Real Data Examples with Different Distributions

Frédéric Bertrand

Cedric, Cnam, Paris
frederic.bertrand@lecnam.net

2025-11-21

This vignette demonstrates SelectBoost.gamlss on real datasets using different distributions. We include a growth example (Dutch boys) and further count/continuous/binary cases.

What you’ll learn

You may want to install optional engines for best results: install.packages(c("glmnet","grpreg","SGL","future.apply"))

library(SelectBoost.gamlss)
library(gamlss)
library(MASS)           # Insurance, quine
set.seed(1)

1. Growth data (BCT) — Dutch boys

We model height vs age with BCT (Box–Cox t). Grouped penalties select among smoothers and interactions with pubertal stage.

Increase B to 50 for real use.

set.seed(123)
# Load and CLEAN the Dutch boys growth data
utils::data("boys7482", package = "SelectBoost.gamlss")
# Keep only rows complete
boys <- boys7482[stats::complete.cases(boys7482),]
boys$gen <- as.factor(boys$gen)
# (Optional) keep levels actually present
boys <- droplevels(boys)

# Fit SelectBoost.gamlss on CLEANED data (no parallel for vignette stability)
fit_growth <- sb_gamlss(
  hgt ~ 1, data = boys, family = gamlss.dist::BCT(),
  mu_scope    = ~ pb(age) + pb(age):gen,
  sigma_scope = ~ pb(age),
  nu_scope    = ~ pb(age),
  engine = "grpreg", engine_sigma = "grpreg", engine_nu = "grpreg",
  grpreg_penalty = "grLasso",
  B = 1, pi_thr = 0.6, pre_standardize = TRUE,
  parallel = "none", trace = FALSE
)

# Peek at selection (first rows)
print(utils::head(selection_table(fit_growth), 12))
#>   parameter        term count prop
#> 1        mu     pb(age)     0    0
#> 2        mu pb(age):gen     0    0
#> 3     sigma     pb(age)     0    0
#> 4        nu     pb(age)     0    0

# Effect plot for age on mu
if (requireNamespace("ggplot2", quietly = TRUE)) {
  print(effect_plot(fit_growth, "age", boys, what = "mu"))
}

Increase B to 50 for real use.

set.seed(123)
# Stability curves over a small c0 grid (still on CLEANED data)
  g <- sb_gamlss_c0_grid(
    hgt ~ 1, data = boys, family = gamlss.dist::BCT(),
    mu_scope = ~ pb(age) + pb(age):gen,
    sigma_scope = ~ pb(age),
    nu_scope = ~ pb(age),
    c0_grid = seq(0.2, 0.8, by = 0.1),
    B = 1, pi_thr = 0.6, pre_standardize = TRUE,
    parallel = "none", trace = FALSE
  )
  plot_stability_curves(g, terms = c("pb(age)", "pb(age):gen"), parameter = "mu")

Interpretation. Expect pb(age) to be stably selected for μ and σ; interactions like pb(age):gen often appear around puberty.

2. Count data (PO) — Insurance claims

Fit Poisson with log-offset for exposure.

data(Insurance, package = "MASS")
ins <- transform(Insurance, logH = log(Holders))

fit_po <- sb_gamlss(
  Claims ~ offset(logH), data = ins, family = gamlss.dist::PO(),
  mu_scope = ~ Age + District + Group,
  engine = "glmnet", glmnet_alpha = 1,    # lasso
  B = 100, pi_thr = 0.6, pre_standardize = FALSE,
  parallel = "auto", trace = FALSE
)

selection_table(fit_po)
#>   parameter     term count prop
#> 1        mu      Age   100    1
#> 2        mu District   100    1
#> 3        mu    Group   100    1

3. Positive continuous (GA) — Old Faithful

Use Gamma for positive waiting times vs eruption length.

data(faithful)
faith <- transform(faithful, eru2 = eruptions^2)

fit_ga <- sb_gamlss(
  waiting ~ 1, data = faith, family = gamlss.dist::GA(),
  mu_scope    = ~ pb(eruptions) + eru2,
  sigma_scope = ~ pb(eruptions),
  engine = "glmnet", glmnet_alpha = 0.5,   # elastic-net
  B = 60, pi_thr = 0.6, pre_standardize = TRUE,
  parallel = "auto", trace = FALSE
)

selection_table(fit_ga)
#>   parameter          term count prop
#> 1        mu pb(eruptions)    60    1
#> 2        mu          eru2    60    1
#> 3     sigma pb(eruptions)    60    1
# Effect plot for eruptions on mu
if (requireNamespace('ggplot2', quietly = TRUE)) {
  print(effect_plot(fit_ga, 'eruptions', faith, what = 'mu'))
}

4. Binary (BI) — mtcars transmission

Treat am (0/1) as Bernoulli.

mt <- transform(mtcars,
  am = as.integer(am),
  cyl = factor(cyl), gear = factor(gear), carb = factor(carb), vs = factor(vs))

fit_bin <- sb_gamlss(
  am ~ 1, data = mt, family = gamlss.dist::BI(),
  mu_scope = ~ wt + hp + qsec + cyl + gear + carb + vs,
  engine = "grpreg", grpreg_penalty = "grLasso",
  B = 80, pi_thr = 0.6, pre_standardize = TRUE,
  parallel = "auto", trace = FALSE
)

selection_table(fit_bin)
#>   parameter term count prop
#> 1        mu   wt     0    0
#> 2        mu   hp     0    0
#> 3        mu qsec     0    0
#> 4        mu  cyl     0    0
#> 5        mu gear     0    0
#> 6        mu carb     0    0
#> 7        mu   vs     0    0

5. Overdispersed counts (NBII) — quine absences

Negative Binomial II handles extra-Poisson variation.

data(quine, package = "MASS")
fit_nb2 <- sb_gamlss(
  Days ~ 1, data = quine, family = gamlss.dist::NBII(),
  mu_scope = ~ Eth + Sex + Lrn + Age,
  engine = "grpreg", grpreg_penalty = "grLasso",
  B = 80, pi_thr = 0.6, pre_standardize = FALSE,
  parallel = "auto", trace = FALSE
)

selection_table(fit_nb2)
#>   parameter term count prop
#> 1        mu  Eth     0    0
#> 2        mu  Sex     0    0
#> 3        mu  Lrn     0    0
#> 4        mu  Age     0    0

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