# Advanced Real Data Examples: Zero-Inflation, Semicontinuous, and Longitudinal Growth

#### Frédéric Bertrand

#### 2025-11-21

This vignette demonstrates SelectBoost.gamlss on three additional real datasets: - Zero-inflated counts (`pscl::bioChemists`): ZIP / ZINB - Semicontinuous (`datasets::airquality` Ozone): ZAGA - Longitudinal growth with random effects (`nlme::Orthodont`): random intercepts

## What you’ll learn

- How to fit `sb_gamlss()` with grouped penalties on real zero-inflated data sets.
- How to adapt SelectBoost scopes to semicontinuous responses (ZAGA) and longitudinal models with random effects.
- How to interpret `selection_table()` outputs when categorical terms are represented by grouped dummy variables.

> Conference highlight. These examples build on the communication “An Improvement for Variable Selection for Generalized Additive Models for Location, Shape and Scale and Quantile Regression” (Frédéric Bertrand & Myriam Maumy) delivered at the Joint Statistics Meetings 2024 in Portland, emphasizing SelectBoost-driven variable selection for GAMLSS and quantile regression through resampling-intensive benchmarking.

    library(SelectBoost.gamlss)
    library(gamlss)
    #> Loading required package: splines
    #> Loading required package: gamlss.data
    #>
    #> Attaching package: 'gamlss.data'
    #> The following object is masked from 'package:datasets':
    #>
    #>     sleep
    #> Loading required package: gamlss.dist
    #> Loading required package: nlme
    #> Loading required package: parallel
    #>  **********   GAMLSS Version 5.5-0  **********
    #> For more on GAMLSS look at https://www.gamlss.com/
    #> Type gamlssNews() to see new features/changes/bug fixes.

> Optional engines: `install.packages(c("glmnet","grpreg","SGL","future.apply"))`

## 1. Zero-inflated counts — `pscl::bioChemists` (ZIP/ZINB)

    bc <- NULL
    if (requireNamespace("pscl", quietly = TRUE)) {
      data("bioChemists", package = "pscl")
      bc <- pscl::bioChemists
      needed <- c("art", "kid5", "phd", "fem", "mar", "ment")
      missing_cols <- setdiff(needed, names(bc))
      if (length(missing_cols)) {
        cat(
          "bioChemists dataset is missing columns:",
          paste(missing_cols, collapse = ", "),
          "— skipping ZIP example.\n"
        )
        bc <- NULL
      } else {
        keep <- stats::complete.cases(bc[, needed])
        bc <- bc[keep, , drop = FALSE]
        bc$fem <- factor(bc$fem)
        bc$mar <- factor(bc$mar)
        bc$kid5 <- factor(bc$kid5)

        # ZIP engine via stepwise (mu) + grouped/elastic features
        set.seed(10)
        fit_zip <- sb_gamlss(
          art ~ 1, data = bc, family = gamlss.dist::ZIP(),
          mu_scope = ~ kid5 + fem + mar + phd + ment,
          engine = "grpreg", grpreg_penalty = "grLasso",
          B = 80, pi_thr = 0.6, pre_standardize = FALSE, parallel = "auto", trace = FALSE
        )
        sel_zip <- selection_table(fit_zip)
        sel_zip <- sel_zip[order(sel_zip$parameter, -sel_zip$prop), , drop = FALSE]
        head(sel_zip, n = min(8L, nrow(sel_zip)))
        stable_zip <- sel_zip[sel_zip$prop >= fit_zip$pi_thr, , drop = FALSE]
        if (nrow(stable_zip)) {
          stable_zip
        } else {
          cat("No terms reached the stability threshold of", fit_zip$pi_thr, "for this run.\n")
        }
      }
    } else {
      cat("Package 'pscl' not installed; skipping bioChemists example.\n")
    }
    #> No terms reached the stability threshold of 0.6 for this run.

The tables above report the eight most stable terms (sorted within each parameter) together with the subset that exceeds the stability threshold `pi_thr`.

### ZINB often handles overdispersion better than ZIP

    if (requireNamespace("pscl", quietly = TRUE) && !is.null(bc)) {
      set.seed(11)
      fit_zinb <- sb_gamlss(
        art ~ 1, data = bc, family = gamlss.dist::ZINBI(),
        mu_scope = ~ kid5 + fem + mar + phd + ment,
        engine = "grpreg", grpreg_penalty = "grLasso",
        B = 80, pi_thr = 0.6, pre_standardize = FALSE, parallel = "auto", trace = FALSE
      )
      sel_zinb <- selection_table(fit_zinb)
      sel_zinb <- sel_zinb[order(sel_zinb$parameter, -sel_zinb$prop), , drop = FALSE]
      head(sel_zinb, n = min(8L, nrow(sel_zinb)))
      stable_zinb <- sel_zinb[sel_zinb$prop >= fit_zinb$pi_thr, , drop = FALSE]
      if (nrow(stable_zinb)) {
        stable_zinb
      } else {
        cat("No terms reached the stability threshold of", fit_zinb$pi_thr, "for this run.\n")
      }
    } else if (!requireNamespace("pscl", quietly = TRUE)) {
      cat("Package 'pscl' not installed; skipping bioChemists example.\n")
    } else {
      cat("bioChemists dataset unavailable; skipping ZINBI example.\n")
    }
    #> No terms reached the stability threshold of 0.6 for this run.

### Side-by-side metrics (ZIP vs ZINB)

    if (requireNamespace("pscl", quietly = TRUE)) {
      if (exists("fit_zip", inherits = FALSE) && exists("fit_zinb", inherits = FALSE)) {
        zip_g <- fit_zip$final_fit
        zinb_g <- fit_zinb$final_fit
        if (inherits(zip_g, "gamlss") && inherits(zinb_g, "gamlss")) {
          safe_scalar <- function(expr) {
            out <- tryCatch(expr, error = function(e) NA_real_)
            if (length(out) == 0L) NA_real_ else as.numeric(out[1L])
          }
          met <- data.frame(
            model = c("ZIP", "ZINBI"),
            AIC = c(safe_scalar(AIC(zip_g)), safe_scalar(AIC(zinb_g))),
            GAIC_k2 = c(safe_scalar(gamlss::GAIC(zip_g, k = 2)), safe_scalar(gamlss::GAIC(zinb_g, k = 2))),
            deviance = c(safe_scalar(zip_g$deviance), safe_scalar(zinb_g$deviance))
          )
          if (any(!is.na(met$AIC)) || any(!is.na(met$GAIC_k2)) || any(!is.na(met$deviance))) {
            print(met)
          } else {
            cat("Model fit statistics unavailable; skipping metric table.\n")
          }
        } else {
          cat("Final fits not found; metrics skipped.\n")
        }
      } else {
        cat("Models not available; run the fitting chunks first.\n")
      }
    } else {
      cat("Package 'pscl' not installed; skipping bioChemists example.\n")
    }
    #>   model      AIC  GAIC_k2 deviance
    #> 1   ZIP 3362.782 3362.782       NA
    #> 2 ZINBI 3225.873 3225.873       NA

Notes. Many `art` values are zero; `ZINB` usually outperforms `ZIP` when overdispersion is present. Group lasso treats factor levels as single grouped terms.

## 2. Semicontinuous (ZAGA) — `airquality::Ozone`

`Ozone` is non-negative and has zeros; positive part is continuous — ideal for ZAGA (zero-adjusted Gamma).

    aq <- subset(airquality, !is.na(Ozone) & !is.na(Wind) & !is.na(Temp) & !is.na(Solar.R))
    aq$Month <- factor(aq$Month)

    set.seed(20)
    fit_zaga <- sb_gamlss(
      Ozone ~ 1, data = aq, family = gamlss.dist::ZAGA(),
      mu_scope    = ~ pb(Temp) + pb(Wind) + pb(Solar.R) + Month,
      sigma_scope = ~ pb(Temp),
      engine = "grpreg", grpreg_penalty = "grLasso",
      B = 80, pi_thr = 0.6, pre_standardize = TRUE, parallel = "auto", trace = FALSE
    )
    sel_zaga <- selection_table(fit_zaga)
    sel_zaga <- sel_zaga[order(sel_zaga$parameter, -sel_zaga$prop), , drop = FALSE]
    head(sel_zaga, n = min(8L, nrow(sel_zaga)))
    #>   parameter        term count   prop
    #> 1        mu    pb(Temp)     0 0.0000
    #> 2        mu    pb(Wind)     0 0.0000
    #> 3        mu pb(Solar.R)     0 0.0000
    #> 4        mu       Month     0 0.0000
    #> 5     sigma    pb(Temp)    71 0.8875
    stable_zaga <- sel_zaga[sel_zaga$prop >= fit_zaga$pi_thr, , drop = FALSE]
    if (nrow(stable_zaga)) {
      stable_zaga
    } else {
      cat("No terms reached the stability threshold of", fit_zaga$pi_thr, "for this run.\n")
    }
    #>   parameter     term count   prop
    #> 5     sigma pb(Temp)    71 0.8875

As with the count model, we present the eight most persistent effects plus the subset clearing the stability requirement.

### Effect plot for Temp on mu (ZAGA)

    if (requireNamespace('ggplot2', quietly = TRUE)) {
      print(effect_plot(fit_zaga, 'Temp', aq, what = 'mu'))
    }

Notes. `ZAGA` models a point mass at zero plus a Gamma for the positive part. Group selection keeps whole spline bases together.

## 3. Longitudinal growth with random effects — `nlme::Orthodont`

Fit random intercepts by subject using `gamlss::random()`, while selecting fixed effects for μ.

    if (requireNamespace("nlme", quietly = TRUE)) {
      data_ok <- tryCatch({
        utils::data("Orthodont", package = "nlme", envir = environment())
        TRUE
      }, error = function(e) FALSE)
      if (!data_ok || !exists("Orthodont", inherits = FALSE)) {
        cat("Dataset 'Orthodont' unavailable; skipping longitudinal example.\n")
      } else {
        od <- get("Orthodont", inherits = FALSE)
        rm(Orthodont)
        od$Subject <- factor(od$Subject)
        od$Sex <- factor(od$Sex)
        set.seed(30)
        fit_long <- sb_gamlss(
          distance ~ gamlss::random(Subject),     # random intercept
          data = od, family = gamlss.dist::NO(),
          mu_scope = ~ pb(age) + Sex + pb(age):Sex,      # select fixed effects
          engine = "grpreg", grpreg_penalty = "grLasso",
          B = 80, pi_thr = 0.6, pre_standardize = TRUE, parallel = "auto", trace = FALSE
        )
      sel_long <- selection_table(fit_long)
      sel_long <- sel_long[order(sel_long$parameter, -sel_long$prop), , drop = FALSE]
      head(sel_long, n = min(8L, nrow(sel_long)))
      stable_long <- sel_long[sel_long$prop >= fit_long$pi_thr, , drop = FALSE]
      if (nrow(stable_long)) {
        stable_long
      } else {
        cat("No terms reached the stability threshold of", fit_long$pi_thr, "for this run.\n")
      }
        if (requireNamespace("ggplot2", quietly = TRUE)) {
          gg <- tryCatch(
            effect_plot(fit_long, "age", od, what = "mu"),
            error = function(e) {
              message("effect_plot() skipped for random-effect example: ", conditionMessage(e))
              NULL
            }
          )
          if (!is.null(gg)) {
            print(gg)
          }
        }
      }
    } else {
      cat("Package 'nlme' not installed; skipping longitudinal example.\n")
    }

Notes. The `random(Subject)` term stays in the base formula (not in `mu_scope`) so it is always included, while SelectBoost focuses on selecting the fixed structure. Some plotting helpers (e.g., `effect_plot()`) may be skipped when random-effect predictions are unavailable in a given setup.