Package 'glmmsel'

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 <[email protected]>

---

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 <[email protected]>

---

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 <[email protected]>

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 <[email protected]>

---

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 <[email protected]>

---

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 <[email protected]>

---

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 <[email protected]>

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 <[email protected]>

---

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 <[email protected]>

---

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 <[email protected]>

---

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 <[email protected]>

---

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 <[email protected]>

---

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 <[email protected]>

---

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 <[email protected]>

---