Fit Likelihood-based Additive Single-Effect Regression (LASER) Model

Fits the LASER model, representing the coefficient vector as a sum of L sparse "single effects." At each iteration, it cyclically applies single_effect_fit to update one effect while holding the others fixed, then updates the intercept (and dispersion, if applicable), until convergence or max_iter is reached.

Arguments

X

Numeric matrix (n × p) of predictors.

y

Response:

For GLMs: numeric vector of length n.
For Cox: numeric matrix with 2 columns (time, status) and n rows.

L

Integer; number of single effects to include (will be set to min(10, L)).

family

A stats::family object (e.g. gaussian(), binomial(), poisson()) or a Cox family list with family = "cox".

standardize

Logical: if TRUE, center and scale each predictor column before fitting (default: TRUE).

ties

Character: ties method for Cox partial likelihood ("efron" or "breslow", default: "efron").

lambda

Numeric penalty weight; if ≤ 0, defaults to \(\sqrt{2\log(n)/n}\) (default: 0.0).

tau

Numeric truncation parameter; if ≤ 0, defaults to 0.5 (default: 0.5).

decompose

Logical: if TRUE, decompose the theta in fitting (default: TRUE).

shrinkage

Logical: if TRUE, shrinkage parameters in fitting (default: TRUE).

alpha

level of significance

tol

Numeric; convergence tolerance on the change in expected log-likelihood (default: 5e-2).

max_iter

Integer; maximum number of coordinate-ascent iterations (default: 100).

Value

A list with components:

niter: Number of iterations performed.
loglik: p × L matrix of univariate log-likelihoods.
expect_loglik: Vector of length niter giving the expected log-likelihood at each iteration.
final_loglik: Expected log-likelihood at convergence.
intercept: Estimated intercept term.
dispersion: Estimated dispersion parameter (for Gaussian/Gamma).
theta: p × L matrix of fitted single-effect coefficients.
pval_intercept: p × L matrix of p-values for fitted single-effect intercepts
pval_theta: p × L matrix of p-values for fitted single-effect coefficients.
pmp: p × L matrix of posterior model probabilities.
bic: p × L matrix of BIC values.
bic_diff: p × L matrix of BIC differences from null.
bf: p × L matrix of Bayes factors.
expect_variance: Length-L vector of PMP-weighted variances.
elapsed_time: Numeric; total computation time in seconds.

Examples

if (FALSE) { # \dontrun{
# Gaussian example with 5 effects
X <- matrix(rnorm(100*20), 100, 20)
y <- rnorm(100)
res <- additive_effect_fit(X, y, L = 5, family = gaussian())

# Cox regression example
times  <- rexp(100)
status <- rbinom(100, 1, 0.5)
y_cox  <- cbind(times, status)
res_cox <- additive_effect_fit(X, y_cox, L = 3,
                               family = list(family = "cox"),
                               ties = "breslow")
} # }