RTMB-based Linear Regression wrapper function

RTMB-based Linear Regression wrapper function

Usage

rtmb_lm(
  formula,
  data,
  penalty = c("none", "rhs", "ssp"),
  y_range = NULL,
  use_weak_info = FALSE,
  prior = list(Intercept_sd = 10, b_sd = 10, sigma_rate = 5, sd_rate = 5, nu_rate = 0.1,
    cutpoint_sd = 2.5, shape_rate = 1, phi_rate = 1),
  weak_info_prior = list(max_beta = 1, sd_ratio = 0.5, expected_vars = 3, slab_scale = 2,
    slab_df = 4, ssp_ratio = 0.25),
  init = NULL,
  null = NULL
)

Arguments

formula

Formula (e.g., Y ~ X1 + X2)

data

Data frame

penalty

Type of regularization for fixed effects: "none", "rhs" (Regularized Horseshoe), or "ssp" (Spike and Slab Prior). Default is "none".

y_range

Theoretical minimum and maximum values of the response variable as a vector c(min, max). Specifying this automatically enables weakly informative priors.

use_weak_info

Logical; whether to explicitly use weakly informative priors.

prior

List of hyperparameters for the default fixed priors.

weak_info_prior

List of hyperparameters for the weakly informative priors and regularization.

init

List of initial values.

null

Character string specifying the target parameter for the null model.

Examples

if (FALSE) { # \dontrun{
  # --- 1. Linear Regression (rtmb_lm) ---
  # Fit a linear regression model using the mtcars dataset
  fit_lm <- rtmb_lm(mpg ~ wt + cyl, data = mtcars)
  map_lm <- fit_lm$optimize()
  map_lm$summary()

  # --- 2. Generalized Linear Model (rtmb_glm) ---
  # Fit a logistic regression model
  fit_glm <- rtmb_glm(am ~ mpg + hp, data = mtcars, family = "binomial")
  map_glm <- fit_glm$optimize()
  map_glm$summary()

  # --- 3. Generalized Linear Mixed Model (rtmb_glmer) ---
  # Fit a linear mixed-effects model with random intercepts
  fit_glmer <- rtmb_glmer(weight ~ Time + (1 | Chick), data = ChickWeight, family = "gaussian")

  # MAP estimation using Laplace approximation for random effects
  map_glmer <- fit_glmer$optimize(laplace = TRUE)
  map_glmer$summary()

  # MCMC sampling (chains and iterations reduced for faster execution)
  mcmc_glmer <- fit_glmer$sample(sampling = 500, warmup = 500, chains = 2)
  mcmc_glmer$summary()

  # --- 4. Linear Mixed Model (rtmb_lmer) ---
  # A convenient wrapper for Gaussian mixed models (identical to rtmb_glmer with family="gaussian")
  fit_lmer <- rtmb_lmer(mpg ~ wt + (1 | cyl), data = mtcars)
  map_lmer <- fit_lmer$optimize()
  map_lmer$summary()

  # --- 5. Regularized Regression (Variable Selection) ---
  # You can apply regularization to the fixed effects to shrink noise variables towards zero.
  # Use penalty = "rhs" for the Regularized Horseshoe prior, or "ssp" for the Spike-and-Slab prior.
  # Note: When using regularization, you must specify 'y_range' (the theoretical minimum and maximum
  # values of the response variable) to automatically set up the required weakly informative priors.

  # Fit a linear regression using all predictors in mtcars with the Horseshoe prior
  # 'mpg' theoretically ranges roughly between 0 and 40
  fit_rhs <- rtmb_lm(mpg ~ ., data = mtcars, penalty = "rhs", y_range = c(0, 40))
  map_rhs <- fit_rhs$optimize()
  # Summarize only the fixed effects (slopes)
  map_rhs$summary("b")

  # Fit a linear regression with the Spike-and-Slab prior
  fit_ssp <- rtmb_lm(mpg ~ ., data = mtcars, penalty = "ssp", y_range = c(0, 40))
  map_ssp <- fit_ssp$optimize()
  map_ssp$summary("b")

  # For models with complex penalties, MCMC often provides more reliable credible intervals
  mcmc_ssp <- fit_ssp$sample(sampling = 500, warmup = 500, chains = 2)
  mcmc_ssp$summary("b")
} # }