anova.gkwreg: Analysis of Deviance for GKw Regression Models

In gkwreg: Generalized Kumaraswamy Regression Models for Bounded Data

Analysis of Deviance for GKw Regression Models

Description

Computes an analysis of deviance table for one or more fitted Generalized Kumaraswamy (GKw) regression model objects. When multiple models are provided, likelihood ratio tests are performed to compare nested models.

Usage

## S3 method for class 'gkwreg'
anova(object, ..., test = c("Chisq", "none"))

Arguments

object	An object of class "gkwreg", typically obtained from gkwreg.
...	Additional objects of class "gkwreg" for model comparison. Models must be nested and fitted to the same dataset.
test	A character string specifying the test statistic to use. Currently only "Chisq" (default) is supported, which performs likelihood ratio tests. Can also be "none" for no tests.

Details

When a single model is provided, the function returns a table showing the residual degrees of freedom and deviance.

When multiple models are provided, the function compares them using likelihood ratio tests (LRT). Models are automatically ordered by their complexity (degrees of freedom). The LRT statistic is computed as:

LRT = 2(\ell_1 - \ell_0)

where \ell_1 is the log-likelihood of the more complex model and \ell_0 is the log-likelihood of the simpler (nested) model. Under the null hypothesis that the simpler model is adequate, the LRT statistic follows a chi-squared distribution with degrees of freedom equal to the difference in the number of parameters between the models.

Important: This method assumes that the models being compared are nested (i.e., one model is a special case of the other) and fitted to the same data. Comparing non-nested models or models fitted to different datasets will produce unreliable results. Use AIC or BIC for comparing non-nested models.

The deviance is defined as -2 \times \text{log-likelihood}. For models fitted by maximum likelihood, smaller (more negative) deviances indicate better fit. Note that deviance can be negative when the log-likelihood is positive, which occurs when density values exceed 1 (common in continuous distributions on bounded intervals). What matters for inference is the change in deviance between models, which should be positive when the more complex model fits better.

Value

An object of class c("anova.gkwreg", "anova", "data.frame"), with the following columns:

Resid. Df

Residual degrees of freedom

Resid. Dev

Residual deviance (-2 × log-likelihood)

Df

Change in degrees of freedom (for model comparisons)

Deviance

Change in deviance (for model comparisons)

Pr(>Chi)

P-value from the chi-squared test (if test = "Chisq")

Author(s)

Lopes, J. E.

References

Wilks, S. S. (1938). The large-sample distribution of the likelihood ratio for testing composite hypotheses. The Annals of Mathematical Statistics, 9(1), 60–62. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1214/aoms/1177732360")}

Pawitan, Y. (2001). In All Likelihood: Statistical Modelling and Inference Using Likelihood. Oxford University Press.

See Also

gkwreg, logLik.gkwreg, AIC.gkwreg, BIC.gkwreg, lrtest

Examples

# Load example data
data(GasolineYield)

# Fit a series of nested models
fit1 <- gkwreg(yield ~ 1, data = GasolineYield, family = "kw")
fit2 <- gkwreg(yield ~ temp, data = GasolineYield, family = "kw")
fit3 <- gkwreg(yield ~ batch + temp, data = GasolineYield, family = "kw")

# ANOVA table for single model
anova(fit3)

# Compare nested models using likelihood ratio tests
anova(fit1, fit2, fit3)
#> Model 1 vs 2: Adding temperature is highly significant (p < 0.001)
#> Model 2 vs 3: Adding batch is highly significant (p < 0.001)

# Compare two models
anova(fit2, fit3, test = "Chisq")

# Suppress test statistics
anova(fit1, fit2, fit3, test = "none")

gkwreg documentation built on Nov. 27, 2025, 5:06 p.m.