dw.reg {DWreg}

DW regression

Description

Parametric regression for discrete response data. The conditional distribution of the response given the predictors is assumed to be DW with parameters q and beta dependent on the predictors.

Usage

dw.reg(formula, data,tau=0.5,para.q1=NULL,para.q2=NULL,para.beta=NULL,...)

Arguments

formula

An object of class "formula": a symbolic description of the model to be fitted.

data

An optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which dw.qr is called.

tau

Quantile value (default 0.5). This is used only to extract the conditional quantile from the fitted distribution.

para.q1, para.q2

logical flag. If TRUE, the model includes a dependency of q on the predictors, as explained below.

para.beta

logical flag. If TRUE, the model includes a dependency of beta on the predictors, as explained below.

...

Additional arguments to the maxLik function

Details

The conditional distribution of Y (response) given x (predictors) is assumed a DW(q(x),beta(x)).

If para.q1=TRUE,

log(q/(1-q))=\theta_0+\theta_1 X_1+\ldots+\theta_pX_p.

If para.q2=TRUE,

log(-log(q))=\theta_0+\theta_1 X_1+\ldots+\theta_pX_p.

This is equivalent to a continuous Weibull regression model with interval-censored data.

If para.q1=NULL and para.q2=NULL, then q(x) is constant.

If para.beta=TRUE,

log(\beta)= \gamma_0+\gamma_1 X_1+\ldots+\gamma_pX_p.

Otherwise beta(x) is constant.

Value

A list of class dw.reg containing the following components:

call

the matched call.

data

the input data as a list of response and covariates.

coefficients

the theta and gamma estimated coefficients.

loglik

the log-likelihood of the model.

fitted.values

fitted values (on the response scale) for the specified quantile tau.

fitted.q

fitted q values.

fitted.beta

fitted beta values.

residuals

randomised quantile residuals of the fitted model.

tTable

coefficients, standard errors, etc.

tTable.survreg

Only for the model para.q2=TRUE. Coefficients, standard errors, etc from the survreg parametrization. These estimates are linked to changes of log(Median+1).

Author(s)

Veronica Vinciotti, Hadeel Kalktawi, Alina Peluso

References

Kalktawi, Vinciotti and Yu (2016) A simple and adaptive dispersion regression model for count data.

Examples

#simulated example (para.q1=TRUE, beta constant)
theta0 <- 2
theta1 <- 0.5
beta<-0.5
n<-500
x <- runif(n=n, min=0, max=1.5)
logq<-theta0 + theta1 * x - log(1+exp(theta0  + theta1 * x))		
y<-unlist(lapply(logq,function(x,beta) rdw(1,q=exp(x),beta),beta=beta)) 
data.sim<-data.frame(x,y) #simulated data
fit<-dw.reg(y~x,data=data.sim,para.q1=TRUE)
fit$tTable	

#simulated example (para.q2=TRUE, beta constant)
theta0 <- -2
theta1 <- -0.5
beta<-0.5
n<-500
x <- runif(n=n, min=0, max=1.5)
logq<--exp(theta0  + theta1 * x)		
y<-unlist(lapply(logq,function(x,beta) rdw(1,q=exp(x),beta),beta=beta)) 
data.sim<-data.frame(x,y) #simulated data
fit<-dw.reg(y~x,data=data.sim,para.q2=TRUE)
fit$tTable	
fit$survreg

#real example
library(Ecdat)
data(StrikeNb)
fit<-dw.reg(strikes~output,data=StrikeNb,para.q2=TRUE)
fit$tTable
fit$survreg