.0.0), knitr, rmarkdown, MASS
VignetteBuilder: knitr
NeedsCompilation: yes
Packaged: 2026-03-08 16:13:58 UTC; peter
Author: Anja Zgodic [aut, cre], Ray Bai ORCID iD [aut], Jiajia Zhang ORCID iD [aut], Alex McLain ORCID iD [aut], Peter Olejua ORCID iD [aut]
Maintainer: Anja Zgodic <anja.zgodic@gmail.com>
Repository: CRAN
Date/Publication: 2026-03-12 09:00:09 UTC

lmmprobe: Sparse High-Dimensional Linear Mixed Modeling with a Partitioned Empirical Bayes ECM Algorithm

Description

Implements a partitioned Empirical Bayes Expectation Conditional Maximization (ECM) algorithm for sparse high-dimensional linear mixed modeling as described in Zgodic, Bai, Zhang, and McLain (2025) doi:10.1007/s11222-025-10649-z. The package provides efficient estimation and inference for mixed models with high-dimensional fixed effects.

Author(s)

Maintainer: Anja Zgodic anja.zgodic@gmail.com

Authors:

See Also

Useful links:

Systemic Lupus Erythematosus (SLE) Gene Expression Data

Description

A subset of longitudinal gene expression data from a pediatric Systemic Lupus Erythematosus (SLE) study. The full dataset contains 15,378 Illumina HumanHT-12 V4.0 probes; this subset includes 500 probes plus 16 clinical variables for a total of 519 columns. Loading this dataset creates an object named real_data.

Usage

data(SLE)

Format

A data frame with 353 observations on 519 variables:

id

Subject ID (integer).

y

Response variable (continuous).

intercept

Intercept column (all ones).

ILMN_*

500 Illumina gene expression probes (numeric).

AGE, WBC, NEUTROPHIL_COUNT, ESR

Continuous clinical predictors.

female, nonwhite

Demographic indicators.

ARTHRITIS, URINARY_CASTS, HEMATURIA, PROTEINURIA, PYURIA, NEW_RASH, MUCOSAL_ULCERS, LOW_COMPLEMENT, INCREASED_DNA_BINDING, LEUKOPENIA

SLEDAI clinical components.

Source

Banchereau, R., Hong, S., Cantarel, B., et al. (2016). Personalized Immunomonitoring Uncovers Molecular Networks that Stratify Lupus Patients. Cell, 165(3), 551–565. doi:10.1016/j.cell.2016.05.057. Gene Expression Omnibus accession GSE65391.

Sparse high-dimensional linear mixed modeling with PaRtitiOned empirical Bayes ECM (LMM-PROBE) algorithm.

Description

Sparse high-dimensional linear mixed modeling with PaRtitiOned empirical Bayes ECM (LMM-PROBE) algorithm. Currently, the package offers functionality for two scenarios. Scenario 1: only a random intercept, each unit has the same number of observations; Scenario 2: a random intercept and a random slope, each unit has the same number of observations. We are actively expanding the package for more flexibility and scenarios.

Arguments

Y

A training-data matrix containing the outcome Y.

Z

A training-data matrix containing the sparse fixed-effect predictors on which to apply the lmmprobe algorithm. The first columns should be the "id" column.

V

A training-data matrix containing non-sparse predictors for the random effects. This matrix is currently only programmed for two scenarios. Scenario 1: only a random intercept, where V is a matrix with one column containing ID's and each unit has the same number of observations. Scenario 2: a random intercept and a random slope, where V is a matrix with two columns. The first column is ID and the second column is a continuous variable (e.g. time) for which a random slope is to be estimated. Each unit has the same number of observations.

ID_data

A factor vector of IDs for subjects in the training set.

Y_test

A testing-data matrix containing the outcome Y. Default is NULL.

Z_test

A testing-data matrix containing the sparse fixed-effect predictors. Default is NULL.

V_test

A testing-data matrix containing non-sparse predictors for the random effects, structured the same as V. Default is NULL.

ID_test

A factor vector of IDs for subjects in the testing set. Default is NULL.

alpha

Type I error; significance level.

ep

Value against which to compare convergence criterion, we recommend 0.05.

B

The number of groups to categorize estimated coefficients in to calculate correlation \rho. We recommend five.

adj

A factor multiplying Silverman’s 'rule of thumb' in determining the bandwidth for density estimation, same as the 'adjust' argument of R's density function. Default is three.

maxit

Maximum number of iterations the algorithm will run for. Default is 10000.

cpus

The number of CPUS user would like to use for parallel computations. Default is four.

LR

A learning rate parameter r. Using zero corresponds to the implementation described in Zgodic et al.

C

A learning rate parameter c. Using one corresponds to the implementation described in Zgodic et al.

sigma_init

An initial value for the residual variance parameter. Default is NULL which corresponds to the sample variance of Y.

Value

A list containing:

beta MAP estimates of the posterior expectation of the prior mean (\beta) of the regression coefficients assuming \gamma=1,

beta_var posterior variance of \beta,

gamma the posterior expectation of the latent \gamma variables,

preds predictions of Y,

PI_lower, PI_upper lower and upper prediction intervals for the predictions,

residual_var MAP estimate of the residual variance,

random_var MAP estimate of the random effect(s) variance,

random_intercept estimated random intercept terms,

random_slope estimated random slope terms, if applicable,

c_coefs calibration regression coefficients,

p_vals p-values for the fixed-effect coefficients,

count number of iterations until convergence.

References

Zgodic, A., Bai, R., Zhang, J. et al. (2025). Sparse high-dimensional linear mixed modeling with a partitioned empirical Bayes ECM algorithm. Stat Comput 35, 109. https://doi.org/10.1007/s11222-025-10649-z

Examples

set.seed(1)
n_subj <- 10
n_obs <- 5
N <- n_subj * n_obs
Y <- matrix(rnorm(N), ncol = 1)
Z <- matrix(rnorm(N * 20), nrow = N, ncol = 20)
V <- matrix(rep(1:n_subj, each = n_obs), ncol = 1)
ID_data <- rep(1:n_subj, each = n_obs)
result <- lmmprobe(Y = Y, Z = Z, V = V, ID_data = ID_data, maxit = 3)

data(SLE)
Y <- matrix(real_data[, "y"], ncol = 1)
Z <- real_data[, 4:ncol(real_data)]
V <- matrix(real_data[, "id"], ncol = 1)
ID_data <- as.numeric(as.character(real_data$id))
full_res <- lmmprobe(Y = Y, Z = Z, V = V, ID_data = ID_data)