Local influence diagnostics for the EVBS regression model

Introduction

The evbsreg package implements local influence diagnostics for the Extreme-Value Birnbaum–Saunders (EVBS) regression model. This vignette walks through the complete workflow: fitting the model, diagnosing influential observations, assessing model adequacy, and interpreting the results, using the bundled Itajaí wind gust dataset.

library(evbsreg)

The data

The itajai dataset contains 124 monthly maximum wind gust speeds and the corresponding daily mean atmospheric pressure, recorded at INMET station A-868 in Itajaí, Brazil, from July 2010 to October 2020.

data(itajai)
str(itajai)
#> 'data.frame':    124 obs. of  3 variables:
#>  $ month   : int  1 2 3 4 5 6 7 8 9 10 ...
#>  $ wind    : num  11.7 16.4 10.5 17.2 11.2 12.3 14 17.1 13.7 14.8 ...
#>  $ pressure: num  1020 1013 1015 1009 1008 ...
summary(itajai$wind)
#>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
#>    8.20   12.15   14.30   14.73   17.02   33.90

Observation 82 is the catastrophic event of 26 April 2017 (33.9 m/s).

Fitting the model

The design matrix must include an intercept column. We model the location of the log-EVBS distribution as a linear function of atmospheric pressure.

X <- cbind(1, itajai$pressure)
fit <- evbsreg.fit(X, itajai$wind)

data.frame(
  Parameter = c("beta0", "beta1", "alpha", "gamma"),
  Estimate  = round(fit$coeff, 4),
  SE        = round(c(fit$stderrors, fit$stderroralpha, fit$stderrorgama), 4)
)
#>   Parameter Estimate     SE
#> 1     beta0  25.5148 3.3338
#> 2     beta1  -0.0227 0.0033
#> 3     alpha   0.1857 0.0127
#> 4     gamma  -0.1551 0.0472

Both regression coefficients are highly significant:

round(fit$pvalues, 4)
#> x1 x2 
#>  0  0

Local influence diagnostics

The cnc_diagnostics() function computes the conformal normal curvature diagnostics from the fitted object.

diag <- cnc_diagnostics(fit)

## Top four normalized eigenvalues
round(head(diag$eigenvalues_norm, 4), 5)
#> [1] 0.69678 0.49511 0.44547 0.26630

## Observations flagged at q = 7
which(diag$Bj[7, ] > diag$bq[7])
#> [1]  27  43  44  47  82  87 108 110 120

The two-panel diagnostic figure shows the normalized eigenvalues (left) and the aggregate contributions (right). Observation 82 dominates.

plot_cnc(diag, q = 7)

Deletion analysis

We refit the model without the flagged observation and measure the relative change in each parameter.

fit82 <- evbsreg.fit(X[-82, ], itajai$wind[-82])
rc <- 100 * (fit82$coeff - fit$coeff) / abs(fit$coeff)
names(rc) <- c("beta0", "beta1", "alpha", "gamma")
round(rc, 2)
#>  beta0  beta1  alpha  gamma 
#>  -3.24   3.64   0.25 -73.67

The tail-shape parameter \(\gamma\) changes by about \(-73.67\%\), while the regression coefficients and the scale parameter change by less than \(4\%\). The influence is therefore concentrated almost entirely on the tail.

Model adequacy

Randomized quantile residuals should be approximately standard normal under a correct specification.

r <- rqrandomized(X, itajai$wind)
shapiro.test(r)
#> 
#>  Shapiro-Wilk normality test
#> 
#> data:  r
#> W = 0.98727, p-value = 0.3021

envelope_qq(X, itajai$wind, nrep = 100)

Density shapes

The package also provides the density-plotting functions used to produce Figures 1 and 2 of the paper.

plot_evbs_alpha()

Reproducing the full study

Five standalone scripts reproduce every figure, table, and simulation in the paper. After installation they are available via system.file():

# Density figures (Figures 1-2)
source(system.file("scripts/script_01_density_figures.R", package = "evbsreg"))

# Itajai application (Tables 1-3, Figures 3-6)
source(system.file("scripts/script_02_itajai_application.R", package = "evbsreg"))

# Monte Carlo (Tables 4-9); set m <- 500 inside for a quick check
source(system.file("scripts/script_03_simulation_scenario1.R", package = "evbsreg"))
source(system.file("scripts/script_04_simulation_scenario2.R", package = "evbsreg"))
source(system.file("scripts/script_05_simulation_scenario3.R", package = "evbsreg"))

References

Ospina, R., Lima, J. I. C., Barros, M., and Macêdo, A. M. S. (2026). Local influence diagnostics for the extreme-value Birnbaum–Saunders regression model: methodology, validation, and application to anomalous wind gusts. Submitted.