gkwreg (version 1.0.7)

plot.gkwreg: Diagnostic Plots for Generalized Kumaraswamy Regression Models

Description

Produces a set of diagnostic plots for assessing the adequacy of a fitted Generalized Kumaraswamy (GKw) regression model (objects of class "gkwreg"). Options allow selection of specific plots, choice of residual type, and plotting using either base R graphics or ggplot2.

Usage

# S3 method for gkwreg
plot(
  x,
  which = 1:6,
  caption = c("Residuals vs. Observation Indices", "Cook's Distance Plot",
    "Generalized Leverage vs. Fitted Values", "Residuals vs. Linear Predictor",
    "Half-Normal Plot of Residuals", "Predicted vs. Observed Values"),
  sub.caption = paste(deparse(x$call), collapse = "\n"),
  main = "",
  ask = prod(par("mfcol")) < length(which) && dev.interactive(),
  ...,
  type = c("quantile", "pearson", "deviance"),
  family = NULL,
  nsim = 100,
  level = 0.9,
  use_ggplot = FALSE,
  arrange_plots = FALSE,
  sample_size = NULL,
  theme_fn = ggplot2::theme_minimal,
  save_diagnostics = FALSE
)

Value

Invisibly returns either the original fitted model object x

(if save_diagnostics = FALSE) or a list containing the calculated diagnostic measures used for plotting (if save_diagnostics = TRUE). Primarily called for its side effect of generating plots.

Arguments

x

An object of class "gkwreg", typically the result of a call to gkwreg.

which

Integer vector specifying which diagnostic plots to produce. If a subset of the plots is required, specify a subset of the numbers 1:6. Defaults to 1:6. The plots correspond to:

1. Residuals vs. Observation Indices: Checks for time trends or patterns.

2. Cook's Distance Plot: Helps identify influential observations.

3. Generalized Leverage vs. Fitted Values: Identifies points with high leverage.

4. Residuals vs. Linear Predictor: Checks for non-linearity and heteroscedasticity.

5. Half-Normal Plot of Residuals (with simulated envelope): Assesses normality of residuals, comparing against simulated quantiles.

6. Predicted vs. Observed Values: Checks overall model prediction accuracy.

caption

Character vector providing captions (titles) for the plots. Its length must be at least max(which). Defaults are provided for plots 1-6.

sub.caption

Character string used as a common subtitle positioned above all plots (especially when multiple plots are arranged). Defaults to the deparsed model call.

main

An optional character string to be prepended to the individual plot captions (from the caption argument).

ask

Logical. If TRUE (and using base R graphics with multiple plots on an interactive device), the user is prompted before displaying each plot. Defaults to TRUE if more plots are requested than fit on the current screen layout.

...

Additional arguments passed to the underlying plotting functions (e.g., graphical parameters like col, pch, cex for base R plots).

type

Character string indicating the type of residuals to be used for plotting. Defaults to "quantile". Valid options are:

• "quantile": Randomized quantile residuals (Dunn & Smyth, 1996). Recommended for bounded responses as they should be approximately N(0,1) if the model is correctly specified.

• "pearson": Pearson residuals (response residual standardized by estimated standard deviation). Useful for checking the variance function.

• "deviance": Deviance residuals. Related to the log-likelihood contribution of each observation.

family

Character string specifying the distribution family assumptions to use when calculating residuals and other diagnostics. If NULL (default), the family stored within the fitted object is used. Specifying a different family can be useful for diagnostic comparisons. Available options match those in gkwreg: "gkw", "bkw", "kkw", "ekw", "mc", "kw", "beta".

nsim

Integer. Number of simulations used to generate the envelope in the half-normal plot (which = 5). Defaults to 100. Must be positive.

level

Numeric. The confidence level (between 0 and 1) for the simulated envelope in the half-normal plot (which = 5). Defaults to 0.90.

use_ggplot

Logical. If TRUE, plots are generated using the ggplot2 package. If FALSE (default), base R graphics are used. Requires the ggplot2 package to be installed if set to TRUE.

arrange_plots

Logical. Only relevant if use_ggplot = TRUE and multiple plots are requested (length(which) > 1). If TRUE, attempts to arrange the generated ggplot objects into a grid using either the gridExtra or ggpubr package (requires one of them to be installed). Defaults to FALSE.

sample_size

Integer or NULL. If specified as an integer less than the total number of observations (x$nobs), a random sample of this size is used for calculating diagnostics and plotting. This can be useful for speeding up plots with very large datasets. Defaults to NULL (use all observations).

theme_fn

A function. Only relevant if use_ggplot = TRUE. Specifies a ggplot2 theme function to apply to the plots (e.g., theme_bw, theme_classic). Defaults to ggplot2::theme_minimal.

save_diagnostics

Logical. If TRUE, the function invisibly returns a list containing the calculated diagnostic measures (residuals, leverage, Cook's distance, etc.) instead of the model object. If FALSE (default), the function invisibly returns the original model object x.

Author

Lopes, J. E.

Details

Diagnostic plots are essential for evaluating the assumptions and adequacy of fitted regression models. This function provides several standard plots adapted for gkwreg objects.

The choice of residual type (type) is important. For models with bounded responses like the GKw family, quantile residuals (type = "quantile") are generally preferred as they are constructed to be approximately normally distributed under a correctly specified model, making standard diagnostic tools like QQ-plots more directly interpretable.

The plots help to assess:

• Plot 1 (Residuals vs. Index): Potential patterns or autocorrelation over time/index.

• Plot 2 (Cook's Distance): Observations with disproportionately large influence on the estimated coefficients.

• Plot 3 (Leverage vs. Fitted): Observations with unusual predictor combinations (high leverage) that might influence the fit.

• Plot 4 (Residuals vs. Linear Predictor): Non-linearity in the predictor-response relationship or non-constant variance (heteroscedasticity).

• Plot 5 (Half-Normal Plot): Deviations from the assumed residual distribution (ideally normal for quantile residuals). Points outside the simulated envelope are potentially problematic.

• Plot 6 (Predicted vs. Observed): Overall goodness-of-fit and potential systematic over- or under-prediction.

The function relies on internal helper functions to calculate the necessary diagnostic quantities and generate the plots using either base R or ggplot2.

See Also

gkwreg, residuals.gkwreg, summary.gkwreg, plot.lm, ggplot, grid.arrange, ggarrange

Examples

# \donttest{
# Assume 'mydata' exists with response 'y' and predictors 'x1', 'x2'
# and that rgkw() is available and data is appropriate (0 < y < 1).
set.seed(456)
n <- 150
x1 <- runif(n, -1, 1)
x2 <- rnorm(n)
alpha <- exp(0.5 + 0.2 * x1)
beta <- exp(0.8 - 0.3 * x1 + 0.1 * x2)
gamma <- exp(0.6)
delta <- plogis(0.0 + 0.2 * x1)
lambda <- exp(-0.2 + 0.1 * x2)
# Use stats::rbeta as placeholder if rgkw is not available
y <- stats::rbeta(n, shape1 = gamma * alpha, shape2 = delta * beta) # Approximation
y <- pmax(pmin(y, 1 - 1e-7), 1e-7)
mydata <- data.frame(y = y, x1 = x1, x2 = x2)

# Fit a GKw model
model <- gkwreg(y ~ x1 | x1 + x2 | 1 | x1 | x2, data = mydata, family = "gkw")

# --- Generate default base R plots (prompts for each plot) ---
plot(model)

# --- Generate specific plots using base R ---
plot(model, which = c(1, 5), type = "quantile") # Residuals vs Index, Half-Normal

# --- Generate plots using ggplot2 (requires ggplot2 package) ---
# Ensure ggplot2 is installed: install.packages("ggplot2")
plot(model, which = c(4, 6), use_ggplot = TRUE) # Res vs Lin Pred, Pred vs Obs

# --- Generate all ggplot2 plots and arrange them (requires gridExtra or ggpubr) ---
# Ensure gridExtra is installed: install.packages("gridExtra")
# plot(model, use_ggplot = TRUE, arrange_plots = TRUE, ask = FALSE)

# --- Generate plots using Pearson residuals ---
plot(model, which = 4, type = "pearson") # Res vs Lin Pred using Pearson residuals

# --- Save diagnostic measures instead of plotting ---
diagnostics <- plot(model, save_diagnostics = TRUE)
head(diagnostics$residuals)
head(diagnostics$cooks_distance)
# }