vasicekreg-package: Overview of the vasicekreg package

In vasicekreg: Regression Modeling Using Vasicek Distribution

Overview of the vasicekreg package

Description

The vasicekreg package provides distribution functions and GAMLSS families for Vasicek-type distributions on the unit interval. Three base families are available:

• NVASIM: normal kernel with mean parameterization, where \mu=E(Y).

• NVASIQ: normal kernel with quantile parameterization, where \mu=Q_Y(\tau) for a fixed \tau\in(0,1).

• LVASIQ: logistic kernel with quantile parameterization, where \mu=Q_Y(\tau) for a fixed \tau\in(0,1).

For responses observed at the boundaries, the normal-kernel mean model is also available as:

• ZANVASIM: point mass at zero and a continuous component on (0,1).

• OANVASIM: point mass at one and a continuous component on (0,1).

• ZOANVASIM: point masses at zero and one and a continuous component on (0,1).

The parameter \sigma\in(0,1) controls dispersion in the continuous Vasicek component. The corresponding d, p, q, and r functions provide density or probability mass values, cumulative probabilities, quantiles, and random observations, respectively.

Details

bodyfat: Body fat dataset.

NVASIM: Normal-kernel mean parameterization and GAMLSS family. In regression models, covariates describe the conditional mean through \mu.

NVASIQ: Normal-kernel quantile parameterization and GAMLSS family. For a fixed quantile level \tau, covariates describe the conditional \tau-th quantile through \mu.

LVASIQ: Logistic-kernel quantile parameterization and GAMLSS family. For a fixed quantile level \tau, covariates describe the conditional \tau-th quantile through \mu. A logistic-kernel mean-regression family is not provided because the mean has no closed-form expression and does not equal \mu under this parameterization.

ZANVASIM: Zero-adjusted normal-kernel mean family. Here \nu=P(Y=0), \mu=E(Y\mid Y>0), and the marginal mean is E(Y)=(1-\nu)\mu.

OANVASIM: One-adjusted normal-kernel mean family. Here \nu=P(Y=1), \mu=E(Y\mid Y<1), and the marginal mean is E(Y)=\nu+(1-\nu)\mu. The parameters \mu and \nu therefore have the same interpretations as their counterparts in the one-inflated beta family BEOI. The shape parameter \sigma is distribution-specific and should not be compared directly between these families.

ZOANVASIM: Zero-and-one-adjusted normal-kernel mean family. Here \nu=P(Y=0), \tau=P(Y=1\mid Y>0), and \mu=E(Y\mid 0<Y<1). Consequently, P(Y=1)=(1-\nu)\tau and E(Y)=(1-\nu)[\tau+(1-\tau)\mu].

The distribution functions dNVASIM, pNVASIM, qNVASIM, dNVASIQ, pNVASIQ, qNVASIQ, dLVASIQ, pLVASIQ, and qLVASIQ call compiled C++ routines through Rcpp. The boundary-adjusted distribution functions are implemented in R and reuse the compiled NVASIM functions for their continuous component. Parameter validation, the GAMLSS family definitions, and all log-likelihood derivatives are implemented in R. The mean and variance components of the LVASIQ() family object are obtained by numerical quadrature because these moments have no closed-form expressions.

For the distribution functions associated with NVASIQ and LVASIQ, tau is supplied as an argument. For GAMLSS fitting, NVASIQ() and LVASIQ() require tau to be defined as a scalar variable in the global environment. The same value must be retained when residuals or other post-fit quantities are computed. This fixed quantile level is distinct from the parameter tau in ZOANVASIM(), which represents the conditional probability at one among nonzero observations.

Author(s)

Josmar Mazucheli [e-mail]

Bruna Alves [e-mail]

Examples

if (requireNamespace("betareg", quietly = TRUE)) {
    data("ReadingSkills", package = "betareg")
    ReadingSkills$dyslexia <- stats::relevel(
        factor(ReadingSkills$dyslexia), ref = "no"
    )

    control <- gamlss::gamlss.control(n.cyc = 200, trace = FALSE)

    ## In both models, mu = E(Y | Y < 1) and nu = P(Y = 1).
    fit_oanvasim <- gamlss::gamlss(
        accuracy1 ~ dyslexia * iq,
        sigma.formula = ~ dyslexia + iq,
        nu.formula = ~ 1,
        family = OANVASIM(),
        data = ReadingSkills,
        control = control
    )

    fit_beoi <- gamlss::gamlss(
        accuracy1 ~ dyslexia * iq,
        sigma.formula = ~ dyslexia + iq,
        nu.formula = ~ 1,
        family = gamlss.dist::BEOI(),
        data = ReadingSkills,
        control = control
    )

    n <- nrow(ReadingSkills)
    comparison <- data.frame(
        family = c("OANVASIM", "BEOI"),
        logLik = -c(
            fit_oanvasim$G.deviance,
            fit_beoi$G.deviance
        ) / 2,
        AIC = c(
            gamlss::GAIC(fit_oanvasim, k = 2),
            gamlss::GAIC(fit_beoi, k = 2)
        ),
        BIC = c(
            gamlss::GAIC(fit_oanvasim, k = log(n)),
            gamlss::GAIC(fit_beoi, k = log(n))
        )
    )
    comparison
}

vasicekreg documentation built on Aug. 20, 2026, 9:08 a.m.