Type: Package
Title: Generalised Linear Mixed Model Selection
Version: 1.0.3
Description: Provides tools for fitting sparse generalised linear mixed models with l0 regularisation. Selects fixed and random effects under the hierarchy constraint that fixed effects must precede random effects. Uses coordinate descent and local search algorithms to rapidly deliver near-optimal estimates. Gaussian and binomial response families are currently supported. For more details see Thompson, Wand, and Wang (2025) <doi:10.48550/arXiv.2506.20425>.
URL: https://github.com/ryan-thompson/glmmsel
BugReports: https://github.com/ryan-thompson/glmmsel/issues
License: GPL-3
Encoding: UTF-8
RoxygenNote: 7.3.2
Depends: R (≥ 4.1.0)
Imports: ggplot2, Rcpp
LinkingTo: Rcpp, RcppArmadillo
Suggests: testthat, knitr, rmarkdown, lme4, MASS, nlme
VignetteBuilder: knitr
Config/testthat/edition: 3
NeedsCompilation: yes
Packaged: 2025-06-26 07:12:34 UTC; ryan
Author: Ryan Thompson ORCID iD [aut, cre]
Maintainer: Ryan Thompson <ryan.thompson-1@uts.edu.au>
Repository: CRAN
Date/Publication: 2025-06-26 08:00:02 UTC

Coefficient function for cv.glmmsel object

Description

Extract cluster coefficients for a cross-validated value of the regularisation parameter.

Usage

## S3 method for class 'cv.glmmsel'
coef(object, lambda = "lambda.min", ...)

Arguments

object

an object of class cv.glmmsel

lambda

a value of the regularisation parameter

...

any other arguments

Value

An array of coefficients.

Author(s)

Ryan Thompson <ryan.thompson-1@uts.edu.au>

Coefficient function for glmmsel object

Description

Extracts coefficients for a specified value of the regularisation parameter.

Usage

## S3 method for class 'glmmsel'
coef(object, lambda = NULL, ...)

Arguments

object

an object of class glmmsel

lambda

a value of the regularisation parameter

...

any other arguments

Value

An array of coefficients.

Author(s)

Ryan Thompson <ryan.thompson-1@uts.edu.au>

Cross-validated generalised linear mixed model selection

Description

Fits the regularisation path for a sparse generalised linear mixed model and then cross-validates this path.

Usage

cv.glmmsel(
  x,
  y,
  cluster,
  family = c("gaussian", "binomial"),
  lambda = NULL,
  nfold = 10,
  folds = NULL,
  cv.loss = NULL,
  interpolate = TRUE,
  ...
)

Arguments

x

a predictor matrix

y

a response vector

cluster

a vector of length nrow(x) with the jth element identifying the cluster that the jth observation belongs to

family

the likelihood family to use; 'gaussian' for a continuous response or 'binomial' for a binary response

lambda

the regularisation parameter for the overlapping penalty on the fixed and random slopes

nfold

the number of cross-validation folds

folds

an optional vector of length nrow(x) with the jth entry identifying the fold that the jth observation belongs to

cv.loss

an optional cross-validation loss-function to use; should accept a vector of predicted values and a vector of actual values

interpolate

a logical indicating whether to interpolate the lambda sequence for the cross-validation fits

...

any other arguments for glmmsel()

Value

An object of class cv.glmmsel; a list with the following components:

cv.mean

a vector of cross-validation means

cv.sd

a vector of cross-validation standard errors

lambda

a vector of cross-validated regularisation parameters

lambda.min

the value of lambda minimising cv.mean

fit

the fit from running glmmsel() on the full data

Author(s)

Ryan Thompson <ryan.thompson-1@uts.edu.au>

References

Thompson, R., Wand, M. P., and Wang, J. J. J. (2025). 'Scalable subset selection in linear mixed models'. arXiv: 2506.20425.

Examples

# Generate data
set.seed(1234)
n <- 100
m <- 4
p <- 10
s <- 5
x <- matrix(rnorm(n * p), n, p)
beta <- c(rep(1, s), rep(0, p - s))
u <- cbind(matrix(rnorm(m * s), m, s), matrix(0, m, p - s))
cluster <- sample(1:m, n, replace = TRUE)
xb <- rowSums(x * sweep(u, 2, beta, '+')[cluster, ])
y <- rnorm(n, xb)

# Fit sparse linear mixed model
fit <- cv.glmmsel(x, y, cluster)
plot(fit)
fixef(fit)
ranef(fit)
coef(fit)
predict(fit, x[1:3, ], cluster[1:3])

Fixed effects function

Description

Generic function for extracting fixed effects from model objects.

Usage

fixef(object, ...)

Arguments

object

a model object

...

any other arguments

Value

Depends on the specific method implementation.

Author(s)

Ryan Thompson <ryan.thompson-1@uts.edu.au>

Fixed effects function for cv.glmmsel object

Description

Extract fixed effects for a cross-validated value of the regularisation parameter.

Usage

## S3 method for class 'cv.glmmsel'
fixef(object, lambda = "lambda.min", ...)

Arguments

object

an object of class cv.glmmsel

lambda

a value of the regularisation parameter

...

any other arguments

Value

A matrix of fixed effects.

Author(s)

Ryan Thompson <ryan.thompson-1@uts.edu.au>

Fixed effects function for glmmsel object

Description

Extracts fixed effects for a specified value of the regularisation parameter.

Usage

## S3 method for class 'glmmsel'
fixef(object, lambda = NULL, ...)

Arguments

object

an object of class glmmsel

lambda

a value of the regularisation parameter

...

any other arguments

Value

A matrix of fixed effects.

Author(s)

Ryan Thompson <ryan.thompson-1@uts.edu.au>

Generalised linear mixed model selection

Description

Fits the regularisation path for a sparse generalised linear mixed model (GLMM).

Usage

glmmsel(
  x,
  y,
  cluster,
  family = c("gaussian", "binomial"),
  local.search = FALSE,
  max.nnz = 100,
  nlambda = 100,
  lambda.step = 0.99,
  lambda = NULL,
  alpha = 0.8,
  intercept = TRUE,
  random.intercept = TRUE,
  standardise = TRUE,
  eps = 1e-04,
  max.cd.iter = 10000,
  max.ls.iter = 100,
  max.bls.iter = 30,
  t.init = 1,
  t.scale = 0.5,
  max.pql.iter = 100,
  active.set = TRUE,
  active.set.count = 3,
  sort = TRUE,
  screen = 100,
  warn = TRUE
)

Arguments

x

a predictor matrix

y

a response vector

cluster

a vector of length nrow(x) with the jth element identifying the cluster that the jth observation belongs to

family

the likelihood family to use; 'gaussian' for a continuous response or 'binomial' for a binary response

local.search

a logical indicating whether to perform local search after coordinate descent; typically leads to higher quality solutions

max.nnz

the maximum number of predictors ever allowed to be active

nlambda

the number of regularisation parameters to evaluate when lambda is computed automatically

lambda.step

the step size taken when computing lambda from the data; should be a value strictly between 0 and 1; larger values typically lead to a finer grid of subset sizes

lambda

an optional vector of regularisation parameters

alpha

the hierarchical parameter

intercept

a logical indicating whether to include a fixed intercept

random.intercept

a logical indicating whether to include a random intercept; applies only when intercept = TRUE

standardise

a logical indicating whether to scale the data to have unit root mean square; all parameters are returned on the original scale of the data

eps

the convergence tolerance; convergence is declared when the relative maximum difference in consecutive parameter values is less than eps

max.cd.iter

the maximum number of coordinate descent iterations allowed

max.ls.iter

the maximum number of local search iterations allowed

max.bls.iter

the maximum number of backtracking line search iterations allowed

t.init

the initial value of the gradient step size during backtracking line search

t.scale

the scaling parameter of the gradient step size during backtracking line search

max.pql.iter

the maximum number of penalised quasi-likelihood iterations allowed

active.set

a logical indicating whether to use active set updates; typically lowers the run time

active.set.count

the number of consecutive coordinate descent iterations in which a subset should appear before running active set updates

sort

a logical indicating whether to sort the coordinates before running coordinate descent; typically leads to higher quality solutions

screen

the number of predictors to keep after gradient screening; smaller values typically lower the run time

warn

a logical indicating whether to print a warning if the algorithms fail to converge

Value

An object of class glmmsel; a list with the following components:

beta0

a vector of fixed intercepts

gamma0

a vector of random intercept variances

beta

a matrix of fixed slopes

gamma

a matrix of random slope variances

u

an array of random coefficient predictions

sigma2

a vector of residual variances

loss

a vector of loss function values

cd.iter

a vector indicating the number of coordinate descent iterations for convergence

ls.iter

a vector indicating the number of local search iterations for convergence

pql.iter

a vector indicating the number of penalised quasi-likelihood iterations for convergence

nnz

a vector of the number of nonzeros

lambda

a vector of regularisation parameters used for the fit

family

the likelihood family used

clusters

a vector of cluster identifiers

alpha

the value of the hierarchical parameter used for the fit

intercept

whether a fixed intercept is included in the model

random.intercept

whether a random intercept is included in the model

Author(s)

Ryan Thompson <ryan.thompson-1@uts.edu.au>

References

Thompson, R., Wand, M. P., and Wang, J. J. J. (2025). 'Scalable subset selection in linear mixed models'. arXiv: 2506.20425.

Examples

# Generate data
set.seed(1234)
n <- 100
m <- 4
p <- 10
s <- 5
x <- matrix(rnorm(n * p), n, p)
beta <- c(rep(1, s), rep(0, p - s))
u <- cbind(matrix(rnorm(m * s), m, s), matrix(0, m, p - s))
cluster <- sample(1:m, n, replace = TRUE)
xb <- rowSums(x * sweep(u, 2, beta, '+')[cluster, ])
y <- rnorm(n, xb)

# Fit sparse linear mixed model
fit <- glmmsel(x, y, cluster)
plot(fit)
fixef(fit, lambda = 10)
ranef(fit, lambda = 10)
coef(fit, lambda = 10)
predict(fit, x[1:3, ], cluster[1:3], lambda = 10)

Plot function for cv.glmmsel object

Description

Plot the cross-validation loss as a function of the regularisation parameter.

Usage

## S3 method for class 'cv.glmmsel'
plot(x, ...)

Arguments

x

an object of class cv.glmmsel

...

any other arguments

Value

A plot of the cross-validation results.

Author(s)

Ryan Thompson <ryan.thompson-1@uts.edu.au>

Plot function for glmmsel object

Description

Plots the coefficients as a function of the regularisation parameter.

Usage

## S3 method for class 'glmmsel'
plot(x, cluster = NULL, ...)

Arguments

x

an object of class glmmsel

cluster

the cluster whose coefficients to plot

...

any other arguments

Value

A plot of the coefficient profiles.

Author(s)

Ryan Thompson <ryan.thompson-1@uts.edu.au>

Predict function for cv.glmmsel object

Description

Generates predictions for new data using a cross-validated value of the regularisation parameter.

Usage

## S3 method for class 'cv.glmmsel'
predict(object, x.new, cluster.new, lambda = "lambda.min", ...)

Arguments

object

an object of class cv.glmmsel

x.new

a matrix of new values for the predictors

cluster.new

a vector identifying the clusters that the rows of x.new belong to

lambda

a value of the regularisation parameter

...

any other arguments

Value

A matrix of predictions.

Author(s)

Ryan Thompson <ryan.thompson-1@uts.edu.au>

Predict function for glmmsel object

Description

Generates predictions for new data using a specified value of the regularisation parameter.

Usage

## S3 method for class 'glmmsel'
predict(object, x.new, cluster.new, lambda = NULL, ...)

Arguments

object

an object of class glmmsel

x.new

a matrix of new values for the predictors

cluster.new

a vector identifying the clusters that the rows of x.new belong to

lambda

a value of the regularisation parameter

...

any other arguments

Value

A matrix of predictions.

Author(s)

Ryan Thompson <ryan.thompson-1@uts.edu.au>

Random effects function

Description

Generic function for extracting random effects from model objects.

Usage

ranef(object, ...)

Arguments

object

a model object

...

any other arguments

Value

Depends on the specific method implementation.

Author(s)

Ryan Thompson <ryan.thompson-1@uts.edu.au>

Random effects function for cv.glmmsel object

Description

Extract random effects for a cross-validated value of the regularisation parameter.

Usage

## S3 method for class 'cv.glmmsel'
ranef(object, lambda = "lambda.min", ...)

Arguments

object

an object of class cv.glmmsel

lambda

a value of the regularisation parameter

...

any other arguments

Value

A matrix of random effects.

Author(s)

Ryan Thompson <ryan.thompson-1@uts.edu.au>

Random effects function for glmmsel object

Description

Extracts random effects for a specified value of the regularisation parameter.

Usage

## S3 method for class 'glmmsel'
ranef(object, lambda = NULL, ...)

Arguments

object

an object of class glmmsel

lambda

a value of the regularisation parameter

...

any other arguments

Value

A matrix of random effects.

Author(s)

Ryan Thompson <ryan.thompson-1@uts.edu.au>