fitted.gkwreg: Extract Fitted Values from a Generalized Kumaraswamy...

In gkwreg: Generalized Kumaraswamy Regression Models for Bounded Data

Extract Fitted Values from a Generalized Kumaraswamy Regression Model

Description

Extracts the fitted mean values (predicted expected values of the response) from a fitted Generalized Kumaraswamy (GKw) regression model object of class "gkwreg". This is an S3 method for the generic fitted.values function.

Usage

## S3 method for class 'gkwreg'
fitted(object, family = NULL, ...)

Arguments

object	An object of class "gkwreg", typically the result of a call to gkwreg.
family	Character string specifying the distribution family under which the fitted mean values should be calculated. If NULL (default), the family stored within the fitted object is used. Specifying a different family (e.g., "beta") will trigger recalculation of the fitted means based on that family's mean structure, using the original model's estimated coefficients mapped to the relevant parameters. Available options match those in gkwreg: "gkw", "bkw", "kkw", "ekw", "mc", "kw", "beta".
...	Additional arguments, currently ignored by this method.

Details

This function retrieves or calculates the fitted values, which represent the estimated conditional mean of the response variable given the covariates (E(Y | X)).

The function attempts to retrieve fitted values efficiently using the following priority:

1. Directly from the fitted.values component stored in the object, if available and complete. It includes logic to handle potentially incomplete stored values via interpolation (approx) for very large datasets where only a sample might be stored.

2. By recalculating the mean using stored parameter vectors for each observation (object$parameter_vectors) and an internal function (calculateMeans), if available.

3. From the fitted component within the TMB report (object$tmb_object$report()), if available, potentially using interpolation as above.

4. As a fallback, by calling predict(object, type = "response", family = family).

Specifying a family different from the one used to fit the model will always force recalculation using the predict method (step 4).

Value

A numeric vector containing the fitted mean values. These values are typically bounded between 0 and 1, corresponding to the scale of the original response variable. The length of the vector corresponds to the number of observations used in the model fit (considering subset and na.action).

Author(s)

Lopes, J. E.

See Also

gkwreg, predict.gkwreg, residuals.gkwreg, fitted.values

Examples

# 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 <- 100
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")

# Extract fitted values (using the original 'gkw' family)
fitted_vals_gkw <- fitted(model)

# Extract fitted values recalculated as if it were a Beta model
# (using the fitted gamma and delta coefficients)
fitted_vals_beta <- fitted(model, family = "beta")

# Plot observed vs. fitted (using original family)
response_y <- model$y # Get the response variable used in the fit
if (!is.null(response_y)) {
  plot(response_y, fitted_vals_gkw,
    xlab = "Observed Response", ylab = "Fitted Mean Value",
    main = "Observed vs Fitted Values (GKw Family)",
    pch = 1, col = "blue"
  )
  abline(0, 1, col = "red", lty = 2) # Line y = x
} else {
  print("Response variable not found in model object to create plot.")
}

# Compare fitted values under different family assumptions
head(data.frame(GKw_Fitted = fitted_vals_gkw, Beta_Fitted = fitted_vals_beta))

gkwreg documentation built on April 16, 2025, 1:10 a.m.