Summary Method for Generalized Kumaraswamy Regression Models

Computes and returns a detailed statistical summary for a fitted Generalized Kumaraswamy (GKw) regression model object of class "gkwreg".

Usage

# S3 method for class 'gkwreg'
summary(object, conf.level = 0.95, ...)

Arguments

object: An object of class "gkwreg", typically the result of a call to gkwreg.
conf.level: Numeric. The desired confidence level for constructing confidence intervals for the regression coefficients. Default is 0.95.
...: Additional arguments, currently ignored by this method.

Value

An object of class "summary.gkwreg", which is a list containing the following components:

call: The original function call that created the object.
family: Character string specifying the distribution family.
coefficients: A data frame (matrix) containing the coefficient estimates, standard errors, z-values, and p-values.
conf.int: A matrix containing the lower and upper bounds of the confidence intervals for the coefficients (if standard errors are available).
link: A list of character strings specifying the link functions used.
fitted_parameters: A list containing the mean values of the estimated distribution parameters.
residuals: A named numeric vector containing summary statistics for the response residuals.
nobs: Number of observations used in the fit.
npar: Total number of estimated regression coefficients.
df.residual: Residual degrees of freedom.
loglik: The maximized log-likelihood value.
aic: Akaike Information Criterion.
bic: Bayesian Information Criterion.
rmse: Root Mean Squared Error of the residuals.
efron_r2: Efron's pseudo-R-squared value.
mean_absolute_error: Mean Absolute Error of the residuals.
convergence: Convergence code from the optimizer.
iterations: Number of iterations reported by the optimizer.
conf.level: The confidence level used for calculating intervals.

Details

This method provides a comprehensive summary of the fitted gkwreg model. It calculates z-values and p-values for the regression coefficients based on the estimated standard errors (if available) and computes confidence intervals at the specified conf.level. The summary includes:

The model call.
The distribution family used.
A table of coefficients including estimates, standard errors, z-values, and p-values. Note: Significance stars are typically added by the corresponding print.summary.gkwreg method.
Confidence intervals for the coefficients.
Link functions used for each parameter.
Mean values of the fitted distribution parameters (\(\alpha, \beta, \gamma, \delta, \lambda\)).
A five-number summary (Min, Q1, Median, Q3, Max) plus the mean of the response residuals.
Key model fit statistics (Log-likelihood, AIC, BIC, RMSE, Efron's R^2).
Information about model convergence and optimizer iterations.

If standard errors were not computed (e.g., hessian = FALSE in the original gkwreg call), the coefficient table will only contain estimates, and confidence intervals will not be available.

Author

Lopes, J. E.

Examples

# \donttest{
set.seed(123)
n <- 100
x1 <- runif(n, -2, 2)
x2 <- rnorm(n)
alpha_coef <- c(0.8, 0.3, -0.2)
beta_coef <- c(1.2, -0.4, 0.1)
eta_alpha <- alpha_coef[1] + alpha_coef[2] * x1 + alpha_coef[3] * x2
eta_beta <- beta_coef[1] + beta_coef[2] * x1 + beta_coef[3] * x2
alpha_true <- exp(eta_alpha)
beta_true <- exp(eta_beta)
# Use stats::rbeta as a placeholder if rkw is unavailable
y <- stats::rbeta(n, shape1 = alpha_true, shape2 = beta_true)
y <- pmax(pmin(y, 1 - 1e-7), 1e-7)
df <- data.frame(y = y, x1 = x1, x2 = x2)

# Fit a Kumaraswamy regression model
kw_reg <- gkwreg(y ~ x1 + x2 | x1 + x2, data = df, family = "kw")

# Generate detailed summary using the summary method
summary_kw <- summary(kw_reg)

# Print the summary object (uses print.summary.gkwreg)
print(summary_kw)
#> 
#> Generalized Kumaraswamy Regression Model Summary
#> 
#> Family: kw 
#> 
#> Call:
#> gkwreg(formula = y ~ x1 + x2 | x1 + x2, data = df, family = "kw")
#> 
#> Residuals:
#>     Min  Q1.25%  Median    Mean  Q3.75%     Max 
#> -0.4910 -0.0942  0.0028  0.0042  0.1329  0.5094 
#> 
#> Coefficients:
#>                   Estimate Std. Error z value Pr(>|z|)    
#> alpha:(Intercept)  0.73589    0.10135   7.261 3.85e-13 ***
#> alpha:x1           0.25878    0.08860   2.921  0.00349 ** 
#> alpha:x2          -0.12441    0.08825  -1.410  0.15863    
#> beta:(Intercept)   1.45325    0.17992   8.077 6.64e-16 ***
#> beta:x1           -0.52161    0.17460  -2.987  0.00281 ** 
#> beta:x2            0.03766    0.18694   0.201  0.84034    
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Confidence intervals (95%):
#>                        3%     98%
#> alpha:(Intercept)  0.5372  0.9345
#> alpha:x1           0.0851  0.4324
#> alpha:x2          -0.2974  0.0486
#> beta:(Intercept)   1.1006  1.8059
#> beta:x1           -0.8638 -0.1794
#> beta:x2           -0.3287  0.4041
#> 
#> Link functions:
#> alpha: log
#> beta: log
#> 
#> Fitted parameter means:
#> alpha: 2.207
#> beta: 5.072
#> gamma: 1
#> delta: 0
#> lambda: 1
#> 
#> Model fit statistics:
#> Number of observations: 100 
#> Number of parameters: 6 
#> Residual degrees of freedom: 94 
#> Log-likelihood: 46.13 
#> AIC: -80.27 
#> BIC: -64.63 
#> RMSE: 0.1728 
#> Efron's R2: 0.5496 
#> Mean Absolute Error: 0.1365 
#> 
#> Convergence status: Successful 
#> Iterations: 27 
#> 

# Extract coefficient table directly from the summary object
coef_table <- coef(summary_kw) # Equivalent to summary_kw$coefficients
print(coef_table)
#>                      Estimate Std. Error    z value     Pr(>|z|)
#> alpha:(Intercept)  0.73589120 0.10135318  7.2606619 3.852007e-13
#> alpha:x1           0.25877630 0.08860253  2.9206422 3.493107e-03
#> alpha:x2          -0.12440703 0.08825176 -1.4096833 1.586332e-01
#> beta:(Intercept)   1.45324717 0.17992343  8.0770311 6.636262e-16
#> beta:x1           -0.52161306 0.17460352 -2.9874143 2.813482e-03
#> beta:x2            0.03766118 0.18693698  0.2014646 8.403353e-01
# }